Vermogenselektronica 2
Jan van Hulzen
September 2018 version 1.0
Inverters
1
Lesprogramma
Lesweek week dag
datum
1
36 wo 05/09/2018
2
37 wo 12/09/2018
3
38 wo 19/09/2018
4
39 wo 26/09/2018
5
40 wo 03/10/2018
6
41 wo 10/10/2018
7
42 wo 10/10/2018
van
11:00
15:00
11:00
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15:00
• NB Lokaal moet nog worden aangepast
tot
12:30
16:30
12:30
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duur
01:30
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lokaal
L0-30B
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Programma van vandaag
• Introductie
• Literatuur
• Introductie inverters
• Periodieke functies en Fourier analyse
• Fourier analyse van een blokgolf
• Karakteriseren van prestaties van inverters
• Single-phase half-bridge inverters
• Voorbeeld opgave inverters
Aanbevolen Literatuur (niet verplicht)
• Deze presentatie is gebaseerd op
Hoofdstuk 6 van het boek;
• Power Electronics: Circuits, Devices &
Applications (4th Edition) 4th Edition
• Muhammad H. Rashid
• ISBN-13: 978-0133125900
• ISBN-10: 0133125904
Toepassingen van inverters : zonne-energie
Toepassingen van inverters : wind energie
Toepassingen van inverters : Brushless DC motor
DEEL 1
Introductie inverters
Van DC naar AC
• Een inverter wordt gebruikt om DC
signalen om te zetten in AC signalen
+
vs
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is
+
vo
DC
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<latexit
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• De analyse van DC-DC converters
wordt voornamelijk gedaan in het
tijddomein
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<latexit
-
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AC
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• Een AC signaal is een periodiek signaal dat kan worden beschreven met een
periodieke functie
• Een functie f(t) is periodiek f(t)= f(t+T), T>0
• Voor de analyse van AC signalen kunnen we gebruik maken van het Fourier
analyse en van het frequentiedomein.
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<latexit
-
DEEL 2
De studie van periodieke signalen
De algemene vorm
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
meer periodieke
functies
te combineren vorm
kunnen bijvoorbeeld blokvormige
Periodieke
signalen
: Algemene
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
De algemene
vormavan
een periodiek signaal is gegeven door
rukking• voor
de getallen
n en bn zodat deze niet allemaal hoeven te worden opgesom
1 ✓
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
2
T
T
n=1
◆
k mogelijk om te starten met een signaal f (t) en daarna de getallen an en bn te be
a0, an en bn zijn de coë ciënten die het signaal beschrijven.
oen door gebruik
te maken van het feit dat f(t) is opgebouwd uit sinus en cosinus sign
• De functie f(t) kan even f(t) = f(-t) of oneven -f(t) = f(-t) zijn...
• De functie f(t) is periodiek f(t)= f(t+T), T>0
5
ffi
• Hoe kunnen we zijn a0, an en bn, uit een gegeven f(t) bepalen?
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
Stel we
de vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
1 ✓
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
2
T
T
n=1
◆
k mogelijk om te starten met een signaal f (t) en daarna de getallen an en bn te be
• met onbekende a0, an en bn, hoe kunnen we deze bepalen uit f(t)?
oen door gebruik te maken
van het feit dat f(t) is opgebouwd uit sinus en cosinus sign
5
ramp.py
plt . c l f ()
f i g , ax1=p l t . s u b p l o t s ( 1 , 1 , s h a r e x= ’ c o l ’ , s h a r e y= ’ row ’ )
ax1 . p l o t ( t , f 3 , t , f 1 0 , t , f 1 0 0 )
ax1 . g r i d ( )
ax1 . s e t t i t l e ( ’ f ( x ) ramp f u n c t i e met 3 , 10 en 100 s i n termen ’ )
plt . xlabel ( ’x ’ )
plt . ylabel ( ’ f (x) ’ )
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n
n
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fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
rukking voor de getallen a en b zodat deze niet allemaal hoeven te worden opgesom
1 ✓
X
◆
ramp.py
1
2⇡
2⇡
f (t) =serieaeen
an cos n door
t +een
bn optelsom
sin n van
t periodieke signalen (sinus
0 +signaal karakteriseert
Wat opvalt is dat de Fourier
2
T
T
en cosinus). Door steeds meer periodieke functies
n=1 te combineren kunnen bijvoorbeeld blokvormige, driehoekige
of zaagtand vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getallen an en bn
kwaarbij
mogelijk
om te nstarten
met
een binnen
signaal
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de getallen
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de parameter
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hetftijdsinterval
T voorstelt.
Voor veel asignalen
er
•
met
onbekende
a
0, an en bn, hoe kunnen we deze bepalen uit f(t)?
ook een
uitdrukking
de getallen
an het
en bnfeit
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deze
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oen
door
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van
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uitworden
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en cosinus sign
Het is ook mogelijk om te starten met een signaal f (t) en daarna de getallen an en bn te berekenen. We
kunnen dit doen door gebruik te maken van het feit dat f(t) is opgebouwd uit sinus en cosinus signalen. Als we
• Integreer van -T/2 tot T/2 zodat volgt:
a0 willen berekenen dan kunnen we f (t) integreren over het interval T2  t  T2 .
T
Z2
T
2
T
Z2
T
2
✓
◆
✓
◆
2⇡
1 T
2⇡
cos n t dt = 5 sin n t
T
n 2⇡
T
✓
◆
2⇡
sin n t dt =
T
T
2
✓
◆
1 T
2⇡
cos n t
n 2⇡
T
5
=0
T
2
T
2
=0
T
2
ramp.py
p l o t s ( 1 , 1 , s h a r e x= ’ c o l ’ , s h a r e y= ’ row ’ )
10 , t , f100 )
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door
steeds
meer
periodieke
functies
te’ combineren
kunnen
bijvoorbeeld blokvormige
signaal
naar
Fourier
reeks
x ) rampVan
f u n c t i periodiek
e met 3 , 10 en 100
s i n termen
)
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
)
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1 ✓
X
◆
1
2⇡
2⇡
f (t)karakteriseert
= a0 + door eenanoptelsom
cos n vant periodieke
+ bn sin n
t (sinus
t de Fourier serie een signaal
signalen
2
T blokvormige, Tdriehoekige
teeds meer periodieke functies te combineren
kunnen bijvoorbeeld
n=1
ge signalen worden geconstrueerd. Het enige wat nodig is, is een serie getallen an en bn
ker mogelijk
te starten
met
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de getallen
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binnen het
tijdsinterval
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Voordaarna
veel signalen
bestaat er an en bn te be
met onbekende
a0, deze
an enniet
bn,allemaal
hoe kunnen
we deze bepalen
uit f(t)?
goen
voordoor
de• getallen
an entebnmaken
zodat
hoeven
opgesomd.
gebruik
van het
feit dat
f(t)teisworden
opgebouwd
uit sinus en cosinus sign
elijk om te starten met een signaal f (t) en daarna de getallen an en bn te berekenen. We
or gebruik te maken van het feit dat f(t) is opgebouwd uit sinus en cosinus signalen. Als we
Integreer
van -T/2
zodat Tvolgt:
T
dan kunnen• we
f (t) integreren
overtot
hetT/2
interval
2  t  2.
T
Z2
T
2
T
2
Z
T
2
✓
cos n
✓
sin n
◆
✓
2⇡
1 T
2⇡
t dt =
sin n t
T
n 2⇡
T
◆
2⇡
t dt =
T
✓
◆
1 T
2⇡
cos n t
n 2⇡
T
5
T
2
T
2
◆
5= 0
T
2
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=0
T
2
T
2
0
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<latexit
<latexit sha1_base64="xVtapoRrAmexsMzQT6RdfHKd/Ic=">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</latexit>
T
2
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
ramp-vormige
functie
arameter n het aantal periodenFiguur
binnen 2:
het Een
tijdsinterval
T voorstelt.
Voor veel signale
Stel we
de vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
Figuur 2:✓ Een ramp-vormige functie
◆
1
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
n met an en bn zijn dus2gelijkn=1
aan nul. Houden
we over
T
T
T
kmet
mogelijk
starten
met een
f (t) en we
daarna
de getallen an en bn te be
an enom
bn te
zijn
dus gelijk
aansignaal
nul.
Houden
over
2
T
Z
• met onbekende a0, an en bn, hoe kunnen we deze bepalen
uit f(t)?
2
oen door gebruik te maken
van het feit 1dat f(t) is opgebouwd
uitTsinus en cosinus sign
1
T
2
• We houden over:
T
2
olgt dat
gt dat
Z
• en dus volgt a0 :
a0 dt =
1T 2
1 2
a0 t
2a0 dt =
2
2
5
2
a0 =Z
2 T
T
2
a0 =
T
T
a0 t
T
2
=
2
T
= a0
2
T
2
T
2
T
2
Z
f (t)dt
T
f (t)dt
2
a0
2ramp.py
T
2
2
T
2
2
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
T
vormige signalen worden geconstrueerd.
Z2 Het enige wat nodig is, is een serie getall
2 het tijdsinterval T voorstelt. Voor veel signale
arameter n het aantal perioden
binnen
a0 =
f (t)dt
Stel we
Tde vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
T
2
◆
1 ✓
X
1
2⇡het interval2⇡ T  t  T een get
oncluderen dat hetf (t)
integreren
van
f
(t)
over
= a0 +
an cos n t + bn sin n t2
2
2
T
T
door a0 en T . De reden is datn=1
alle sinus en cosinus termen door nul gaan op t
van n. Deze
eigenschap
kunnen
we ookf (t)
gebruiken
bij de
hetgetallen
berekenen
vanbnate
n en
kk mogelijk
om te
starten met
een signaal
en daarna
an en
be
• met onbekende
amet
en bntest
, hoefunctie
kunnen waarvan
we deze bepalen
uit f(t)?
0, an een
enigvuldigen
we te
f (t)
we weten
dat deze
er voorsign
zo
oen
door gebruik
maken
van
het
feit
dat
f(t)
is
opgebouwd
sinus
en de
cosinus
waarbij m een geheel getal is dat aangeeftuit
welke
van
termen a
product f (t)g(t) naar nul gaat voor alle termen in de som behalve voor de term
bijvoorbeeld m = 3 in dan kunnen we de term a3 bepalen.
• Vermenigvuldig
f(t) met een functie
g(t) en integreer
. Een functie
met deze
Deeigenschap
termen de istermen met a en b worden 0 voor alle n ongea
n
 t  T2 (zie2⇡bijlage)
g(t) = cos m t
5T
0
0 T
T
T
*
Z2
Z2
Z2
1
X
heel getal is dat aangeeft welke van de termen
an2⇡uit de serie B
we willen bepalen.
2⇡
1
f (t)g(t)dt
= ? 2 a0 cos m tdt +
@ an cos n t cos
3 in dan kunnen we de term
a3 bepalen.
T
T
n=1
T
T
termen met a0 en bn worden
0 voor alle
n ongeacht de gekozen mT2als we integrere
2
2
T
(zie bijlage)
interval
T
2
0
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
Stel we
de vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
1 ✓
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
2
T
T
n=1
◆
waarbijom
m te
eenstarten
geheel getal
datsignaal
aangeeftf (t)
welke
de termen
an uit de
willen
k mogelijk
met iseen
envan
daarna
de getallen
anserie
en bwe
n te be
bijvoorbeeld
m = 3 ain0, dan
kunnen
de term
bepalen.
• met onbekende
an en
bn, hoewekunnen
wea3deze
bepalen uit f(t)?
oen doorDe
gebruik
te
maken
van
het
feit
dat
f(t)
is
opgebouwd
uit sinus en cosinus sign
termen de termen met a en b worden 0 voor alle n ongeacht de gekozen m als we
0
n
interval T2  t  T2 (zie bijlage)
en geheel• getal
is dat aangeeft
welke
vanfunctie
de termen
an integreer
uit de serie we willen bepalen. Vullen we
Vermenigvuldig
f(t) met
een
g(t) en
m = 3 in dan kunnen we de term a3 bepalen. 0
0 T
T
T
T
*
2
2 gekozen m als we integreren Z
2
n de termen
worden
0 voor alle n ongeacht
de
over
het
Z2 met a0 en bn Z
Z
1
X
2⇡
2⇡
2⇡
2⇡
T
B
1
 t  2 (ziefbijlage)
(t)g(t)dt =
+5
bn sin
n⇠
@ an cos n t cos m tdt +
⇠
2 a0 cos m T tdt
⇠
T
T
T
⇠
⇠
n=1
⇠
T
T
T
0T
0
1
T
Z2
2
*
2
1
X
2⇡
B
1
we
over
houden
)dt = zodat
a
cos
m
tdt
+
@
2 0
T
n=1
T
2
2
T
Z2
T
2
an cos n
T
Z2
2⇡
2⇡
t cos m tdt +
T
T 0
T
f (t)g(t)dt =
1
X
B
⇠0
⇠:
⇠
2⇡ ⇠⇠⇠ 2⇡
C
⇠
bn sin
n
t
cos
m
tdt
A
⇠T
⇠
T
⇠
1
⇠
2
T
Z2
Z2
⇠T
2
a cos n
2⇡
t cos m
2⇡
tdt
C
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
Stel we
de vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
1 ✓
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
2
T
T
n=1
◆
waarbijom
m te
eenstarten
geheel getal
datsignaal
aangeeftf (t)
welke
de termen
an uit de
willen
k mogelijk
met iseen
envan
daarna
de getallen
anserie
en bwe
n te be
bijvoorbeeld
m = 3 ain0, dan
kunnen
de term
bepalen.
• met onbekende
an en
bn, hoewekunnen
wea3deze
bepalen uit f(t)?
oen doorDe
gebruik
te
maken
van
het
feit
dat
f(t)
is
opgebouwd
uit sinus en cosinus sign
termen de termen met a en b worden 0 voor alle n ongeacht de gekozen m als we
0
n
interval T2  t  T2 (zie bijlage)
en geheel• getal
is dat aangeeft
welke
vanfunctie
de termen
an integreer
uit de serie we willen bepalen. Vullen we
Vermenigvuldig
f(t) met
een
g(t) en
m = 3 in dan kunnen we de term a3 bepalen. 0
0 T
T
T
T
*
2
2 gekozen m als we integreren Z
2
n de termen
worden
0 voor alle n ongeacht
de
over
het
Z2 met a0 en bn Z
Z
1
X
2⇡
2⇡
2⇡
2⇡
T
B
1
 t  2 (ziefbijlage)
(t)g(t)dt =
+5
bn sin
n⇠
@ an cos n t cos m tdt +
⇠
2 a0 cos m T tdt
⇠
T
T
T
⇠
⇠
n=1
⇠
T
T
T
0T
0
1
T
Z2
2
*
2
1
X
2⇡
B
1
we
over
houden
)dt = zodat
a
cos
m
tdt
+
@
2 0
T
n=1
T
2
2
T
Z2
T
2
an cos n
T
Z2
2⇡
2⇡
t cos m tdt +
T
T 0
T
f (t)g(t)dt =
1
X
B
⇠0
⇠:
⇠
2⇡ ⇠⇠⇠ 2⇡
C
⇠
bn sin
n
t
cos
m
tdt
A
⇠T
⇠
T
⇠
1
⇠
2
T
Z2
Z2
⇠T
2
a cos n
2⇡
t cos m
2⇡
tdt
C
ramp.py
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
Stel we
de vorm
rukking• voor
dehebben
getalleneen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
1 ✓
X
1
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin n t
2
T
T
n=1
◆
k mogelijk om te starten met een signaal f (t) en daarna de getallen an en bn te be
• met onbekende a0, an en bn, hoe kunnen we deze bepalen uit f(t)?
oen door gebruik te maken
van het feit dat f(t) is opgebouwd uit sinus en cosinus sign
• Vermenigvuldig f(t) met een functie g(t) en integreer
zodat we over houden
0 T
1
T
Z2
Z2
1
X
2⇡
2⇡ C
5
B
• We houden over:
f (t)g(t)dt =
a
cos
n
t
cos
m
tdtA
@
n
T
T
n=1
T
2
T
2
De optelling
van functies
is nu
verdwenen
en vervangen
• Waarvan
elke term
verdwijnt
behalve
die van mdoor
= n een enkele functie.
Op een soortgelijke manier kan gesteld worden dat voor alle m 6= n de tweede term verd
fo
In
interval 2  t  ramp.py
2 (zie bijlage)
nnen we de term a3 bepalen.
a0 en bn worden 0 voor alle n ongeacht de gekozen m als 0we integreren
over het
0
T
T
lt is dat de Fourier serie een
signaal karakteriseert
door een
* optelsom T2van periodieke sig
2
2
age)
Z
Z
Z
1
X
Door steeds
meer
periodieke
functies
te
combineren
kunnen
bijvoorbeeld
blokvormige
2⇡
2⇡
B
1 Fourier reeks
Van periodiek signaal
naar
f (t)g(t)dt =
a0 cos m tdt +
@ an cos n t cos m
2Het
0
vormige
signalen
worden
geconstrueerd.
enige
wat
nodig
is,
is een serie
T
0 T
1T getall
T
*
n=1
0
T
T
T
:
⇠
2
2
Z
Z
⇠
1
2
2
2
arameter
n
het
aantal
perioden
binnen
het
tijdsinterval
T
voorstelt.
Voor
veel
signale
⇠
XB
⇠
2⇡ • Stel we
2⇡
2⇡
2⇡
2⇡
C
⇠
⇠
in
de
vorm
⇠
m tdt voor
+ dehebben
aneen
cos
n
t
cos
m
tdt
+
b
sin
n
t
cos
m
tdt
rukking
getallen
ansignaal
en
b
zodat
deze
niet
allemaal
hoeven
te
worden
@ zodat
Aopgesom
n ⇠⇠
n houden
we
over
T
T
T
T
T
⇠
⇠
n=1
⇠
T
T
0 T
✓
◆
1
T
2
2
X
1
2⇡ Z2
2⇡ X
Z2
1
2⇡
f (t) = a0 +
an cos n t + bn sin n t
B
f (t)g(t)dt
@ an cos n t c
2
T
T=
n=1
T
0
1
n=1
T
T
T
T
2
2
2
Z met een signaal f (t) en daarna de getallen an2 en bn te be
1
k Zmogelijk om teX
starten
2⇡we C
B a0, an en bn,2⇡
• met onbekende
hoe kunnen
deze bepalen uit f(t)?
(t)g(t)dt
= te maken
anvan
cos n
t cos
m f(t)
tdtnu
oen fdoor
gebruik
het
feit
dat
isAopgebouwd
uitvervangen
sinus en cosinus
@
De optelling
van
functies
is
verdwenen en
door eensign
en
T
T
n=1
T
2
Op een soortgelijke manier kan gesteld worden dat voor alle m 6=
• Vermenigvuldig
f(t) metwe
eendus
functie
houden
over g(t) en integreer
T
2
u verdwenen en vervangen doorT een enkele functie.
T
T
2
2
2
Z
Z
Z
• Weworden
houdendat
over:
r kan gesteld
voor alle m 6= n de tweede term
verdwijnt.
Uiteindelijk
2⇡
2⇡
2 2⇡
f (t)g(t)dt =
a
cos
n
t
cos
n
tdt
=
a
cos
n
5
n
n
T
T
2
Z
T
2
T
T
2
T
T
2
T
2
2⇡
2⇡
an t
4⇡
T
2m.2⇡
waarbij
n
=
Het
eindresultaat
van
het
vermenigvuldigen
van f
cos n t cos n tdt =
aTn cos n Ttdt =
+ sin n t
= an
T
T
2
T de integraal
over 2  t T 2 is dus2dat2 de term Tam uit
te voor
2
T
2
de basis
van de Fourier transformatie. Op een soortgelijke manier k
n
n
T ramp.py
T
T
2
T
2
T
2
2
bn sin n
T
2
t cos ✓
n
fo
In
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
eDoor
de steeds
laatste
term
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
T
T
arameter n het aantal
perioden binnen het tijdsinterval
T voorstelt. Voor veel signale
2
2
Zgetalleneen
Z
Stel we
in
de
vorm
rukking• voor
dehebben
ansignaal
en
b
zodat
deze
niet
allemaal
hoeven
2⇡ n
2⇡
2⇡ te worden
2⇡opgesom
tdt =
cos n
tdb
◆ n sin n
1
T
1 T X T
2⇡ T
2⇡
f (t) = a0 +
an cos n t +2 bn sin n t
2
T
T
n=1
T
t
◆
1 ✓
X
k mogelijk om 1te starten met een signaal
2⇡ f (t) en daarna
2⇡ de getallen an enTbn te be
met=
onbekende
a0, an en
, hoe
we
bepalen
f(t)?
n
f•(t)
ate
anbhet
cos
nkunnen
t+
bnisdeze
sin
n
t uit
with
 tsign

0+
oen door
gebruik
maken
van
feit
dat
f(t)
opgebouwd
uit
sinus
en
cosinus
2
T
T
2
n=1
• Vermenigvuldig
f(t) met een2⇡
functie g(t) enTintegreer T
2⇡
f (t) cos n T t and f (t) sin n T t over
• Conclusie:
T
2
a0 =
T
Z
2
T
2
2
f (t)dt, an =
T
T
2
Z
2
5
t
2
to get
2⇡
2
f (t) cos n tdt, bn =
T
T
T
2
T
2
Z
T
2
7
f (t) sin n
2
2
2
ramp.py
fo
In
cties
is nu verdwenen en vervangen door een enkele functie.
lt is dat de Fourier serie een signaal karakteriseert door een optelsom van periodieke sig
ke manier
worden
dattevoor
alle m kunnen
6= n debijvoorbeeld
tweede term
verdwijn
Door
steeds kan
meergesteld
periodieke
functies
combineren
blokvormige
Van periodiek signaal naar Fourier reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter
n het aantal perioden binnenThet tijdsinterval T voorstelt. Voor veel signale
T
2
2
T
Z
Z
•
Stel
we
hebben
een
signaal
in
de
vorm
2
rukking voor de getallen
an2⇡
en bn zodat deze niet allemaal
hoeven
2⇡
2⇡
an t te worden4⇡opgesom
t=
an cos n
tdt = ✓ an cos2 n tdt =
+ sin n t
◆
1
T
T
2 2
T
X
1
2⇡
2⇡
t cos n
T
T
2
T
f (t) = a0 +
t + bn sin n t
2an cos n
2
T
T
n=1
=
T
2
eindresultaat van het vermenigvuldigen van f (t) met g(t) en het integrere
k mogelijk om te starten met een signaal f (t) en daarna de getallen an en bn te be
soen
dus
termmaken
am
•dat
metde
onbekende
a0, auit
bn, integraal
hoe kunnente
wevoorschijn
deze bepalenkomt.
uit f(t)? Dit opmerkelijk
n ende
door gebruik tewaarbij
van
het
feit
dat
f(t)
is
opgebouwd
uit
sinusvan
en de
cosinus
signa
m
een
geheel
getal
is
dat
aangeeft
welke
termen
ier transformatie. Op een soortgelijke manier kunnen de termen bn naar bu
bijvoorbeeld m = 3 in dan kunnen we de term a3 bepalen.
t) te kiezen
• Vermenigvuldig f(t) met een functie g(t) en integreer
De termen de termen met a0 en bn worden 0 voor alle n ongea
interval T2  t  T2 (zie2⇡
bijlage)
g(t) = sin m
T
2
*0
T
2
1
2 a0
sin m
2⇡
tdt
Z
T
2
f (t)g(t)dt
=
0
T
2
Z
?
5 T
1
2 a0
t
*0
2⇡
cos m tdt
T
T
2
Z
1
X
2⇡
B
+
@ T an cos n t cos
T
0
:n=1
⇠
2
Z
⇠
1
T
⇠
X
2
⇠
2⇡
2⇡
B
⇠
⇠
+
an cos⇠
n ⇠ t sin m tdt
@
T
2
0
+
ZT
2
bn sin n
2⇡
t si
n=1
ramp.py
2⇡
2⇡T2 C
an cos n t cos m tdtA
T door een enkele functie.
De optelling
van functies
is nuTverdwenenTen vervangen
n=1
T
lt is dat Op
de Fourier
serie een signaal karakteriseert door een optelsom van periodieke sig
2
een
soortgelijke manier 2kan gesteld worden dat voor alle m 6= n de tweede term verdwij
Door houden
steeds
meer
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
we
dus
over
Van
periodiek
signaal
Fourier
reeks
uncties is nu verdwenen en vervangen door een enkele functie.
vormige signalen
worden
geconstrueerd.
Het
enige
watterm
nodig
is, is een
serie getall
T
T
T
lijke manier kan
gesteld
worden
dat
voor
alle
m
=
6
n
de
tweede
verdwijnt.
Uiteindelijk
T
Z2
Z2
Z2
arameter
n
het
aantal
perioden
binnen
het
tijdsinterval
T
voorstelt.
Voor
veel
signale
2⇡
2⇡
an t
4⇡ 2
2 2⇡
r
f (t)g(t)dteen
=
a cos n det cos
n tdt =
an cos n tdt =
+ sin n t
Stel we
rukkingT• voor
dehebben
getallen ansignaal
enn bTn in
zodat
deze
te2worden
opgesom
T vorm
T niet allemaal hoeven
T
2
T
T
2
1
X
B
f (t)g(t)dt =
@
T
2
fo
In
Z2
T
2
Z2
T
2
T
2
T
2
2⇡
2⇡
an t
4⇡ ◆
T
1 ✓ 2 2⇡
X
dt = waarbij
an cosn n= m.t cos
n
tdt
=
a
cos
n
tdt
=
+
sin
n
t
=
a
n
2⇡ 2 2 van 2⇡
van het vermenigvuldigen
fT(t) met
g(t)nen
T Het eindresultaat
T 1
T
2 het integrer
T
f (t) = a +
a cos n
t + b sin n
t
0 T
n
n
T
T
2
T
over

t

is
dus
dat
de
term
a
uit
de
integraal
te voorschijn
komt. Dit opmerkeli
m
2
T
T
2
2
2
2
n=1
de basis van de Fourier transformatie.
Op een soortgelijke manier kunnen de termen bn naar b
eindresultaat
van
hetg(t)
vermenigvuldigen
van ff(t)
en het
f (t)g(t)
wordenom
door
temet
kiezen
ket mogelijk
tevoor
starten
een signaal
(t)met
en g(t)
daarna
de integreren
getallen avan
n en bn te be
metdeonbekende
a0, de
an en
bn, hoetekunnen
we deze bepalen
uit f(t)?
is dus •dat
term am uit
integraal
voorschijn
Dit opmerkelijke
resultaat is
oen
door gebruik
te maken
van
het feit dat
f(t) is komt.
opgebouwd
uit
sinus
en
cosinus sign
2⇡
urier transformatie. Op een soortgelijke manier kunnen
g(t) = de
sintermen
m t bn naar buiten gebracht
T
g(t) te kiezen
• Vermenigvuldig f(t) met een functie g(t) en integreer
2⇡0
0 T
T
T
*
g(t)
=
sin
m
t
: 0 ZT2
⇠
2
Z2
Z2
Z
⇠
1
XB
2⇡ T
2⇡ ⇠⇠⇠
2⇡
2⇡
1
2 a0
f (t)g(t)dt =
*0
T
tdt
+
5 @
n=1
⇠
⇠
an cos
n
t sin m tdt
⇠
⇠
T
T
⇠T⇠⇠
+
bn sin n
1
T
0
:
⇠
Z
Z
Z2
⇠
1
⇠
X
⇠m
2⇡ verdwijnt de
2⇡⇠⇠
2⇡6= n en houden we over
2⇡
2⇡ C
B derde term voor
alle
1 In dit geval
⇠
a
sin
m
tdt
+
a
cos
n
t
sin
m
tdt
+
b
sin
n
t
sin
m
tdtA
@
n ⇠⇠
n
2 0
TT
T
T
T
T
⇠
T ⇠
T
n=1
⇠
T
T
T
Z2
Z2
Z2
T
2
T
2
T
2
0
sin m
2
T
2
2
f (t)g(t)dt =
bn sin n
2⇡
t sin n
2⇡
2
2
tdt =
bn sin2 n
2⇡
tdt =
an t
T
T
2
+ cos n
4⇡
T
2
t
ts
n=1
ramp.py
2⇡
2⇡T2 C
an cos n t cos m tdtA
T door een enkele functie.
De optelling
van functies
is nuTverdwenenTen vervangen
n=1
T
lt is dat Op
de Fourier
serie een signaal karakteriseert door een optelsom van periodieke sig
2
een
soortgelijke manier 2kan gesteld worden dat voor alle m 6= n de tweede term verdwij
Door houden
steeds
meer
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
we
dus
over
Van
periodiek
signaal
Fourier
reeks
uncties is nu verdwenen en vervangen door een enkele functie.
vormige signalen
worden
geconstrueerd.
Het
enige
watterm
nodig
is, is een
serie getall
T
T
T
lijke manier kan
gesteld
worden
dat
voor
alle
m
=
6
n
de
tweede
verdwijnt.
Uiteindelijk
T
Z2
Z2
Z2
arameter
n
het
aantal
perioden
binnen
het
tijdsinterval
T
voorstelt.
Voor
veel
signale
2⇡
2⇡
an t
4⇡ 2
2 2⇡
r
f (t)g(t)dteen
=
a cos n det cos
n tdt =
an cos n tdt =
+ sin n t
Stel we
rukkingT• voor
dehebben
getallen ansignaal
enn bTn in
zodat
deze
te2worden
opgesom
T vorm
T niet allemaal hoeven
T
2
T
T
2
1
X
B
f (t)g(t)dt =
@
T
2
fofo
InIn
Z2
T
2
Z2
T
2
T
2
T
2
2⇡
2⇡
an t
4⇡ ◆
T
1 ✓ 2 2⇡
X
dt = waarbij
an cosn n= m.t cos
n
tdt
=
a
cos
n
tdt
=
+
sin
n
t
=
a
n
2⇡ 2 2 van 2⇡
van het vermenigvuldigen
fT(t) met
g(t)nen
T Het eindresultaat
T 1
T
2 het integrer
T
f (t) = a +
a cos n
t + b sin n
t
0 T
n
n
T
T
2
T
over

t

is
dus
dat
de
term
a
uit
de
integraal
te voorschijn
komt. Dit opmerkeli
m
2
T
T
2
2
2
2
n=1
de basis van de Fourier transformatie.
Op een soortgelijke manier kunnen de termen bn naar b
eindresultaat
van
hetg(t)
vermenigvuldigen
van ff(t)
en het
f (t)g(t)
wordenom
door
temet
kiezen
ket mogelijk
tevoor
starten
een signaal
(t)met
en g(t)
daarna
de integreren
getallen avan
n en bn te be
metdeonbekende
a0, de
an en
bn, hoetekunnen
we deze bepalen
uit f(t)?
is dus •dat
term am uit
integraal
voorschijn
Dit opmerkelijke
resultaat is
oen
door gebruik
te maken
van
het feit dat
f(t) is komt.
opgebouwd
uit
sinus
en
cosinus sign
2⇡
urier transformatie. Op een soortgelijke manier kunnen
g(t) = de
sintermen
m t bn naar buiten gebracht
T
g(t) te kiezen
• Vermenigvuldig f(t) met een functie g(t) en integreer
2⇡0
0 T
T
T
*
g(t)
=
sin
m
t
: 0 ZT2
⇠
2
Z2
Z2
Z
⇠
1
XB
2⇡ T
2⇡ ⇠⇠⇠
2⇡
2⇡
1
2 a0
f (t)g(t)dt =
*0
T
tdt
+
5 @
n=1
⇠
⇠
an cos
n
t sin m tdt
⇠
⇠
T
T
⇠T⇠⇠
+
bn sin n
1
T
0
:
⇠
Z
Z
Z2
⇠
1
⇠
X
⇠m
2⇡ verdwijnt de
2⇡⇠⇠
2⇡6= n en houden we over
2⇡
2⇡ C
B derde term voor
alle
1 In dit geval
⇠
a
sin
m
tdt
+
a
cos
n
t
sin
m
tdt
+
b
sin
n
t
sin
m
tdtA
@
n ⇠⇠
n
2 0
TT
T
T
T
T
⇠
T ⇠
T
n=1
⇠
T
T
T
Z2
Z2
Z2
T
2
T
2
T
2
0
sin m
2
T
2
2
f (t)g(t)dt =
bn sin n
2⇡
t sin n
2⇡
2
2
tdt =
bn sin2 n
2⇡
tdt =
an t
T
T
2
+ cos n
4⇡
T
2
t
ts
ramp.py
houden we dus over
T
2
T
2
T
2
fo
In
Z
Z
Z
lt is dat de Fourier
serie een
signaal 2⇡
karakteriseert
door
een optelsom
van
2⇡
an periodieke
t
4⇡sig
2 2⇡
f (t)g(t)dt =
an cos n t cos n tdt =
an cos n tdt =
+ sin n t
Door steeds
meer
periodieke
functies
te
combineren
kunnen
bijvoorbeeld
blokvormige
2 2
T
VanTperiodiek TsignaalT naar TFourier
reeks T
T
2
2
vormige signalen
worden geconstrueerd.
Het enige 2 wat nodig is, is een serie getall
arameter
n nhet
binnen
het vermenigvuldigen
tijdsinterval T voorstelt.
Voor
signale
waarbij
= aantal
m. Het perioden
eindresultaat
van het
van f (t) met
g(t)veel
en het
integ
T we hebben
T
Stel
een
interm
de vorm
over• voor

t

dat
adeze
de integraal
voorschijn
komt. Dit
opmer
rukking
de
getallen
ansignaal
en bde
allemaaltehoeven
te worden
opgesom
m uit niet
n zodat
2
2 is dus
de basis van de Fourier transformatie. Op een soortgelijke manier kunnen de termen bn na
◆
1 ✓
worden door voor g(t) te 1
kiezen X
2⇡
2⇡
f (t) = a0 +
an cos n t + bn sin
n t
2⇡
2
T = sin m t T
g(t)
n=1
T
k mogelijk om te starten met een signaal
f (t)
en daarna de getallen an en bn te be
0
0
T
T
• T2met onbekendeT2a0, an en bn, hoe
bepalen uit f(t)? ⇠
*kunnen we deze
0
:
2
2
Z gebruik te maken
Z
Z
Z
oen door
van het feit
datX
f(t)
is
opgebouwd
uit
sinus
en
cosinus
sign
1
⇠⇠
2⇡
2⇡⇠⇠⇠ 2⇡
B
f (t)g(t)dt =
sin m tdt +
an cos
n ⇠ t sin m tdt
@
⇠
⇠
T
T
T
⇠
• TVermenigvuldigTf(t) met een functie g(t)
en integreer
n=1
⇠T⇠
1
2 a0
2
2
• We houden over:
+
T
2
2
T
2
Z
T
2
0
T
2
2
bn sin n
T
1
Z
1
X
2⇡
2⇡ C
B
5
f (t)g(t)dt =
@ bn sin n t sin m tdtA
T
T
n=1
T
2
In dit geval verdwijnt de derde term voor alle m 6= n en houden we over
• Waarvan
elke termT verdwijnt behalve die van m
=n
T
T
Z2
Z2
Z2
2⇡
2⇡
an t
2 2⇡
4⇡
fo
In
aat van het vermenigvuldigen
van fT(t)
met g(t) en het integreren van f (t)g(t)
ramp.py
T
over 2  t  2 is dus dat de term am uit de integraal te voorschi
de term am uit de integraal
te voorschijn komt. Dit opmerkelijke resultaat is
de basis van de Fourier transformatie. Op een soortgelijke manier kun
rmatie.
OpFourier
een soortgelijke
manier
kunnen
de termen
naar buiten
gebracht sig
lt
is dat de
serie
een signaal
karakteriseert
door eenbnoptelsom
van periodieke
worden
door
voor
g(t) te kiezen
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
nDoor steeds
Van meer
periodiek
signaal
Fourier
reeks
2⇡
= sin
t getall
vormige signalen worden geconstrueerd.
Het enige wat nodig g(t)
is, is
eenmserie
2⇡
T
g(t) =perioden
sin m binnen
t
arameter n het aantal
het tijdsinterval T voorstelt. Voor veel signale
T
0 hoeven
0 Tte worden opgesom
Stel we
de vorm
T
rukking• voor
dehebben
getalleneen
aT2nsignaal
en bn in
zodat
deze
niet
allemaal
*
Z
Z2
Z2
1
X
⇠⇠
2⇡
2⇡
2⇡
0
0
1
B
⇠
1
⇠
✓
◆
T
T
*
1
⇠
f
(t)g(t)dt
=
a
sin
m
tdt
+
a
cos
n
t
sin
m
@
0 TZ2
n ⇠⇠
X
2 0
:2⇡
⇠
2
Z
1
2⇡
⇠
1
T
⇠
⇠
⇠ 2⇡ T C
X B f (t) =T a02⇡
n=1
⇠
⇠
2⇡
2⇡
2⇡
T
T
+
a
cos
n
t
+
b
sin
n
t
⇠ n2
n
⇠
2
2
⇠
m tdt +
a
cos
n
t
sin
m
tdt
+
b
sin
n
t
sin
m tdtA
2
T
T
@
n ⇠⇠
n
n=1
T
T
T
T 0 T
⇠
n=1 ⇠T⇠
T T
T
2
2
Z
Z
1
2
2
k mogelijk om te starten
met een signaal f (t) en daarna
de getallen
an en bn2⇡te be
X
B
• met onbekende a0, an en bn, hoe kunnen we dezef (t)g(t)dt
bepalen uit
f(t)?@ bn sin n t sin m
=
oen
door
gebruik
te
maken
van
het
feit
dat
f(t)
is
opgebouwd
uit
sinus en cosinus
sign
0
1
T
T
T
n=1
2
T
T
Z2
Z
1
2
2
XB
2⇡
2⇡
C
• Vermenigvuldig
een
functie
integreer
f (t)g(t)dt
=
bmet
sin
nverdwijnt
t sing(t)
mdeen
tdt
@Inf(t)dit
Aterm voor alle m 6= n en houden we ove
ngeval
derde
T
T
n=1
T
2
T
2
• We houden over:
T
2
Z
f (t)g(t)dt
5
term voor alle m 6= n en houden
we over=
2⇡
2⇡
sin n t sin n tdt =
T
T
T
2
Z
T
2
T
2
Z
2⇡
2⇡
bn sin n t sin n tdt =
T
T
T
2
Integreren
2⇡de laatste
bnterm
t
2 we
T
2
4⇡
bn sin n tdt =
+ cos n t
T
T
2 Z22
T
bn sin n
2⇡
T
2
Z
2⇡
bn sin n tdt
T
2
T
2
T
2
T
2
t cos n
T
= bn T
2Z2
2⇡
tdt =
cos n
2⇡
tdb
fo
In
ramp.py
2
2⇡
2⇡
b
t
4⇡
T
n
2
tdt =
bn sin n tdt =
+ cos n t
= bn
T signaal karakteriseert
2 2
T een optelsom
2van periodieke sig
T
ltTis dat de Fourier serie een
door
2
Door steeds
periodieke
functies naar
te combineren
kunnen
bijvoorbeeld blokvormige
Van meer
periodiek
signaal
Fourier
reeks
vormige signalen worden geconstrueerd. Het enige wat nodig is, is een serie getall
arameter n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
T
Stel we
een
de vorm
rukking• voor
dehebben
getallen
ansignaal
en bn in
zodat
deze niet allemaal hoeven te worden opgesom
Z2
T
2
2⇡
cos n tdt =
T
T
2
2⇡
2⇡
✓
◆
1
cos n 1 tdbX
sin
n
t
n
2⇡
2⇡
T
T
f (t) = a0 +
an cos n t + bn sin n t
2
T
n=1
T
k mogelijk om te starten ◆
met een signaal f (t) en daarna de getallen an en bn te be
2⇡• met
2⇡a0, anvan
T f(t)
onbekende
en bn, hoe kunnen
we dezeTbepalen uit f(t)?
oen
door
gebruik
te
maken
het
feit
dat
opgebouwd uit sinus en cosinus sign
os n t + bn sin n t with
 tis
⇡
2
T
T
t
T
2
2
• Vermenigvuldig f(t) met een functie g(t) en integreer
over T2  t  T2 to get
• Conclusie:
T
T
Z2
2⇡
2
f (t) cos n tdt, bn =
T
T
T
2
Z2
T
2
7
5
2⇡
f (t) sin n tdt
T
fo
In
T
ramp.py
Z2
Figuur 2: Een ramp-vormige
functie
2
T
T
2⇡
2⇡
2⇡
b
t
4⇡
T
n
2
2
2
sin
t sin
n serie
tdt =
bZn sin
n tdt =door een optelsom
+ cos nZ vant periodieke
= bnsig
lt isndat
de
Fourier
een
signaal
karakteriseert
T
T
T 2⇡
2 2⇡
2
T
2
T2⇡
bnnaar
nFourier
t coskunnen
nreeks
tdt
=
cosblokvormige
n2 tdbn
Tfuncties
Door steeds
periodieke
tesin
combineren
bijvoorbeeld
Van meer
periodiek
signaal
2
T enige watT nodig is, is een serie
T getall
vormige
signalen
worden
geconstrueerd.
Het
T over
T
dus gelijk aan nul. Houden we
2
2
m
arameter
n het aantal perioden binnen het tijdsinterval T voorstelt. Voor veel signale
Samenvattend:
weakunnen
alle
onbekende
a0, allemaal
an en bn bepalen
uit
f(t)
T getallen
rukking• voor
de
en
b
zodat
deze
niet
hoeven
te
worden◆opgesom
✓
T
n
n
1
2
T
X
2
Z
1
2⇡
2⇡
2
1
1
T
✓
◆sin n
2⇡
2⇡
2⇡
1
f=
(t)1=a t aX
a2⇡
t+
b
t with
0+
n cos n 2⇡
n
a
dt
=
a
2⇡
0
0
0
bn sin n t cos
n(t) =tdt2a=+
n2cos ntdbnt +sin
nT
t t
2 Tcosan=1
T
2
f
b
sin
n
0
n
n
TT
T 2
T T
T T
2
T
n=1
2
2⇡
T
T
2
tegrate f (t) , f (t) cos n T t and
f (t) sin n 2⇡
t
over

t

to get
T
2
2
• met
k mogelijk
om te starten met een signaal◆f (t) en daarna de getallen an en bn te be
✓
1
X gebruik te maken
2⇡ vanTThet feit
2⇡dat f(t) is opgebouwd
T uit sinus
T en cosinus sign
oen door
T
an cos n t + bZZn22sin n t with Z2
t
0+
T 22
T
2
2
2
2⇡
2
n=1
=
(t)dt, an =
f (t) cos n tdt, bn =
aa00 =
ff(t)dt
T
T
TTT  t  T to get T
nd f (t) sin n 2⇡
t
over
T
T
2 TT
2
Z
22
T
2
5
2
T
2
Z van f (t) over het intervalZ T  t7  T een getal op
dat het integreren
2
2
2
2⇡
2
2⇡
= is dat
f (t)
cossinus
n en
tdt,cosinus
bn = termen
f (t)
sinnul
n gaan
tdt op t =
n(t)dt,
T . Deanreden
alle
door
T
T
T
T
T
T berekenen van an en bn . O
eze eigenschap kunnen
we
ook
gebruiken
bij
het
2
2
n we f (t) met een test functie waarvan we weten dat deze er voor zorgt d
f (t)g(t)dt =
bn sin n
t sin m tdtA
T
T
n=1
T
T
al verdwijnt de derde term
voor alle m 6= n en
houden we over
2
2
@
t s ( 1 , 1 , s h a r e x= ’ c o l ’ , s h a r e y= ’ row ’ )
, f100 )
T, t verdwijnt
T
al
de derde
term voor alle
T houden we over
m 6= n en
Z
Z2
Periodieke
signalen
:
Blokgolf
2⇡100 s i n2⇡termen ’ ) T
an t
4⇡
T
T
2 2⇡
f
u
n
c
t
i
e
met
3
,
10
en
2 ramp
2
2
f (t)g(t)dt = Z bn sin n t sin n tdt = Z bn sin n tdt =
+ cos n t
2⇡
2⇡
2⇡
b2n 2t
4⇡
T
T
T
T
f (t)g(t)dt = T bn sin n t sin n tdt = T bn sin2 n tdt =
+ cos n t
2
2
T :
T
T
• Gegeven
de functieT in het guur
+12 2
2
2
T
T
2
T
/ j a n v a n h u l z e n / Documents
/ C o u r s e s / I n h o l l a n d / t e 2l e c o m / s l i d e s / f o u r i e r /ramp . pd f ” ,
2
ren we de•laatste
term periodiek?
Is de functie
Figuur
ramp-vormige
functie
ren we 2:de Een
laatste
term
T
T
ramp.py
2
• Is de functie
ZT even of oneven?
ZT2
T
T
2
2
2⇡
2⇡
2⇡
2⇡
Z
Z
b
sin
n
t
cos
n
tdt
=
nperiodieke
n 2⇡ t2(sinus
2⇡
2⇡
2⇡2 tdbn sin
nn en bn in f(t)door een optelsomcos
e Fourier serie
een signaal
van
signalen
• Bereken
a0,bkarakteriseert
a
cos n T tdbn sin n T t
n sin n T t cos n T tdt =
ds
functies
te combineren
kunnen
bijvoorbeeld
blokvormige,
driehoekige
T
T
T
T
T
T
ijkmeer
aan periodieke
nul. Houden
we over
2
2
T
T
1
ignalen worden geconstrueerd.
Het enige wat nodig is,
2
2 is een serie getallen an en bn
1
n hetZT2aantal perioden binnen
het✓
tijdsinterval T voorstelt. Voor◆
veel signalen bestaat er
T
✓
◆
X
1
1
2⇡
2⇡
TT
TT
2
X
1 f (t)
1
T
1
2⇡
2⇡
oor de getallen
a
en
b
zodat
deze
niet
allemaal
hoeven
te
worden
opgesomd.
with
t
a dt =n= a ant 0 + = aan cos n t + bn sin n t
2
0 f (t)
= 20a0 +
a0 cos n T t + bn sin n T t
2 2 1T ✓n=12 n
T
T
◆
2 n=1
X
12⇡
2⇡
2⇡
2⇡
T
f
(t)
=
a
+
a
cos
n
t
+
b
sin
n
T t t 
0t and f (t)
n sin n 2⇡ t over
n
ff (t)
(t) ,, ff (t)
(t) cos
cos n
n22⇡
t
and
f
(t)
sin
n
t
over
T
T
22 T t 
TT
T
n=1
T
2
T
T
T
22
22  t  22
with
to
to get
get
T
T
T
T
2
2
k om te starten met
daarna
de getallen an en bn te Z
berekenen.
We
Z22
ZZ2T2een signaal f (t) en Z
2⇡
22van het feit dat f(t) is
2 opgebouwd uit 2⇡
2 signalen. Als we2⇡
gebruik teaa
maken
sinus
en
cosinus
(t) sin
sin nn tdt
tdt
==
ff(t)dt,
f (t) cos n tdt, b =
ff(t)
(t)dt a =
00
n
TT
T
TT
22
T
T
T
2
2
fi
t integreren van f (t) over het interval
n
n
T
TT
T
T
22
T
2
 7t 
T
2
een getal oplevert
T
2
T
2
T
2
=b
=b
Periodieke signalen : Blokgolf
• Voor f(t) geldt:
f (t) =
1,
T
2
<t<0
T
2
f (t) = 1, 0 < t <
• met
2
bn =
T
2
bn =
T
2
bn =
T
Z
(Z
(
T
2
T
2
2⇡
f (t) sin
ntdt
T
0
volgt
2⇡
( 1) sin
ntdt +
T
T
2
T
2⇡
cos
nt
2⇡n
T
0
T
2
f (t + T ) = f (t)
Z

T
2
0
2⇡
(+1) sin
ntdt
T
T
2⇡
cos
nt
2⇡n
T
T
2
0
)
)
Periodieke signalen : Blokgolf
2
bn =
T
(
T
2⇡
cos
nt
2⇡n
T
1
bn =
{[1
n⇡
2
bn =
(1
n⇡
cos( n⇡)]
0
T
2

T
2⇡
cos
nt
2⇡n
T
[cos(n⇡)
cos(n⇡))
bn = 0, n even
4
bn =
, n oneven
n⇡
0]}
T
2
0
)
Periodieke signalen : Blokgolf
2
an =
T
2
an =
T
2
an =
T
Z
T
2
T
2
(Z
2⇡
f (t) cos
ntdt
T
0
2⇡
( 1) cos
ntdt +
T
T
2
( 
T
2⇡
sin
nt
2⇡n
T
1
an =
{ [0
n⇡
an = 0
0
T
2
Z
)
T
2
2⇡
(+1) cos
ntdt
T
0
T )

2
T
2⇡
+
sin
nt
2⇡n
T
0
sin( n⇡)] + [sin(n⇡)
0]}
Periodieke signalen : Blokgolf
bn = 0, n even
4
bn =
, n oneven
n⇡
• De blokgolf is opgebouwd uit sinusvormige signalen
Periodieke signalen : Blokgolf
bn = 0, n even
4
bn =
, n oneven
n⇡
• De blokgolf is opgebouwd uit sinusvormige signalen
• De fundamentele sinus is de 1e of fundamentele harmonische en is het
gewenste uitgangssignaal van de inverter
• De hogere harmonischen worden gezien als verstorende invloeden
Periodieke signalen : Blokgolf
1e harmonische
b1 = ⇡4 = 1.27
!1 = 2⇡/T = 0.78
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<latexit sha1_base64="z693djqbI3SEP7CtZwqnZbQpi/M=">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</latexit>
<latexit sha1_base64="4YgsznBlLki45PWRlYeR8gHRjEA=">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</latexit>
• De RMS waarde van de fundamentele harmonische is Vo1
<latexit sha1_base64="qYS/f2VWkcgV2W4UuMkRdtIFs0Y=">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</latexit>
Vo1 =
<latexit sha1_base64="O4+EyXGwWKB/bNX56o6uZYYH5LA=">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</latexit>
s
1
T
Z
T
0
b21 sin2 (!1 t)dt =
r
b21 h
t
2T
1
2!1
sin(2!1 t)
iT
0
b1
= p = 0.9
2
DEEL 3
Performance parameters van Inverters
Performance parameters
• De ingangsspanning van een inverter is DC
+
vs
• De uitgangsspanning van een inverter is AC
is
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
<latexit sha1_base64="cg8fYsKxh/oQS9hH6Uu2OICAtQE=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWBWFhGMR+QHGFvM5cs2ds7dveEcOQf2FgoYus/svPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wacz9zhMqzWP5aKYJ+hEdSR5yRo2VHm4bg3LFrboLkHXi5aQCOZqD8ld/GLM0QmmYoFr3PDcxfkaV4UzgrNRPNSaUTegIe5ZKGqH2s8WlM3JhlSEJY2VLGrJQf09kNNJ6GgW2M6JmrFe9ufif10tNeO1nXCapQcmWi8JUEBOT+dtkyBUyI6aWUKa4vZWwMVWUGRtOyYbgrb68Ttq1qudWvftapX6Tx1GEMziHS/DgCupwB01oAYMQnuEV3pyJ8+K8Ox/L1oKTz5zCHzifPyBYjQ8=</latexit>
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
<latexit sha1_base64="xa9KoQiBR8neG4ecPhW2iZUw9S4=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD+gCWWznbRLN5uwuymU0B/hxYMiXv093vw3btsctPXBwOO9GWbmhang2rjut1Pa2t7Z3SvvVw4Oj45PqqdnHZ1kimGbJSJRvZBqFFxi23AjsJcqpHEosBtO7hd+d4pK80Q+mVmKQUxHkkecUWOlrt+fDrQfDKo1t+4uQTaJV5AaFGgNql/+MGFZjNIwQbXue25qgpwqw5nAecXPNKaUTegI+5ZKGqMO8uW5c3JllSGJEmVLGrJUf0/kNNZ6Foe2M6ZmrNe9hfif189MdBvkXKaZQclWi6JMEJOQxe9kyBUyI2aWUKa4vZWwMVWUGZtQxYbgrb+8STqNuufWvcdGrXlXxFGGC7iEa/DgBprwAC1oA4MJPMMrvDmp8+K8Ox+r1pJTzJzDHzifPzNMj3I=</latexit>
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
• In het ideale geval is de uitgangsspanning
een sinusvormige, periodieke functie
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
AC
-
Vs
<latexit sha1_base64="72tRoxQkyf1I8zPKbjOfOZa9VRo=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWRNJZRzAckR9jb7CVL9vaO3TkhHPkHNhaK2PqP7Pw3bpIrNPHBwOO9GWbmBYkUBl332ylsbG5t7xR3S3v7B4dH5eOTtolTzXiLxTLW3YAaLoXiLRQoeTfRnEaB5J1g0pj7nSeujYjVI04T7kd0pEQoGEUrPdw2BuWKW3UXIOvEy0kFcjQH5a/+MGZpxBUySY3peW6CfkY1Cib5rNRPDU8om9AR71mqaMSNny0unZELqwxJGGtbCslC/T2R0ciYaRTYzoji2Kx6c/E/r5dieO1nQiUpcsWWi8JUEozJ/G0yFJozlFNLKNPC3krYmGrK0IZTsiF4qy+vk3at6rlV775Wqd/kcRThDM7hEjy4gjrcQRNawCCEZ3iFN2fivDjvzseyteDkM6fwB87nDxvJjQw=</latexit>
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
-
vo
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
<latexit sha1_base64="C1UkHj5lOKBeOYoDq+6H6Ie228M=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcDvDkwQDmp1t+EuQNaJV5I6lGgPal/BMGV5whUySY3xPTfDsKAaBZN8Vg1ywzPKJnTEfUsVTbgJi8W5M3JplSGJU21LIVmovycKmhgzTSLbmVAcm1VvLv7n+TnGN2EhVJYjV2y5KM4lwZTMfydDoTlDObWEMi3srYSNqaYMbUJVG4K3+vI66TYbntvwHpr11m0ZRwXO4QKuwINraME9tKEDDCbwDK/w5mTOi/PufCxbN5xy5gz+wPn8AQJMj1I=</latexit>
• Een praktisch realiseerbare inverter heeft
echter een uitgangsspanning waarin ook
hogere harmonischen voorkomen
0
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
• De ingangsstroom uit de DC bron is geen
gelijkstroom maar is afhankelijk van de tijd
dat de bron verbonden is met de belasting
+
vo
DC
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Vs
<latexit sha1_base64="DYjx/AUhdRjOWXWjpTPRVCdp90w=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4sSS96EkKXjxWsB+QhLLZTtqlm03c3Qil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5USa4Nq777aytb2xubZd2yrt7+weHlaPjtk5zxbDFUpGqbkQ1Ci6xZbgR2M0U0iQS2IlGtzO/84RK81Q+mHGGYUIHksecUWOlbuBftns6CHuVqltz5yCrxCtIFQo0e5WvoJ+yPEFpmKBa+56bmXBCleFM4LQc5BozykZ0gL6lkiaow8n83ik5t0qfxKmyJQ2Zq78nJjTRepxEtjOhZqiXvZn4n+fnJr4OJ1xmuUHJFoviXBCTktnzpM8VMiPGllCmuL2VsCFVlBkbUdmG4C2/vEra9Zrn1rz7erVxU8RRglM4gwvw4AoacAdNaAEDAc/wCm/Oo/PivDsfi9Y1p5g5gT9wPn8AbQiPiQ==</latexit>
is
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
Ip
Is
Ii
0
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+
sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
Hoe karakteriseren we
de prestaties van de inverter?
<latexit sha1_base64="BVkZx3YhbUh8LSCN2fD4ldcliSY=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPhB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHfGY87</latexit>
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Performance parameters
• De performance parameters die gebruikt worden zijn
• Ripple factor
• Harmonic Factor
• Total Harmonic Distortion
• Distortion Factor
• Lowest order Harmonic
Performance parameters
• Het uitgangsvermogen wordt gegeven door
+
vs
Pac = IO VO cos ✓
is
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
AC
-
Vs
<latexit sha1_base64="72tRoxQkyf1I8zPKbjOfOZa9VRo=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWRNJZRzAckR9jb7CVL9vaO3TkhHPkHNhaK2PqP7Pw3bpIrNPHBwOO9GWbmBYkUBl332ylsbG5t7xR3S3v7B4dH5eOTtolTzXiLxTLW3YAaLoXiLRQoeTfRnEaB5J1g0pj7nSeujYjVI04T7kd0pEQoGEUrPdw2BuWKW3UXIOvEy0kFcjQH5a/+MGZpxBUySY3peW6CfkY1Cib5rNRPDU8om9AR71mqaMSNny0unZELqwxJGGtbCslC/T2R0ciYaRTYzoji2Kx6c/E/r5dieO1nQiUpcsWWi8JUEozJ/G0yFJozlFNLKNPC3krYmGrK0IZTsiF4qy+vk3at6rlV775Wqd/kcRThDM7hEjy4gjrcQRNawCCEZ3iFN2fivDjvzseyteDkM6fwB87nDxvJjQw=</latexit>
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
-
vo
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
<latexit sha1_base64="C1UkHj5lOKBeOYoDq+6H6Ie228M=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcDvDkwQDmp1t+EuQNaJV5I6lGgPal/BMGV5whUySY3xPTfDsKAaBZN8Vg1ywzPKJnTEfUsVTbgJi8W5M3JplSGJU21LIVmovycKmhgzTSLbmVAcm1VvLv7n+TnGN2EhVJYjV2y5KM4lwZTMfydDoTlDObWEMi3srYSNqaYMbUJVG4K3+vI66TYbntvwHpr11m0ZRwXO4QKuwINraME9tKEDDCbwDK/w5mTOi/PufCxbN5xy5gz+wPn8AQJMj1I=</latexit>
• Voor een zuiver ohmse belasting volgt
0
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
Pac = IO VO cos ✓
• Het ingangsvermogen (AC) van de inverter is
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
<latexit sha1_base64="cg8fYsKxh/oQS9hH6Uu2OICAtQE=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWBWFhGMR+QHGFvM5cs2ds7dveEcOQf2FgoYus/svPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wacz9zhMqzWP5aKYJ+hEdSR5yRo2VHm4bg3LFrboLkHXi5aQCOZqD8ld/GLM0QmmYoFr3PDcxfkaV4UzgrNRPNSaUTegIe5ZKGqH2s8WlM3JhlSEJY2VLGrJQf09kNNJ6GgW2M6JmrFe9ufif10tNeO1nXCapQcmWi8JUEBOT+dtkyBUyI6aWUKa4vZWwMVWUGRtOyYbgrb68Ttq1qudWvftapX6Tx1GEMziHS/DgCupwB01oAYMQnuEV3pyJ8+K8Ox/L1oKTz5zCHzifPyBYjQ8=</latexit>
<latexit sha1_base64="xa9KoQiBR8neG4ecPhW2iZUw9S4=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD+gCWWznbRLN5uwuymU0B/hxYMiXv093vw3btsctPXBwOO9GWbmhang2rjut1Pa2t7Z3SvvVw4Oj45PqqdnHZ1kimGbJSJRvZBqFFxi23AjsJcqpHEosBtO7hd+d4pK80Q+mVmKQUxHkkecUWOlrt+fDrQfDKo1t+4uQTaJV5AaFGgNql/+MGFZjNIwQbXue25qgpwqw5nAecXPNKaUTegI+5ZKGqMO8uW5c3JllSGJEmVLGrJUf0/kNNZ6Foe2M6ZmrNe9hfif189MdBvkXKaZQclWi6JMEJOQxe9kyBUyI2aWUKa4vZWwMVWUGZtQxYbgrb+8STqNuufWvcdGrXlXxFGGC7iEa/DgBprwAC1oA4MJPMMrvDmp8+K8Ox+r1pJTzJzDHzifPzNMj3I=</latexit>
• Hierin zijn Vo , Io RMS waarden en is ✓ de
hoek tussen de impedantie en de ohmse
weerstand van de belasting
2
= IO
R
+
vo
DC
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Vs
<latexit sha1_base64="DYjx/AUhdRjOWXWjpTPRVCdp90w=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4sSS96EkKXjxWsB+QhLLZTtqlm03c3Qil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5USa4Nq777aytb2xubZd2yrt7+weHlaPjtk5zxbDFUpGqbkQ1Ci6xZbgR2M0U0iQS2IlGtzO/84RK81Q+mHGGYUIHksecUWOlbuBftns6CHuVqltz5yCrxCtIFQo0e5WvoJ+yPEFpmKBa+56bmXBCleFM4LQc5BozykZ0gL6lkiaow8n83ik5t0qfxKmyJQ2Zq78nJjTRepxEtjOhZqiXvZn4n+fnJr4OJ1xmuUHJFoviXBCTktnzpM8VMiPGllCmuL2VsCFVlBkbUdmG4C2/vEra9Zrn1rz7erVxU8RRglM4gwvw4AoacAdNaAEDAc/wCm/Oo/PivDsfi9Y1p5g5gT9wPn8AbQiPiQ==</latexit>
is
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
Ip
Is
Ii
0
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+
sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
PS = I S V S
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
<latexit sha1_base64="BVkZx3YhbUh8LSCN2fD4ldcliSY=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPhB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHfGY87</latexit>
• Hierin zijn Vs , Is de gemiddelde waarde
van de ingangsspanning en stroom
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Performance parameters
• Nog even voor de duidelijkheid:
• De gemiddelde waarde van een spanning of stroom wordt gegeven door
1
Vs =
T
<latexit sha1_base64="IylNRM514PDJthC7HMLvEkzJrk8=">AAACDXicbVC7SgNBFJ2NrxhfUUubwSjEJuym0UYJ2FhGyAuy6zI7mU2GzM4uM3cDYckP2PgrNhaK2Nrb+TdOHoUmHrhwOOde7r0nSATXYNvfVm5tfWNzK79d2Nnd2z8oHh61dJwqypo0FrHqBEQzwSVrAgfBOoliJAoEawfD26nfHjGleSwbME6YF5G+5CGnBIzkF8/cbsvX126oCM2cSdaYuFyCbz80Rr4uwwXugev5xZJdsWfAq8RZkBJaoO4Xv9xeTNOISaCCaN117AS8jCjgVLBJwU01Swgdkj7rGipJxLSXzb6Z4HOj9HAYK1MS8Ez9PZGRSOtxFJjOiMBAL3tT8T+vm0J45WVcJikwSeeLwlRgiPE0GtzjilEQY0MIVdzciumAmGDABFgwITjLL6+SVrXi2BXnvlqq3SziyKMTdIrKyEGXqIbuUB01EUWP6Bm9ojfryXqx3q2PeWvOWswcoz+wPn8AoaGbPA==</latexit>
Z
T
vs (t)dt
0
• De e ectieve waarde of RMS waarde van een spanning of stroom wordt
gegeven door
s
Vo =
<latexit sha1_base64="F0HSVQEJVDM+OehhIZG3sV2qpeQ=">AAACFnicbVA9SwNBEN3z2/gVtbRZDIIWhrs02iiCjWWEJAq589jb7CWLe7vn7lwgHPcrbPwrNhaK2Iqd/8bNR6GJDwYe780wMy9KBTfgut/O3PzC4tLyymppbX1jc6u8vdMyKtOUNakSSt9GxDDBJWsCB8FuU81IEgl2E91fDv2bPtOGK9mAQcqChHQljzklYKWwfOy3W6E6882DhtyPNaG5V+SNwucSQveu0Q/VXe0QjnAHCj8IyxW36o6AZ4k3IRU0QT0sf/kdRbOESaCCGNP23BSCnGjgVLCi5GeGpYTeky5rWypJwkyQj94q8IFVOjhW2pYEPFJ/T+QkMWaQRLYzIdAz095Q/M9rZxCfBjmXaQZM0vGiOBMYFB5mhDtcMwpiYAmhmttbMe0Rmw3YJEs2BG/65VnSqlU9t+pd1yoX55M4VtAe2keHyEMn6AJdoTpqIooe0TN6RW/Ok/PivDsf49Y5ZzKzi/7A+fwBCrqfPA==</latexit>
1
T
Z
T
0
vo2 (t)dt
ff
ff
• De betekenis van de e ectieve waarde of RMS waarde is de waarde van
een denkbeeldige gelijkspanning die in de zelfde tijd dezelfde warmte
ontwikkeling geeft in de zelfde weerstand
Performance parameters
• De e ectieve waarde (RMS) van de rimpel op
de ingangsstroom wordt gegeven door
Ir =
q
+
vs
Is2
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
AC
<latexit sha1_base64="72tRoxQkyf1I8zPKbjOfOZa9VRo=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWRNJZRzAckR9jb7CVL9vaO3TkhHPkHNhaK2PqP7Pw3bpIrNPHBwOO9GWbmBYkUBl332ylsbG5t7xR3S3v7B4dH5eOTtolTzXiLxTLW3YAaLoXiLRQoeTfRnEaB5J1g0pj7nSeujYjVI04T7kd0pEQoGEUrPdw2BuWKW3UXIOvEy0kFcjQH5a/+MGZpxBUySY3peW6CfkY1Cib5rNRPDU8om9AR71mqaMSNny0unZELqwxJGGtbCslC/T2R0ciYaRTYzoji2Kx6c/E/r5dieO1nQiUpcsWWi8JUEozJ/G0yFJozlFNLKNPC3krYmGrK0IZTsiF4qy+vk3at6rlV775Wqd/kcRThDM7hEjy4gjrcQRNawCCEZ3iFN2fivDjvzseyteDkM6fwB87nDxvJjQw=</latexit>
<latexit sha1_base64="J2gNY8+t+OndqEWsNVGtu8MwX4M=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD8gCWWz3bRLN7thd1MooT/CiwdFvPp7vPlv3LQ5aOuDgcd7M8zMi1LOtHHdb6eytb2zu1fdrx0cHh2f1E/PelpmitAukVyqQYQ15UzQrmGG00GqKE4iTvvR9L7w+zOqNJPiycxTGiZ4LFjMCDZW6gf+bCiDcFhvuE13CbRJvJI0oERnWP8KRpJkCRWGcKy177mpCXOsDCOcLmpBpmmKyRSPqW+pwAnVYb48d4GurDJCsVS2hEFL9fdEjhOt50lkOxNsJnrdK8T/PD8z8W2YM5FmhgqyWhRnHBmJit/RiClKDJ9bgoli9lZEJlhhYmxCNRuCt/7yJum1mp7b9B5bjfZdGUcVLuASrsGDG2jDA3SgCwSm8Ayv8Oakzovz7nysWitOOXMOf+B8/gAtNI9u</latexit>
0
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ff
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Vs
<latexit sha1_base64="DYjx/AUhdRjOWXWjpTPRVCdp90w=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4sSS96EkKXjxWsB+QhLLZTtqlm03c3Qil9E948aCIV/+ON/+N2zYHbX0w8Hhvhpl5USa4Nq777aytb2xubZd2yrt7+weHlaPjtk5zxbDFUpGqbkQ1Ci6xZbgR2M0U0iQS2IlGtzO/84RK81Q+mHGGYUIHksecUWOlbuBftns6CHuVqltz5yCrxCtIFQo0e5WvoJ+yPEFpmKBa+56bmXBCleFM4LQc5BozykZ0gL6lkiaow8n83ik5t0qfxKmyJQ2Zq78nJjTRepxEtjOhZqiXvZn4n+fnJr4OJ1xmuUHJFoviXBCTktnzpM8VMiPGllCmuL2VsCFVlBkbUdmG4C2/vEra9Zrn1rz7erVxU8RRglM4gwvw4AoacAdNaAEDAc/wCm/Oo/PivDsfi9Y1p5g5gT9wPn8AbQiPiQ==</latexit>
is
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
Ip
Is
Ii
0
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+
sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
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<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
ff
-
vo
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
1 T 2
Ii =
is (t)dt
T 0
Z T
1
Is =
is (t)dt
T 0
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
<latexit sha1_base64="C1UkHj5lOKBeOYoDq+6H6Ie228M=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcDvDkwQDmp1t+EuQNaJV5I6lGgPal/BMGV5whUySY3xPTfDsKAaBZN8Vg1ywzPKJnTEfUsVTbgJi8W5M3JplSGJU21LIVmovycKmhgzTSLbmVAcm1VvLv7n+TnGN2EhVJYjV2y5KM4lwZTMfydDoTlDObWEMi3srYSNqaYMbUJVG4K3+vI66TYbntvwHpr11m0ZRwXO4QKuwINraME9tKEDDCbwDK/w5mTOi/PufCxbN5xy5gz+wPn8AQJMj1I=</latexit>
• Ii , Is Worden gegeven door
Z
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
<latexit sha1_base64="cg8fYsKxh/oQS9hH6Uu2OICAtQE=">AAAB6XicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SaCWBWFhGMR+QHGFvM5cs2ds7dveEcOQf2FgoYus/svPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wacz9zhMqzWP5aKYJ+hEdSR5yRo2VHm4bg3LFrboLkHXi5aQCOZqD8ld/GLM0QmmYoFr3PDcxfkaV4UzgrNRPNSaUTegIe5ZKGqH2s8WlM3JhlSEJY2VLGrJQf09kNNJ6GgW2M6JmrFe9ufif10tNeO1nXCapQcmWi8JUEBOT+dtkyBUyI6aWUKa4vZWwMVWUGRtOyYbgrb68Ttq1qudWvftapX6Tx1GEMziHS/DgCupwB01oAYMQnuEV3pyJ8+K8Ox/L1oKTz5zCHzifPyBYjQ8=</latexit>
-
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• Hierin zijn Ii , Is de e ectieve en
gemiddelde waarde van de ingangsstroom
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<latexit sha1_base64="xa9KoQiBR8neG4ecPhW2iZUw9S4=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvHisYD+gCWWznbRLN5uwuymU0B/hxYMiXv093vw3btsctPXBwOO9GWbmhang2rjut1Pa2t7Z3SvvVw4Oj45PqqdnHZ1kimGbJSJRvZBqFFxi23AjsJcqpHEosBtO7hd+d4pK80Q+mVmKQUxHkkecUWOlrt+fDrQfDKo1t+4uQTaJV5AaFGgNql/+MGFZjNIwQbXue25qgpwqw5nAecXPNKaUTegI+5ZKGqMO8uW5c3JllSGJEmVLGrJUf0/kNNZ6Foe2M6ZmrNe9hfif189MdBvkXKaZQclWi6JMEJOQxe9kyBUyI2aWUKa4vZWwMVWUGZtQxYbgrb+8STqNuufWvcdGrXlXxFGGC7iEa/DgBprwAC1oA4MJPMMrvDmp8+K8Ox+r1pJTzJzDHzifPzNMj3I=</latexit>
<latexit sha1_base64="kQR9TlvhviD2K0kmEBVxqPRSNX4=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgY7hLo5UEbCwTMB+QHGFvM5es2ds7dveEcOQX2FgoYutPsvPfuEmu0MQHA4/3ZpiZFySCa+O6305hY3Nre6e4W9rbPzg8Kh+ftHWcKoYtFotYdQOqUXCJLcONwG6ikEaBwE4wuZv7nSdUmsfywUwT9CM6kjzkjBorNa8G5YpbdRcg68TLSQVyNAblr/4wZmmE0jBBte55bmL8jCrDmcBZqZ9qTCib0BH2LJU0Qu1ni0Nn5MIqQxLGypY0ZKH+nshopPU0CmxnRM1Yr3pz8T+vl5rwxs+4TFKDki0XhakgJibzr8mQK2RGTC2hTHF7K2FjqigzNpuSDcFbfXmdtGtVz616zVqlfpvHUYQzOIdL8OAa6nAPDWgBA4RneIU359F5cd6dj2VrwclnTuEPnM8fcrmMqw==</latexit>
<latexit
Ii2
+
vo
DC
<latexit sha1_base64="3hF5ETs9hTZRt9jcP4jRe67x9tc=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBZBEErSi56k4MVjC/YD2lA220m7drMJuxuhhP4CLx4U8epP8ua/cdvmoK0PBh7vzTAzL0gE18Z1v53CxubW9k5xt7S3f3B4VD4+aes4VQxbLBax6gZUo+ASW4Ybgd1EIY0CgZ1gcjf3O0+oNI/lg5km6Ed0JHnIGTVWal4NyhW36i5A1omXkwrkaAzKX/1hzNIIpWGCat3z3MT4GVWGM4GzUj/VmFA2oSPsWSpphNrPFofOyIVVhiSMlS1pyEL9PZHRSOtpFNjOiJqxXvXm4n9eLzXhjZ9xmaQGJVsuClNBTEzmX5MhV8iMmFpCmeL2VsLGVFFmbDYlG4K3+vI6adeqnlv1mrVK/TaPowhncA6X4ME11OEeGtACBgjP8ApvzqPz4rw7H8vWgpPPnMIfOJ8/b7GMqQ==</latexit>
<latexit
T
2
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<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
Performance parameters (voorbeeld)
• Het signaal wordt gegeven door
is
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
Ip
Is
Ii
0
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
Ip Ii
2
is (t) = Ii +
t = Ii + (Ip
T /2
T
• De gemiddelde waarde is
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
Ii )t
<latexit sha1_base64="BVkZx3YhbUh8LSCN2fD4ldcliSY=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPhB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHfGY87</latexit>
<latexit sha1_base64="y0JQfKQlL5fbdq6ymxH71dJ0LFA=">AAACKnicbVDLSsNAFJ34rPUVdelmsAgVsSbd6EapuNGdQh9CEsJkOmmHTh7M3Agl5Hvc+CtuulDErR/itGah1QMXzpxzL3PvCVLBFVjWu7GwuLS8slpZq65vbG5tmzu7XZVkkrIOTUQiHwKimOAx6wAHwR5SyUgUCNYLRtdTv/fIpOJJ3IZxyryIDGIeckpAS755hbHrcF/V4eji1ufHbigJzW/99ES/irx92izgh9HUUlEv7SNwPVz1zZrVsGbAf4ldkhoqceebE7ef0CxiMVBBlHJsKwUvJxI4FayoupliKaEjMmCOpjGJmPLy2akFPtRKH4eJ1BUDnqk/J3ISKTWOAt0ZERiqeW8q/uc5GYTnXs7jNAMW0++PwkxgSPA0N9znklEQY00IlVzviumQ6ExApzsNwZ4/+S/pNhu21bDvm7XWZRlHBe2jA1RHNjpDLXSD7lAHUfSEXtArejOejYnxbnx8ty4Y5cwe+gXj8wug86Tr</latexit>
Ii =
<latexit sha1_base64="VHAlEQxGm9hInPfUos08uZzdQJY=">AAACCnicbVDLSsNAFJ3UV62vqEs3o0WoCCUpgm6Ughu7q2AfkIQwmU7aoZNJmJkIJXTtxl9x40IRt36BO//GSZuFVg9cOJxzL/feEySMSmVZX0ZpaXllda28XtnY3NreMXf3ujJOBSYdHLNY9AMkCaOcdBRVjPQTQVAUMNILxte537snQtKY36lJQrwIDTkNKUZKS755CCF0nZZPL10VCoQze5qdTWtaOG35yYnrVXyzatWtGeBfYhekCgq0ffPTHcQ4jQhXmCEpHdtKlJchoShmZFpxU0kShMdoSBxNOYqI9LLZK1N4rJUBDGOhiys4U39OZCiSchIFujNCaiQXvVz8z3NSFV54GeVJqgjH80VhyqCKYZ4LHFBBsGITTRAWVN8K8QjpRJROLw/BXnz5L+k26rZVt28b1eZVEUcZHIAjUAM2OAdNcAPaoAMweABP4AW8Go/Gs/FmvM9bS0Yxsw9+wfj4BvE/mH0=</latexit>
1
4 (Ii
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
+ Ip )
<latexit sha1_base64="zztW96h9btToV2A2bWMbF6pA3M8=">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</latexit>
ir
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
0
• De e ectieve waarde is
q
Is = 16 Ip2 + 16 Ip Ii + 16 Ii2
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
T
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
t
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
<latexit sha1_base64="aFlAhvUI2exI9gSndJYDAFsTN4o=">AAACMHicbZDLSsNAFIYn9VbrrerSTbAIglCSLtSNUnCh3VWwF2jSMJlO2qGTizMnQgl5JDc+im4UFHHrUzhts9DUHwZ+vnPOzJzfjTiTYBhvWmFpeWV1rbhe2tjc2t4p7+61ZRgLQlsk5KHoulhSzgLaAgacdiNBse9y2nHHV9N654EKycLgDiYRtX08DJjHCAaFnPK11Ws48sKS9wISCzyBSWKmyWnacKJ+7SRHGg7LIdavpSXLLjnlilE1ZtIXjZmZCsrUdMrP1iAksU8DIBxL2TONCOwEC2CEU3VnLGmEyRgPaU/ZAPtU2sls4VQ/UmSge6FQJwB9Rn9PJNiXcuK7qtPHMJL52hT+V+vF4J3bCQuiGGhA5g95Mdch1Kfp6QMmKAE+UQYTwdRfdTLCKg9QGU9DMPMrL5p2rWoaVfO2VqlfZnEU0QE6RMfIRGeojm5QE7UQQY/oBb2jD+1Je9U+ta95a0HLZvbRH2nfPwB2qXY=</latexit>
• Waarna volgt dat de e ectieve waarde van de rimpel kan worden berekend met
Ir =
q
Ii2
Is2 =
q
5 2
48 Ii
+
1
24 Ii Ip
+
5 2
48 Ip
• Dit resultaat volgt ook uit
Ir =
ff
<latexit sha1_base64="cJkzQysvITXF0vKy+k79E6DRscY=">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</latexit>
s
1
T
Z
T
0
✓
2
Ii + (Ip
T
ff
<latexit sha1_base64="cR/rW2tCaMUmKpBHLz/mb9z9JRk=">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</latexit>
Ii )t
1
4 (Ii
Ip )
◆2
dt =
q
5 2
48 Ii
+
1
24 Ii Ip
+
5 2
48 Ip
Performance parameters : Ripple factor
• De ripple factor is de verhouding tussen de e ectieve waarde van de
rimpel en de gemiddelde waarde van het signaal
Ir
RFs =
Is
<latexit sha1_base64="hxU0/tWl8EfKPTvD/XONQa4yxWo=">AAAHKniclVXLbtNAFDWPhBJeBZZsRlSpEkpTOxTBxqgSqGqlSpQqDUiZxJo4k3SEPQ6eSUVlzfew4VfYsAAhtnwI84ybEiSYhT2+j3PvOXM1Hk4Twrjv/7h0+crVSvXayvXajZu3bt9ZvXuvy7JZHuPjOEuy/N0QMZwQio854Ql+N80xSocJfjt8/1L5357inJGMdvjZFPdTNKFkTGLEpSm6W9mBvaPdiIVwnKO42I9yIR9MwH6tDnt7uxG1nm5UZFQI9X4dCOvv7L2y7qD0sA85LyCbpVFBw/bjJ49brZYYQELH/AwYmEHbArza/c98mOAxbyy2RBVcTiYnvHkOeFnnWSB0MMcfeQHkOs2yHABBXwQmrRtloW1A57ZF0Yl8IYvzqPDFQH1tSQALzCRYsS1GXMxrMVG4Hk4j35qRxJDmDccqcHwMHRRRGGfMkqMwS/EEAW45bQylmxH6F7d76ZLDOWspKJwSoXN6pn/ItWdT2WU3YuCb0E3XtSyyvAYYNZwFNDc0mj9weA5uUYF/wzK2vu253ZW5VLet2AzxhNACJWRCH4laXcq5Hs4VlHPxdHEyLEQ0x1CaldVhrb4e+u7o9cELNV/bCqVWBwBiOiqrye+emZjwPLIZDsnPNqnCiDrnf+7LIBwN2huL+hyUI6xbL4UDm5CfYC6npOlK2u8QojzmqIw92DpyMRfUA+BQs1kPDat9/VRjZ8GD0JgG7SOlFQBSbDM8y+mXPNx5HpjezZFKmOWi2unpnEaswZtEP0c8LM2+Nvva7Phqr4ssLwwmXJprzJDT+jn5msA5wX6ULbicsIHC7Ug3cwX351eiQTTVVL5UrDFPk+HR6prf8vUCf24Cu1nz7DqMVr/CURbPUkx5nCDGeoE/5f0C5ZzECRY1OGN4iuL3aIJ7cktRilm/0Fe9AHVpGYGxHN5xRjnQ1vMZBUoZO0uHMjJF/IRd9CnjMl9vxsfP+wWh0xnHNDaFxrME8Ayo/wYYkRzHPDmTGxTnRPYK4hMkBeLy76JECC5S/nPTbbcCvxW8aa/tvLByrHgPvIdewwu8Z96Ot+cdesdeXPlU+VL5Vvle/Vz9Wv1R/WlCL1+yOfe9hVX99RvIs26l</latexit>
• Het is een maat voor de hoeveelheid energie in het variërende deel van het
signaal. (DC signaal heeft een ripple factor van 0)
is
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
Ip
is
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
Gemiddelde waarde
<latexit sha1_base64="U40WKx0SjOi7JqPQiuVTfJN5Ek8=">AAAB7nicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48V7AckoWy2m3bpZhN2J0IJ/RFePCji1d/jzX/jts1BWx8MPN6bYWZelElh0HW/nY3Nre2d3cpedf/g8Oi4dnLaNWmuGe+wVKa6H1HDpVC8gwIl72ea0ySSvBdN7uZ+74lrI1L1iNOMhwkdKRELRtFKvcAXAxOEg1rdbbgLkHXilaQOJdqD2lcwTFmecIVMUmN8z80wLKhGwSSfVYPc8IyyCR1x31JFE27CYnHujFxaZUjiVNtSSBbq74mCJsZMk8h2JhTHZtWbi/95fo7xTVgIleXIFVsuinNJMCXz38lQaM5QTi2hTAt7K2FjqilDm1DVhuCtvrxOus2G5za8h2a9dVvGUYFzuIAr8OAaWnAPbegAgwk8wyu8OZnz4rw7H8vWDaecOYM/cD5/AB9kj2U=</latexit>
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
Ip
<latexit sha1_base64="nHERyqISlbm5Ob62LZn+2+1k9ZI=">AAAB+3icbVC7TsMwFHV4lvIKZWSxqJCYqqQLTKgSA4xFog+pjSrHuWmt2k5kO0AV9VdYGECIlR9h429w2wzQcqSre3TOvfL1CVPOtPG8b2dtfWNza7u0U97d2z84dI8qbZ1kikKLJjxR3ZBo4ExCyzDDoZsqICLk0AnH1zO/8wBKs0Tem0kKgSBDyWJGibHSwK3cgGBRBDwC/EiIsm3gVr2aNwdeJX5BqqhAc+B+9aOEZgKkoZxo3fO91AQ5UYZRDtNyP9OQEjomQ+hZKokAHeTz26f4zCoRjhNlSxo8V39v5ERoPRGhnRTEjPSyNxP/83qZiS+DnMk0MyDp4qE449gkeBYEjpgCavjEEkIVs7diOiKKUGPjKtsQ/OUvr5J2veZ7Nf+uXm1cFXGU0Ak6RefIRxeogW5RE7UQRU/oGb2iN2fqvDjvzsdidM0pdo7RHzifP1Ork/E=</latexit>
<latexit sha1_base64="QRyDx7xUnUiwFR0vrQ+EDGl4vs8=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJJTNdtMu3WyW3Y1QQn+EFw+KePX3ePPfuE1z0NYHA4/3ZpiZF0nOtHHdb6eysbm1vVPdre3tHxwe1Y9PejrNFKFdkvJUDSKsKWeCdg0znA6kojiJOO1H09uF33+iSrNUPJqZpGGCx4LFjGBjpX7g3w9lEA7rDbfpFkDrxCtJA0p0hvWvYJSSLKHCEI619j1XmjDHyjDC6bwWZJpKTKZ4TH1LBU6oDvPi3Dm6sMoIxamyJQwq1N8TOU60niWR7UywmehVbyH+5/mZia/DnAmZGSrIclGccWRStPgdjZiixPCZJZgoZm9FZIIVJsYmVLMheKsvr5Neq+m5Te+h1WjflHFU4QzO4RI8uII23EEHukBgCs/wCm+OdF6cd+dj2VpxyplT+APn8wfpw49C</latexit>
Is
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
Is
0
<latexit sha1_base64="7rwaiFGrAAiYqwjkzRPIARmvGZQ=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0l60ZMUvOitgv2AJpTNdtMu3WzC7kQooT/CiwdFvPp7vPlv3LY5aOuDgcd7M8zMC1MpDLrut1Pa2Nza3invVvb2Dw6PqscnHZNkmvE2S2SieyE1XArF2yhQ8l6qOY1Dybvh5Hbud5+4NiJRjzhNeRDTkRKRYBSt1PX79wPjB4Nqza27C5B14hWkBgVag+qXP0xYFnOFTFJj+p6bYpBTjYJJPqv4meEpZRM64n1LFY25CfLFuTNyYZUhiRJtSyFZqL8nchobM41D2xlTHJtVby7+5/UzjK6DXKg0Q67YclGUSYIJmf9OhkJzhnJqCWVa2FsJG1NNGdqEKjYEb/XlddJp1D237j00as2bIo4ynME5XIIHV9CEO2hBGxhM4Ble4c1JnRfn3flYtpacYuYU/sD5/AHuVY9F</latexit>
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
0
p
RFs = 1.6
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
<latexit sha1_base64="4Rj7YOK7cbVasuizzNWypNvq40Y=">AAAB+HicbVBNS8NAEJ3Ur1o/GvXoZbEInkrSi56k4MVjhX5BEspmu2mXbjZhdyPUkF/ixYMiXv0p3vw3btsctPXBwOO9GWbmhSlnSjvOt1XZ2t7Z3avu1w4Oj47r9slpXyWZJLRHEp7IYYgV5UzQnmaa02EqKY5DTgfh7G7hDx6pVCwRXT1PaRDjiWARI1gbaWTXfc+PJCZ5t8hbhR+M7IbTdJZAm8QtSQNKdEb2lz9OSBZToQnHSnmuk+ogx1IzwmlR8zNFU0xmeEI9QwWOqQry5eEFujTKGEWJNCU0Wqq/J3IcKzWPQ9MZYz1V695C/M/zMh3dBDkTaaapIKtFUcaRTtAiBTRmkhLN54ZgIpm5FZEpNjlok1XNhOCuv7xJ+q2m6zTdh1ajfVvGUYVzuIArcOEa2nAPHegBgQye4RXerCfrxXq3PlatFaucOYM/sD5/ALlxkxk=</latexit>
<latexit sha1_base64="cZuUVgqUp7iSoFzI1bPT5Oj5PvY=">AAAB/HicbVDLSsNAFJ3UV62vaJduBovgKiRdqBulIIjLKvYBSQiT6aQdOpnEmYkQQv0VNy4UceuHuPNvnLZZaOuBC4dz7uXee8KUUals+9uorKyurW9UN2tb2zu7e+b+QVcmmcCkgxOWiH6IJGGUk46iipF+KgiKQ0Z64fhq6vceiZA04fcqT4kfoyGnEcVIaSkw6557dx3IC08+CFU41unE8wOzYVv2DHCZOCVpgBLtwPzyBgnOYsIVZkhK17FT5RdIKIoZmdS8TJIU4TEaEldTjmIi/WJ2/AQea2UAo0To4grO1N8TBYqlzONQd8ZIjeSiNxX/89xMRed+QXmaKcLxfFGUMagSOE0CDqggWLFcE4QF1bdCPEICYaXzqukQnMWXl0m3aTm25dw2G63LMo4qOARH4AQ44Ay0wA1ogw7AIAfP4BW8GU/Gi/FufMxbK0Y5Uwd/YHz+AMgrlC0=</latexit>
T
2
<latexit sha1_base64="RdL4HsN7EnAmYduMd5Grh/Z2RXs=">AAAB7HicbVBNS8NAEJ2tX7V+VT16WSyCp5L0oicpePFYoWkLSSib7aZdutmE3Y1QQn+DFw+KePUHefPfuG1z0NYHA4/3ZpiZF2WCa+M436iytb2zu1fdrx0cHh2f1E/PejrNFWUeTUWqBhHRTHDJPMONYINMMZJEgvWj6f3C7z8xpXkqu2aWsTAhY8ljTomxkhf43SAc1htO01kCbxK3JA0o0RnWv4JRSvOESUMF0dp3ncyEBVGGU8HmtSDXLCN0SsbMt1SShOmwWB47x1dWGeE4VbakwUv190RBEq1nSWQ7E2Imet1biP95fm7i27DgMssNk3S1KM4FNilefI5HXDFqxMwSQhW3t2I6IYpQY/Op2RDc9Zc3Sa/VdJ2m+9hqtO/KOKpwAZdwDS7cQBseoAMeUODwDK/whiR6Qe/oY9VaQeXMOfwB+vwBcuOOag==</latexit>
<latexit
T
t
p
RFs = 2
<latexit sha1_base64="4xWBgxEnaEH/kyeKxkHaL+sd21g=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwwwjPq1uttwFyDrxCtJHUq0+7WvcJCxIuUKmaTGBJ6bYzSlGgWTfFYNC8NzysZ0yANLFU25iaaLY2fk0ioDkmTalkKyUH9PTGlqzCSNbWdKcWRWvbn4nxcUmNxEU6HyArliy0VJIQlmZP45GQjNGcqJJZRpYW8lbEQ1ZWjzqdoQvNWX10mn2fDchvfQrLduyzgqcA4XcAUeXEML7qENPjAQ8Ayv8OYo58V5dz6WrRtOOXMGf+B8/gCjo46K</latexit>
<latexit
<latexit sha1_base64="pb29lM9HMVK1NraSUOVO8beNK8k=">AAAB+nicbVDLSsNAFJ3UV62vVJduBovgqiTd6EYpCOKyin1AEsJkOmmHTh7O3Cgl9lPcuFDErV/izr9x2mahrQcuHM65l3vvCVLBFVjWt1FaWV1b3yhvVra2d3b3zOp+RyWZpKxNE5HIXkAUEzxmbeAgWC+VjESBYN1gdDn1uw9MKp7EdzBOmReRQcxDTgloyTerrnN75atzV91LyBsT1/PNmlW3ZsDLxC5IDRVo+eaX209oFrEYqCBKObaVgpcTCZwKNqm4mWIpoSMyYI6mMYmY8vLZ6RN8rJU+DhOpKwY8U39P5CRSahwFujMiMFSL3lT8z3MyCM+8nMdpBiym80VhJjAkeJoD7nPJKIixJoRKrm/FdEgkoaDTqugQ7MWXl0mnUbetun3TqDUvijjK6BAdoRNko1PURNeohdqIokf0jF7Rm/FkvBjvxse8tWQUMwfoD4zPH9wRk7Y=</latexit>
ff
<latexit sha1_base64="krLSXuTEkDEsx8Zc0imuqxchFtQ=">AAAB7HicbVBNS8NAEJ34WetX1aOXxSJ4KkkvepKCF48VTFtIQtlsN+3SzSbsToRS+hu8eFDEqz/Im//GbZuDtj4YeLw3w8y8OJfCoOt+OxubW9s7u5W96v7B4dFx7eS0Y7JCM+6zTGa6F1PDpVDcR4GS93LNaRpL3o3Hd3O/+8S1EZl6xEnOo5QOlUgEo2glPwzcMOrX6m7DXYCsE68kdSjR7te+wkHGipQrZJIaE3hujtGUahRM8lk1LAzPKRvTIQ8sVTTlJpoujp2RS6sMSJJpWwrJQv09MaWpMZM0tp0pxZFZ9ebif15QYHITTYXKC+SKLRclhSSYkfnnZCA0ZygnllCmhb2VsBHVlKHNp2pD8FZfXiedZsNzG95Ds966LeOowDlcwBV4cA0tuIc2+MBAwDO8wpujnBfn3flYtm445cwZ/IHz+QM8C45G</latexit>
<latexit
Performance parameters
• De harmonic factor HFn Is gede nieerd als
<latexit sha1_base64="XMrqSCd3PpuQyR8BK40cMQ0qCXY=">AAAFkXichVTbbtNAEHXbBEqA0tJHXizaSqlofVk7JDxsVUpVBYHUu1spTqyNs0ms+hK8G0Rk+Xv4H974G8bxJqRuBZYSz5454zlndrXdke8xrmm/l5ZXSuUnT1efVZ6/eLn2an3jtcWicezSazfyo/i2Sxj1vZBec4/79HYUUxJ0fXrTvfuU5W++05h5UXjFJyPaDsgg9PqeSzhAzsbKzx27ZTkMmw2b0x88ka3UblcAvMBIMQW2bZ8GdEC2RcpykkgX8ZkTzcGjCwF+dlgefD1tLpZgTTFrNvcCyswGRrryvtA0o6UY9KgIFMEfMgsM6Af5qINUEGjCC1RCoAnazVzBCNBpUp/lPs5z5yBE6NA1XCvkcycY5QRkPpwN+MMgRM0GB71VMPPIR2aGrdk0LGeIbfYt5onNxoGThNjYq+3V9xRFSTu2F/b5RM7qwrSDUsG0HK2D9vOvZaimIL1eHNtV8xhX8ww021Wrou0uSFcMMUJ7R7D/I8H2aZ9X7X5M3CRXkyYhtLZjbzDku3+lFYkGEI1F4rsiowaM2j8ZdWDU7zPcXsRZZlxD5nyUxydzYMFtTTEaqOA2V4bzCapGDjZPHAPnGdjERIOd0lUDG4ZiGIX644yayxQF4FHIU8Uu6yqqY0Opa8VRw/kXbfL1pWPsXTpmvoBdvVTRTGWE9+fubD6knDgarKZaQ7vtrG+B4ekjPwx0EWxJ4jlz1n/ZvcgdBzTkrk8Ya+naiLcTEnPP9WlasceMjoh7Rwa0BWFI4Ky3k+mNkso7gPTkfhTDL+TyFF2sSEjA2CToAjMgfMiKuQx8LNca836jnXjhaMxp6OaN+mNf5pGcXU9yz4upy/0JBMSNPdAqu0MCp4PDJVaBIehFyw8DCym6pujnaOvwQIxjVXojvZWqki7VpUOpKZ1J15JbWiuZJVw6KG+WP5QPy0c5dXlJ1GxK957ylz8SPbiS</latexit>
Von
HFn =
Vo1
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• De HFn is de verhouding tussen de RMS waarde van de n-de
harmonische ten opzichte van de 1e of fundamentele harmonische
<latexit sha1_base64="XMrqSCd3PpuQyR8BK40cMQ0qCXY=">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</latexit>
• De total harmonic distortion T HD is gede nieerd als
v
u X
1
u
1 t
2
T HD =
Von
Vo1 n=2,3,...
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<latexit sha1_base64="70Or7yFv3oSD5nDq1tiXvdqQqQk=">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</latexit>
• De T HD is geeft de mate waarin een signaal overeenkomt met zijn
fundamentele component
fi
fi
<latexit sha1_base64="LpCQifUsz0XIjJ+XNgAZ512zWOU=">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</latexit>
Performance parameters
• De distortion factor DF geeft de harmonic distortion na lteren van het
uitgangssignaal door een tweede orde lter
<latexit sha1_base64="pAOJMzay1rMyTOR+v5mJZP79QIw=">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</latexit>
v
u X
✓
◆2
1
u
1 t
Von
DF =
Vo1 n=2,3,... n2
<latexit sha1_base64="WHDptkgQ8ZPrA7masFx9BZRrGL4=">AAAHU3iclVVNb9tGEGXcyE6dpnXaYy9EHAMSKvNjSZXqYYukMQIHKBAnluUAWpmgqJW1CL/KXRU1CP7HIEAP/SO95NAOuSvaoo0GJWB7OPNm5s2bXXOWRYwLy/rr3tYX9zvbOw++3H341aOvv9l7/O2Yp6s8pGdhGqX5u1nAacQSeiaYiOi7LKdBPIvo+ez9iyp+/jvNOUuTkbjK6DQOLhO2YGEgwOU/7rADMhn7HLtDIugfotDHJZnugvMtRoarfE/J65heBk9VaOwXqa3sEz9tnL+8Vc5XPpfGr6+Pb6Zgy3AHRLCYcneIkW382GpawUoMfEwEjOAXclsI6Afx9AKZQNCFP8ASDEvBzhsGGXjroL2OPW9ib4CI4mFbeNCKy0kwkgDk3tYG5sNAxKyEg94mDHNHkfXA47UaY3+JCf8tFwXhq9gvEuz0B32vbxhGeUFYshBXepWXlBeoVMixb12gQ1mt8loGsr22bKPjI9yVEWjWM7uqbQ+oG46SkBwo9GcokIguRJcs8iAsJJuySKA1ydnlUvSuqbWBDgCdm8Af2ogBIAb/ifAA4W0iwnkqeDW4hdxGyqOXjePGtAPDGaLWtJIZlgqajnQev/QdLCOwxMKCTdmmgx3HcJxW/lEFlTRVAsyo6Jlqy7aJPOwYntWWGs6/aiPfT32nf+q78gW2emqiNcsUHzbTEbGkIvCthmyy9tdCjcoC3XEVZ76NFcItC5IxIGYgb+M8qs3VILuESrBzAUdsBMkwFmew6S5Jq9vu26I3F5spNQq6Q16lyEQcqoZQC63TyqpMt3nVRU/KNa36QL11JeBYl0Zltd2f1IgqC65fxswRBLzhtQx481jKoa4vwfVtaCZcQzbOPOo7d186KFCfrf+X/vkbA3V3/b19OLL1o982bGXsa+o58fc+knkarmKaiDAKOJ/YViamRZALFka03CUrTrMgfB9c0gmYSQD/raZF/U0o9QPwzPVFmsNPIvTaezOjCGLOr+IZIONALHk7Vjnvik1WYjGcFizJVoImoWy0WEW6SPXqA6PPWU5DEV2BEYQ5A656uAxAGgGfoUoEuz3ybWOMDNsy7Ddo/9nPSo4H2vfaE62r2ZqnPdOOtRPtTAs7Hzp/d/7Z1rb/3P60s7VzX0K37qmc77SNZ+fRv4zdW5Y=</latexit>
• De distortion factor van een speci eke, hogere harmonische is gegeven door
Von
DFn =
voor n > 1
2
Vo1 n
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• De LOH is de harmonische component waarvoor
• de frequentie het dichtste bij de fundamentele frequentie ligt en
• de amplitude gelijk is aan of groter is dan 3% van de fundamentele
harmonische
<latexit sha1_base64="T0IBKftrGWAmmKFy6AYaO+Td5T4=">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</latexit>
fi
fi
fi
<latexit sha1_base64="4T6T22Px2HFHox1TshSQe+dFUZI=">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</latexit>
DEEL 4
De single-phase half-bridge inverter
Single-phase half-bridge inverter
i1
+
Vs
2
Q1
C1
L
Vs
+
Vs
2
0
R
a
i2
io (t)
C2
D1
Q2
D2
Single-phase half-bridge inverter
i1
+
<latexit sha1_base64="0xCs/SAA7evdDz/bmVd1ruQdJK4=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKqMeCF48V7Ae0oWy2m3bpZhN3J4US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSMnGqGW+yWMa6E1DDpVC8iQIl7ySa0yiQvB2M7+Z+e8K1EbF6xGnC/YgOlQgFo2glvxdqyrJW38yy2qxfrrhVdwGyTrycVCBHo1/+6g1ilkZcIZPUmK7nJuhnVKNgks9KvdTwhLIxHfKupYpG3PjZ4ugZubDKgISxtqWQLNTfExmNjJlGge2MKI7MqjcX//O6KYa3fiZUkiJXbLkoTCXBmMwTIAOhOUM5tYQyLeythI2ozQFtTiUbgrf68jpp1aqeW/Uerir16zyOIpzBOVyCBzdQh3toQBMYPMEzvMKbM3FenHfnY9lacPKZU/gD5/MH/86SMg==</latexit>
Vs
2
Q1
C1
L
Vs
+
0
R
a
<latexit sha1_base64="EP1u5569Uf07N9VDVEgVYyKO59E=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGtn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv1Wh5HEc7gHC7Bgxuowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AdX2MqA==</latexit>
<latexit
✓
<latexit sha1_base64="XvwFxXapCS/be2ilCx192L3/p8I=">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</latexit>
<latexit
<latexit sha1_base64="fxWLHdy4k1f4Vu4VU5FJVEg6FUU=">AAAB9XicbVBNS8NAEJ34WetX1aOXxSJ4sSRF1GPBi8cK9gPaWjbbSbt0swm7G6WE/A8vHhTx6n/x5r9x2+agrQ8GHu/NMDPPjwXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY1FGiGDZYJCLV9qlGwSU2DDcC27FCGvoCW/74Zuq3HlFpHsl7M4mxF9Kh5AFn1Fjp4bwbKMrSZl9naTXrl8puxZ2BLBMvJ2XIUe+XvrqDiCUhSsME1brjubHppVQZzgRmxW6iMaZsTIfYsVTSEHUvnV2dkVOrDEgQKVvSkJn6eyKlodaT0LedITUjvehNxf+8TmKC617KZZwYlGy+KEgEMRGZRkAGXCEzYmIJZYrbWwkbUZuDsUEVbQje4svLpFmteG7Fu7so1y7zOApwDCdwBh5cQQ1uoQ4NYKDgGV7hzXlyXpx352PeuuLkM0fwB87nD2tWkmk=</latexit>
Vs
2
i
Vs 1
2R
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
<latexit sha1_base64="VoaGCyCFwGZKiRR0S0dUyXB2SvE=">AAAB9XicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rGK/YC2ls120y7dbMLuRCkh/8OLB0W8+l+8+W/ctjlo64OBx3szzMzzYykMuu63s7K6tr6xWdgqbu/s7u2XDg6bJko04w0WyUi3fWq4FIo3UKDk7VhzGvqSt/zx9dRvPXJtRKTucRLzXkiHSgSCUbTSQzfQlKXNvsnS6l3WL5XdijsDWSZeTsqQo94vfXUHEUtCrpBJakzHc2PspVSjYJJnxW5ieEzZmA55x1JFQ2566ezqjJxaZUCCSNtSSGbq74mUhsZMQt92hhRHZtGbiv95nQSDq14qVJwgV2y+KEgkwYhMIyADoTlDObGEMi3srYSNqA0CbVBFG4K3+PIyaVYrnlvxbs/LtYs8jgIcwwmcgQeXUIMbqEMDGGh4hld4c56cF+fd+Zi3rjj5zBH8gfP5A6Y4ko4=</latexit>
0
<latexit sha1_base64="EP1u5569Uf07N9VDVEgVYyKO59E=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGtn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv1Wh5HEc7gHC7Bgxuowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AdX2MqA==</latexit>
<latexit
Vs
2
C2
Q2
T0
2
t
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
T0
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
<latexit sha1_base64="x5C1KzfjROdiU4Uvp+UtSPxDJUE=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GPBi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9xm+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVDFssFrHqBlSj4BJbhhuB3UQhjQKBnWByO/c7T6g0j+WjmSboR3QkecgZNVZ64ANvUK25dTcHWSVeQWpQoDmofvWHMUsjlIYJqnXPcxPjZ1QZzgTOKv1UY0LZhI6wZ6mkEWo/y0+dkTOrDEkYK1vSkFz9PZHRSOtpFNjOiJqxXvbm4n9eLzXhjZ9xmaQGJVssClNBTEzmf5MhV8iMmFpCmeL2VsLGVFFmbDoVG4K3/PIqaV/UPbfu3V/WGldFHGU4gVM4Bw+uoQF30IQWMBjBM7zCmyOcF+fd+Vi0lpxi5hj+wPn8AfErjYU=</latexit>
i2
io (t)
<latexit sha1_base64="6DpZglibkrPb8bx68MebDoym5Tg=">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
sha1_base64="6DpZglibkrPb8bx68MebDoym5Tg=">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</latexit>
<latexit sha1_base64="rP5BOiehBYoBjcm6VsM56MuE4lw=">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</latexit>
0
D1
Fundamental current io1
va0
Vs
2
D2
Vs i2
2R
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T0
2
T0
T0
2
T0
t
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
<latexit sha1_base64="8h/KWJ6zD7e6vfE24vOXcPxzfgU=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKVI8FLx4r2g9oQ9lsJ+3SzSbsboQS+hO8eFDEq7/Im//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ7dzvPKHSPJaPZpqgH9GR5CFn1FjpgQ9qg3LFrboLkHXi5aQCOZqD8ld/GLM0QmmYoFr3PDcxfkaV4UzgrNRPNSaUTegIe5ZKGqH2s8WpM3JhlSEJY2VLGrJQf09kNNJ6GgW2M6JmrFe9ufif10tNeONnXCapQcmWi8JUEBOT+d9kyBUyI6aWUKa4vZWwMVWUGZtOyYbgrb68Ttq1qudWvfurSqOex1GEMziHS/DgGhpwB01oAYMRPMMrvDnCeXHenY9la8HJZ07hD5zPH/KvjYY=</latexit>
<latexit sha1_base64="VoaGCyCFwGZKiRR0S0dUyXB2SvE=">AAAB9XicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rGK/YC2ls120y7dbMLuRCkh/8OLB0W8+l+8+W/ctjlo64OBx3szzMzzYykMuu63s7K6tr6xWdgqbu/s7u2XDg6bJko04w0WyUi3fWq4FIo3UKDk7VhzGvqSt/zx9dRvPXJtRKTucRLzXkiHSgSCUbTSQzfQlKXNvsnS6l3WL5XdijsDWSZeTsqQo94vfXUHEUtCrpBJakzHc2PspVSjYJJnxW5ieEzZmA55x1JFQ2566ezqjJxaZUCCSNtSSGbq74mUhsZMQt92hhRHZtGbiv95nQSDq14qVJwgV2y+KEgkwYhMIyADoTlDObGEMi3srYSNqA0CbVBFG4K3+PIyaVYrnlvxbs/LtYs8jgIcwwmcgQeXUIMbqEMDGGh4hld4c56cF+fd+Zi3rjj5zBH8gfP5A6Y4ko4=</latexit>
0
<latexit sha1_base64="EP1u5569Uf07N9VDVEgVYyKO59E=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGtn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv1Wh5HEc7gHC7Bgxuowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AdX2MqA==</latexit>
<latexit
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
• De converter bestaat uit twee choppers, Q1 en Q2.
• Gedurende interval 0-T0/2 is Q1 actief en gedurende interval T0/2-T0 Q2
• De spanning over de belasting is Vs/2 als Q1 actief is en -Vs/2 als Q2
actief is
• Het mag niet voorkomen dat Q1 en Q2 tegelijk actief zijn
• Een ‘three wire’ DC bron is nodig.
• Voor puur ohmse belastingen is ✓ = 0
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
t
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
Single-phase half-bridge inverter
• De uitgangsspanning van de inverter is een periodieke functie in de vorm
1
<latexit sha1_base64="GD+BzTI5o3Ut58gG0xZaCu5SX9Q=">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</latexit>
a0 X
v0 =
+
(an cos (n!t) + bn sin (n!t))
2
n=1
• Omdat de functie oneven is (f(-x)=-f(x)) volgt
1
bn =
⇡
<latexit sha1_base64="ZEIL5Uld7pltUVQ5Uo1BqTQWfBs=">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</latexit>
"Z
0
⇡
2
Vs
sin (n!t) d(!t) +
2
Z
⇡
2
0
Vs
2V s
sin (n!t) d(!t) =
2
n⇡
• Waarmee volgt dat
1
X
2Vs
v0 =
sin n!t
n⇡
n=1,3,5,...
<latexit sha1_base64="9z9Xq1kBG//0FkmwfNKzsXomyJ8=">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</latexit>
#
= 0 voor n = 2, 4, ...
Single-phase half-bridge inverter
1
X
• Met
2Vs
v0 =
sin n!t
n⇡
n=1,3,5,...
= 0 voor n = 2, 4, ...
<latexit sha1_base64="9z9Xq1kBG//0FkmwfNKzsXomyJ8=">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</latexit>
• Volgt dat de fundamentele harmonische gelijk is aan
Vo1
<latexit sha1_base64="+WTkyiPI6IEjAYxLo5YgmYcgUDc=">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</latexit>
i0 =
1
X
2Vs
p
=
= 0.45Vs
2⇡
n=1,3,5,...
<latexit sha1_base64="VPCfVmD8od7mRIhPHaMUNXM+3ts=">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</latexit>
n⇡
q
2Vs
R2 + (n!L)
2
sin(n!t
✓n )
Single-phase half-bridge inverter met inductieve
belasting
i1
+
<latexit sha1_base64="0xCs/SAA7evdDz/bmVd1ruQdJK4=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKqMeCF48V7Ae0oWy2m3bpZhN3J4US+ju8eFDEqz/Gm//GbZuDtj4YeLw3w8y8IJHCoOt+O4WNza3tneJuaW//4PCofHzSMnGqGW+yWMa6E1DDpVC8iQIl7ySa0yiQvB2M7+Z+e8K1EbF6xGnC/YgOlQgFo2glvxdqyrJW38yy2qxfrrhVdwGyTrycVCBHo1/+6g1ilkZcIZPUmK7nJuhnVKNgks9KvdTwhLIxHfKupYpG3PjZ4ugZubDKgISxtqWQLNTfExmNjJlGge2MKI7MqjcX//O6KYa3fiZUkiJXbLkoTCXBmMwTIAOhOUM5tYQyLeythI2ozQFtTiUbgrf68jpp1aqeW/Uerir16zyOIpzBOVyCBzdQh3toQBMYPMEzvMKbM3FenHfnY9lacPKZU/gD5/MH/86SMg==</latexit>
Vs
2
Q1
C1
D1
Vs
2
0
<latexit sha1_base64="EP1u5569Uf07N9VDVEgVYyKO59E=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q7KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGtn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv1Wh5HEc7gHC7Bgxuowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8AdX2MqA==</latexit>
<latexit
L
Vs
+
Vs
2
0
R
Fundamental current io1
<latexit sha1_base64="6DpZglibkrPb8bx68MebDoym5Tg=">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</latexit>
<latexit sha1_base64="rP5BOiehBYoBjcm6VsM56MuE4lw=">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</latexit>
✓
<latexit sha1_base64="XvwFxXapCS/be2ilCx192L3/p8I=">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</latexit>
<latexit
a
i2
io (t)
C2
va0
Q2
<latexit sha1_base64="fxWLHdy4k1f4Vu4VU5FJVEg6FUU=">AAAB9XicbVBNS8NAEJ34WetX1aOXxSJ4sSRF1GPBi8cK9gPaWjbbSbt0swm7G6WE/A8vHhTx6n/x5r9x2+agrQ8GHu/NMDPPjwXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY1FGiGDZYJCLV9qlGwSU2DDcC27FCGvoCW/74Zuq3HlFpHsl7M4mxF9Kh5AFn1Fjp4bwbKMrSZl9naTXrl8puxZ2BLBMvJ2XIUe+XvrqDiCUhSsME1brjubHppVQZzgRmxW6iMaZsTIfYsVTSEHUvnV2dkVOrDEgQKVvSkJn6eyKlodaT0LedITUjvehNxf+8TmKC617KZZwYlGy+KEgEMRGZRkAGXCEzYmIJZYrbWwkbUZuDsUEVbQje4svLpFmteG7Fu7so1y7zOApwDCdwBh5cQQ1uoQ4NYKDgGV7hzXlyXpx352PeuuLkM0fwB87nD2tWkmk=</latexit>
Vs
2
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
t
T0
2
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
T0
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
D2
• Voor inductieve belastingen ( R ⇡ 0 )
• Een inductieve belasting heeft een hoge impedantie bij een snelle verandering
van de spanning.
• De feedback dioden zullen de uitgangsstroom terugvoeren naar de DC bron
• Als Q2 net gesloten is op t=0 zal D1 in geleiding gaan totdat i0 = 0 Waarna
Q1 zal gaan geleiden en de stroom positief wordt (van DC bron naar last)
• Als Q1 net gesloten is op t=T/2 zal D2 in geleiding gaan totdat i0 = 0 waarna
Q2 zal gaan geleiden en de stroom negatief wordt (van DC bron naar last)
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Single-phase half-bridge inverter
• Voor een algemene RL belasting kan de uitgangsstroom gevonden worden
door de uitgangsspanning te delen door de impedantie Z = R + j!L
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• Het volgt dat
i0 =
1
X
n=1,3,5,...
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• Met ✓n = arctan n!L/R
n⇡
q
2Vs
R2 + (n!L)
2
sin(n!t
✓n )
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• Het in de belasting gedissoneerde vermogen voor de fundamentele
harmonische is
2
Po1 = Vo1 Io1 cos ✓1 = Io1
R
"
#2
2Vs
= p p
R
2
2
2⇡ R + (!L)
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Single-phase half-bridge inverter : ingangsstroom
• De ingangsstroom geleverd door de DC bron kan worden bepaald door het
gemiddelde vermogen dat wordt geleverd door de bron met het gemiddelde
vermogen geleverd door de bron (de verliezen worden verwaarloosd)
Z
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T
vs (t)is (t)dt =
0
Z
T
v0 (t)i0 (t)dt
0
• Bij een hoge schakelfrequentie is de uitgangsstoom bijna sinusvormig zodat
Z
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T
0
1
is (t)dt =
Vs
Z
T
p
p
2Vo1 sin(!t) 2Io sin(!t
0
• Waarna volgt
Vo1
Is =
Io cos(✓1 )
Vs
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✓1 )dt = T Is
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
R = 2.4 ⌦
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Vs = 48 V
Vs
2
Q1
C1
R
Vs
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i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
+
0
io (t)
• Bereken:
Vs
Q2
C2
• De RMS uitgangsspanning bij de
2
fundamentele frequentie Vo1
• Het uitgangsvermogen Po
• De gemiddelde stroom door de transistoren
• De piekstroom door de transistoren
• De peak reverse blocking spanning van elke transistor VBR
• De gemiddelde ingangsstroom Is
• De total harmonic distortion T HD
• De distortion factor DF
• De harmonic factor HF
• De lowest order harmonic LOH
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D1
a
i2
D2
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">AAAFIHichVTLbtNAFHVJgFJeLSzZWLSVUlH8GDt1NkYFqipISH2oTStlEmvijBOrfgTPGBFZ/hQ2/AobFiAEO/garuNpSd0KRkpyc86Ze8+9Y89gEviMa9qvhRu1+s1btxfvLN29d//Bw+WVRx0Wp4lLj904iJPTAWE08CN6zH0e0NNJQkk4COjJ4Ox1wZ+8pwnz4+iITye0F5JR5Hu+SzhAzkptax13Ow6zzRbm9APP5E6Oe0u4e2gjxRTQGt4L6YisFcxMnsV6bmuK2cTcDykzWzbSla35BEKW25BbRZAdvpBZUew7MfBxH6lQzYQfKAmBJmQnQvbGmQA6I/Vz7uUFdwBGhA9ds5sVHky8OsxRySOz0uYsAbPBh1rMAEqr0Ms1Oc77BdU5NrYxe5fwDLM0dLLINjabm9amoih5H/uRx6dysS/K+ygXyo6j9dHzMluBagrSrerUjto7dqNkoNiG2hBlN8C6YogJ4nWh/o8FHFCPN7CXEDcr3eRZBKVx4o/GfOOvtarQAKExL3xWVTRB0fynwgKFdVnhDmPOisY1ZF6Mcmf3ApjrtqkYLVTptnRmlxNUjRJs7zqGXTIqnGKmwVHpqmEbhmIYlQQ7hbb0KXZAk8KfKo5ZV5FlG4qlVWf9dq8t6sB/Z3kVTM+WfDXQRbAqibXvLP/Ew9hNQxpxNyCMdXVtwnsZSbjvBjRfwimjE+KekRHtQhgReF572ewFz+V1QIayFyfwibg8Q+d3ZCRkbBoOQBkSPmZVrgCv47op91q9zI8mKaeRWxby0kDmsVzcFvLQT6jLgykExE188Cq7YwInzOFOKYagV1u+GnSQomuKfoBWt1+IcSxKT6SnUkPSJUvaltrSvnQsubWPtc+1r7Vv9U/1L/Xv9R+l9MaC2PNYurTqv/8AiXGanA==</latexit>
i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs
2
C1
Q1
R
Vs = 48 V
Vs
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• Bereken:
• De RMS uitgangsspanning bij de
fundamentele frequentie Vo1
• Het uitgangsvermogen Po
+
0
C2
a
i2
io (t)
Vs
2
D1
Q2
D2
<latexit sha1_base64="STXvgDZGW/I5vwOAx605N/gWz5w=">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</latexit>
<latexit sha1_base64="bKSl30W5oxDbqoxHXKjOF/qJQoI=">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</latexit>
• Antwoord
• Uit de formule Vo1 = 0.45Vs volgt Vo1 = 0.45 ⇥ 48 = 21.6 V
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<latexit sha1_base64="gZIaSgWRUoYlW0KJo6uvhwGHxAQ=">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</latexit>
• Het uitgangsvermogen kan worden bepaald uit Vo = Vs /2 = 48/2 = 24 V
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Po = Vo2 /R = 242 /2.4 = 240 W
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en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
R = 2.4 ⌦
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i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs
2
C1
Q1
R
Vs = 48 V
Vs
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De gemiddelde en de piekstroom
door de transistoren
+
0
Vs
2
a
i2
io (t)
C2
D1
Q2
D2
• Antwoord
• De piekstroom door de transistor is Ip = 24/2.4 = 10 A
<latexit sha1_base64="KV1ycnlQAVUycDCwvT90NGPfhOA=">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</latexit>
• De gemiddelde stroom bij een 50% duty cycle is
IQ = 0.5 ⇥ 10 = 5 A
<latexit sha1_base64="xlBgpj8BgvzmgbNWybdtppHC4FU=">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</latexit>
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
Vs = 48 V
Vs
2
• Bereken:
• De peak reverse blocking
spanning van elke transistor VBR
• De gemiddelde ingangsstroom Is
Q1
C1
R
Vs
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
+
Vs
2
0
Q2
C2
<latexit sha1_base64="gfXaU9T+0mIcKAJvoeDenjX4gZs=">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</latexit>
<latexit sha1_base64="wPaHJFBrIlZBPRO4HmVr7ej+Q/Q=">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</latexit>
• Antwoord
• De peak reverse blocking spanning van elke transistor is
VBR = 2 ⇥ 24 = 48 V
<latexit sha1_base64="k30afkl4yXGFz71RkgrOXbsuMGQ=">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</latexit>
• De gemiddelde ingangsstroom kan worden bepaald met Is
<latexit sha1_base64="wPaHJFBrIlZBPRO4HmVr7ej+Q/Q=">AAAFSnichVTLbtNAFHVJCqW8WliysWgrpaL4MXZINkYFqiqVkPpQ61bKJGbiTBKrfuGZICLL38eGFTs+gg0LEGLDdTxNU7cCS0luzjkz99wz1vRi32Nc074t3KpUF2/fWbq7fO/+g4ePVlYf2ywaJy49cSM/Ss56hFHfC+kJ97hPz+KEkqDn09Pe+ducP/1IE+ZF4TGfxLQTkGHoDTyXcICc1cr7Ddy2HWaZTczpJ57KdoY7ywAeWUgxBbaO9wM6JOuCsp000kV94EQz8M1RDuL2nsPmhZammHXMvYAys2khXXlZapXLMgtcqAh8wBcySwroAnzURSrYMuEHvEGhCdmpkO05MaBTUr/gXs+4QzAifOiaVS/xhX9U8Mi8HghMZYEPNU8LWqswyw17XMxrX2YwsjD7kPAUs3HgpKFlbNW3GluKomRd7IUDPpHzdWHWRZlQ2o7WRS+K3XJUU5DeKKd23NqxagUDzTbVmmi7CdYVQySIN4T6PxawTwe8hgcJcdPCTZaG0Bon3nDENy+tlYUGCI154fOyog6K+j8VDVA0rircfsRZPriGzFmUO7szYG7aumI0UWnawplVJKgaBdjadQyrYFQ4xVSDo9JVwzIMxTBKG+zk2sKnWAFDCn+qOGZdRQ3LUBpaOet3+y3RB/47K2tgevrI1wtdFGuSeA6cla+4H7njgIbc9QljbV2LeSclCfdcn2bLeMxoTNxzMqRtKEMC72snnV4FmbwBSF8eRAl8Qi5P0fkVKQkYmwQ9UAaEj1iZy8GbuPaYD5qd1AvjMaehWzQajH2ZR3J+r8h9L6Eu9ydQEDfxwKvsjgicMIfbJw9BL498vbCRomuKfojWtl+JOJakp9IzqSbpUkPallrSgXQiuZXPle+Vn5Vf1S/VH9Xf1T+F9NaCWPNEuvIsVv8CBQ2ohA==</latexit>
<latexit sha1_base64="h4r3Qhe5autirZav6WLxTQW04Ck=">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</latexit>
a
i2
io (t)
Is = Po /Vs = 240/48 = 5 A
D1
D2
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
Vs = 48 V
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs
2
C1
Q1
R
Vs
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De total harmonic distortion T HD
+
Vs
2
<latexit sha1_base64="i1L+c169oaOQsgodHivOuDxUFg8=">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</latexit>
0
a
i2
io (t)
C2
D1
Q2
• Antwoord
• De RMS waarde van de som van de harmonischen 3,5,7,… kan is
v
u
u
Vh = t
<latexit sha1_base64="iTa295jxakZa63zd3t/5pwsnl0Y=">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</latexit>
1
X
2 =
Von
n=3,5,7,...
q
V02
2 = 0.2176 V
Vo1
• De total harmonic distortion T HD daarna kan berekend worden met
<latexit sha1_base64="i1L+c169oaOQsgodHivOuDxUFg8=">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</latexit>
<latexit sha1_base64="kJrwgDxliuREAU7auuqEt5mt7N8=">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</latexit>
T HD = (0.2176Vs )/(0.45Vs ) = 48.34%
D2
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
Vs = 48 V
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De distortion factor DF
<latexit sha1_base64="szA/gXdLGyfEdYMEy8jx2slWtss=">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</latexit>
i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs
2
C1
Q1
R
Vs
+
0
C2
a
i2
io (t)
Vs
2
D1
Q2
D2
• Antwoord
• De distortion factor kan worden bepaald met
v
u X
✓
◆2 s✓
◆2 ✓
◆2 ✓
◆2
1
u
V
V
V
V
on
o3
o5
o7
t
=
+
+
+ · · · = 0.024Vs
2
2
2
2
n
3
5
7
n=3,5,7,...
<latexit sha1_base64="MNrHuVEIbtWx4PSoeNKZvMUE4wM=">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</latexit>
• Waarna volgt
DF = 0.024Vs /(0.45Vs ) = 5.382%
<latexit sha1_base64="SJXLDG1WuN6Zf3rXpMcNLkN9uh4=">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</latexit>
en
am
nt
Te
Parameters van de
Single-Phase Half-Bridge Inverter
R = 2.4 ⌦
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i1
+
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs
2
C1
R
Vs = 48 V
Vs
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• Bereken:
• De harmonic factor HF
• De lowest order harmonic LOH
+
0
Vs
2
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• Antwoord
• De LOH is de derde harmonische Vo3 = Vo1 /3
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HF3 = Vo3 /V01 = 1/3 = 33.33%
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• De distortion factor van de derde harmonische is
DF3 = Vo3 /32 /Vo1 = 1/27 = 3.704%
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Q1
a
i2
io (t)
C2
D1
Q2
D2
Volgende week:
• Single-phase full-bridge inverter
• Three-phase inverters
• Spanningsregelingen voor inverters
i1
+
Vs
2
Vs
+
Vs
2
C1
Q1
i3
a
0
Q3
D1
L
R
i4
C2
Q4
D4
Q2
D3
io (t) b
i2
D2
Vermogenselektronica 2
Jan van Hulzen
September 2018 version 1.0
Inverters
2
Lesprogramma
Lesweek week dag
datum
1
36 wo 05/09/2018
2
37 wo 12/09/2018
3
38 wo 19/09/2018
4
39 wo 26/09/2018
5
40 wo 03/10/2018
6
41 wo 10/10/2018
7
42 wo 10/10/2018
van
11:00
15:00
11:00
15:00
15:00
15:00
15:00
• NB Lokaal moet nog worden aangepast
tot
12:30
16:30
12:30
16:30
16:30
16:30
16:30
duur
01:30
01:30
01:30
01:30
01:30
01:30
01:30
lokaal
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
Programma van vandaag
• Introductie
• Literatuur
• Single-phase Full-bridge inverters
• Karakteriseren van prestaties van inverters
• Single-phase half-bridge inverters ohmse belasting
• Single-phase half-bridge inverters met RLC load
• Voorbeeld opgave inverters
Aanbevolen Literatuur (niet verplicht)
• Deze presentatie is gebaseerd op
Hoofdstuk 6 van het boek;
• Power Electronics: Circuits, Devices &
Applications (4th Edition) 4th Edition
• Muhammad H. Rashid
• ISBN-13: 978-0133125900
• ISBN-10: 0133125904
DEEL 5
De single-phase Full-bridge inverter
Single-phase full-bridge inverter
i1
+
Vs
2
Q1
C1
L
Vs
+
Vs
2
0
R
i2
io (t)
C2
Q2
Vs
2
D1
a
D2
i1
+
Vs
+
Vs
2
C1
Q1
i3
a
0
Q3
D1
L
R
i4
C2
Q4
D4
• De full bridge inverter gebruikt vier choppers in plaats van twee
•
Q2
D3
io (t) b
i2
D2
Single-phase full-bridge inverter
i1
+
Vs
2
Vs
+
Vs
2
•
•
•
•
C1
Q1
i3
Q3
D1
a
0
R
i4
C2
Q4
Q2
D4
Als Q1 en Q2 aangestuurd worden volgt Vab = Vs
Als Q3 en Q4 aangestuurd worden volgt Vab = Vs
Voor een zuiver ohmse belasting zijn er drie states
Voor RL belasting zijn er vijf states
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<latexit sha1_base64="TjE6WGGVFiJCRjuJkUbR3Q25bM0=">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</latexit>
D3
io (t) b
i2
D2
Schakel schema
Single-phase full-bridge inverter : RL belasting
i1
+
Vs
2
Vs
+
C1
Q1
i3
Q3
D1
L
a
0
i4
R
VS /2
D3
io (t) b
i2
<latexit sha1_base64="KYV0hwgWMfCIgTypYhHopto+gC8=">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</latexit>
Vs
2
C2
Q4
D4
<latexit sha1_base64="tTU06wC+M7DShZAgZmkj6SXAtew=">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</latexit>
VS /2
• Transistoren S1 , S2 worden aangestuurd, S4 , S3 zijn uit
• Transistoren S1 , S2 zijn in geleiding
• De uitgangsspanning tussen a en b is Vo = Vs
<latexit sha1_base64="0urybl1Dcy90+U6DKs8hve+crWE=">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</latexit>
<latexit sha1_base64="h/c8M0RBmYu6/SvhO4z6VQxUA4E=">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</latexit>
<latexit sha1_base64="0urybl1Dcy90+U6DKs8hve+crWE=">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</latexit>
<latexit sha1_base64="SvQx4xCDW8wnQrS+DClt0J/0LbE=">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</latexit>
Q2
D2
Single-phase full-bridge inverter : RL belasting
i1
+
Vs
2
Vs
+
C1
Q1
i3
Q3
D1
L
a
0
i4
VS /2
<latexit sha1_base64="tTU06wC+M7DShZAgZmkj6SXAtew=">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</latexit>
Vs
2
C2
Q4
D4
VS /2
<latexit sha1_base64="KYV0hwgWMfCIgTypYhHopto+gC8=">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</latexit>
• Transistoren S1 , S2 worden aangestuurd, S4 , S3 zijn uit
• Dioden D1 , D2 zijn in geleiding
• De uitgangsspanning tussen a en b is Vo = Vs
<latexit sha1_base64="0urybl1Dcy90+U6DKs8hve+crWE=">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</latexit>
<latexit sha1_base64="h/c8M0RBmYu6/SvhO4z6VQxUA4E=">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</latexit>
<latexit sha1_base64="IvJXD/4rW1/mQGxG5g/bMkmshS4=">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</latexit>
<latexit sha1_base64="RIWUraeLtra9zY8zB3ZiMYnLBYg=">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</latexit>
R
Q2
D3
io (t) b
i2
D2
Single-phase full-bridge inverter : RL belasting
i1
+
Vs
2
Vs
+
Q1
C1
0
<latexit sha1_base64="tTU06wC+M7DShZAgZmkj6SXAtew=">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</latexit>
VS /2
VS /2
i3
Q3
D1
L
a
R
i4
D3
io (t) b
i2
<latexit sha1_base64="KYV0hwgWMfCIgTypYhHopto+gC8=">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</latexit>
Vs
2
C2
Q4
Q2
D4
• Transistoren S3 , S4 worden aangestuurd, S1 , S2 zijn uit
• Transistoren S3 , S4 zijn in geleiding
• De uitgangsspanning tussen a en b is Vo = Vs
<latexit sha1_base64="JCfJS1hAPWpuzPVAjjcuGXEL4mc=">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</latexit>
<latexit sha1_base64="0urybl1Dcy90+U6DKs8hve+crWE=">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</latexit>
<latexit sha1_base64="JCfJS1hAPWpuzPVAjjcuGXEL4mc=">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</latexit>
<latexit sha1_base64="RIWUraeLtra9zY8zB3ZiMYnLBYg=">AAAFenichVTbbtNAEHVpAqXcWnhESFYvkKipL2uH5GVRgaoKElLvbqU4sTbOJrHqS/BuEJHlf+DbeONLeOGBcbwNqVvBSnHGZ854zpldbW/se4xr2s+le8ul8v0HKw9XHz1+8vTZ2vpzi0WT2KXnbuRH8WWPMOp7IT3nHvfp5TimJOj59KJ39THLX3ylMfOi8IxPx7QTkGHoDTyXcICc9eXv23bbchg2mzan33giW6ndWQXwBCPFFNiWfRjQIdkSKctJIl3ER040Bz+cCPCTw/Lg82FrsQRrilm3uRdQZjYx0pW3haYZLcWgR0WgCB7ILDCgH+SjLlJBoAl/oBICTdAu5grGgM6S+nXu/Tx3DEKEDl3D9UI+d4JRTkDm7dmAPwxC1Gxw0FsFM3d85NqwdT0Nyxlhm32JeWKzSeAkITZq9VqjpihK2rW9cMCnclYXpl2UCqblaF20m38tQzUF6Y3i2M5a+7iSZ6BZVa2ItlWQrhhihPa2YP9Hgu3TAa/Yg5i4Sa4mTUJobcfecMSrf6UViQYQjUXiTpFRB0b9n4wGMBo3GW4/4iwzriFzPsr9gzmw4LauGE1UcJsrw/kEVSMHWweOgfMMbGKiwU7pqoENQzGMQv1+Rs1ligLwKOSpYpd1FTWwoTS04qjh/Is2+fupY9ZOHSECdvVURRBnIiO8m5tz1jbB2WzJtwNdBJuSWEfO2g+7H7mTgIbc9QljbV0b805CYu65Pk1X7QmjY+JekSFtQxgSONSdZHZ1pPI2IH15EMXwC7k8QxcrEhIwNg16wAwIH7FiLgPvyrUnfNDsJF44nnAaunmjwcSXeSRn95Dc92Lqcn8KAXFjD7TK7ojAMeBwW2VD0IuWbwcWUnRN0Y/R5t47MY4V6aW0IVUkXWpIe1JLOpLOJXf5V+lV6XXpTel3eaNcLe/k1HtLouaFdGOVzT90dLIa</latexit>
D2
Single-phase full-bridge inverter : RL belasting
i1
+
Vs
2
Vs
+
Q1
C1
0
Q3
D1
L
a
R
<latexit sha1_base64="KYV0hwgWMfCIgTypYhHopto+gC8=">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</latexit>
<latexit sha1_base64="tTU06wC+M7DShZAgZmkj6SXAtew=">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</latexit>
Vs
2
VS /2
VS /2
i3
C2
Q4
i4
Q2
D4
• Transistoren S4 , S3 worden aangestuurd, S1 , S2 zijn uit
• Dioden D3 , D4 zijn in geleiding
• De uitgangsspanning tussen a en b is Vo = Vs
<latexit sha1_base64="h/c8M0RBmYu6/SvhO4z6VQxUA4E=">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</latexit>
<latexit sha1_base64="0urybl1Dcy90+U6DKs8hve+crWE=">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</latexit>
<latexit sha1_base64="p9XG0Pos8onbng2FxtLc4IRnlzc=">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</latexit>
<latexit sha1_base64="RIWUraeLtra9zY8zB3ZiMYnLBYg=">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</latexit>
D3
io (t) b
i2
D2
Single-phase full-bridge inverter: output golfvorm
• De RMS uitgangsspanning is
Vo =
s
2
T0
Z
Vs
2
Vs
T0 /2
0
Vs2 dt = Vs
+
C1
<latexit sha1_base64="eO69UFidCMkLcT4BHir8uuDbeSY=">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</latexit>
Vs
2
Q1
a
C2
Q4
Vo1
4Vs
=p
= 0.9Vs
2⇡
D4
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
<latexit sha1_base64="KuIBDCDkYiI7u8SXZ/rKA31vIdk=">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</latexit>
T0
2
io (t) b
i2
Q2
D2
<latexit sha1_base64="wP5zns9mbbKW1pvDO4O4i5xyFgo=">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</latexit>
<latexit
Vab
T0
t
T0
t
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
0
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
T0
2
<latexit sha1_base64="VVrkTN5LLl5vpDiRK7ZomSMN+L8=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqseCF48V+wVtKJvtpF262YTdjVBCf4IXD4p49Rd589+4bXPQ1gcDj/dmmJkXJIJr47rfTmFjc2t7p7hb2ts/ODwqH5+0dZwqhi0Wi1h1A6pRcIktw43AbqKQRoHATjC5m/udJ1Sax7Jppgn6ER1JHnJGjZUemwN3UK64VXcBsk68nFQgR2NQ/uoPY5ZGKA0TVOue5ybGz6gynAmclfqpxoSyCR1hz1JJI9R+tjh1Ri6sMiRhrGxJQxbq74mMRlpPo8B2RtSM9ao3F//zeqkJb/2MyyQ1KNlyUZgKYmIy/5sMuUJmxNQSyhS3txI2pooyY9Mp2RC81ZfXSfuq6rlV7+G6Uq/lcRThDM7hEjy4gTrcQwNawGAEz/AKb45wXpx352PZWnDymVP4A+fzB8+pjW8=</latexit>
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
Fundamental current io1
<latexit sha1_base64="GWhvAsyye2eB2/LDg7aSozqIrJk=">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</latexit>
• De fundamentele component is
R
<latexit sha1_base64="Er5pBdQ+aYg5lDJcxaNkZ2CNu1I=">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</latexit>
Vb0
<latexit sha1_base64="HhmnRRZRg1EPpmoJJg8lm/fG/CM=">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</latexit>
L
D3
Va0
0
Vs
2
Q3
i4
<latexit sha1_base64="wP5zns9mbbKW1pvDO4O4i5xyFgo=">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</latexit>
<latexit
4Vs
vo =
sin n!t
n⇡
n=1,3,5,...
i3
D1
0
Vs
2
• De Fourier reeks van de
uitgangsspanning is
1
X
i1
+
Vs
<latexit sha1_base64="hvqiqcZukJriCFk9MscUY02Xt/M=">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</latexit>
0
<latexit sha1_base64="wP5zns9mbbKW1pvDO4O4i5xyFgo=">AAAFgHichVTbbtNAEHXbBEq4tfDIi0VaKR
<latexit
sha1_base64="wP5zns9mbbKW1pvDO4O4i5xyFgo=">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</latexit>
✓0
<latexit sha1_base64="c80HU7Cb+pOUJa0lptfD9PA9K9Q=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KkkR9Vjw4rFCv6ANZbPdtEs3m7g7KZTQ3+HFgyJe/THe/Ddu2xy09cHA470ZZuYFiRQGXffb2djc2t7ZLewV9w8Oj45LJ6ctE6ea8SaLZaw7ATVcCsWbKFDyTqI5jQLJ28H4fu63J1wbEasGThPuR3SoRCgYRSv5vVBTljX67iyrzvqlsltxFyDrxMtJGXLU+6Wv3iBmacQVMkmN6Xpugn5GNQom+azYSw1PKBvTIe9aqmjEjZ8tjp6RS6sMSBhrWwrJQv09kdHImGkU2M6I4sisenPxP6+bYnjnZ0IlKXLFlovCVBKMyTwBMhCaM5RTSyjTwt5K2IjaHNDmVLQheKsvr5NWteK5Fe/xuly7yeMowDlcwBV4cAs1eIA6NIHBEzzDK7w5E+fFeXc+lq0bTj5zBn/gfP4AliKR7Q==</latexit>
T0
2
T0
t
<latexit sha1_base64="jiys47PY+g806Z8/lmrepZFZhP8=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUREPRa8eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBtMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5ep1HkcBTuEMLsCHG6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDcjYzs</latexit>
<latexit
Single-phase full-bridge inverter: output golfvorm
• De uitgangsspanning van de inverter is een periodieke functie in de vorm
1
<latexit sha1_base64="GD+BzTI5o3Ut58gG0xZaCu5SX9Q=">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</latexit>
a0 X
v0 =
+
(an cos (n!t) + bn sin (n!t))
2
n=1
• Omdat de functie oneven is (f(-x)=-f(x)) volgt
1
bn =
⇡
<latexit sha1_base64="8btXJBpm3hyZq6NlGURetaG9Ynw=">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</latexit>
"Z
0
⇡
2
Vs sin (n!t) d(!t) +
Z
⇡
2
0
4V s
Vs sin (n!t) d(!t) =
n⇡
• Waarmee volgt dat
1
X
4Vs
v0 =
sin n!t
n⇡
n=1,3,5,...
<latexit sha1_base64="XDjqF0iOlfbp07e84dBSb3yitCM=">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</latexit>
#
= 0 voor n = 2, 4, ...
Single-phase full-bridge inverter: output golfvorm
• De uitgangsspanning is
1
X
4Vs
v0 =
sin n!t
n⇡
n=1,3,5,...
<latexit sha1_base64="XDjqF0iOlfbp07e84dBSb3yitCM=">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</latexit>
= 0 voor n = 2, 4, ...
• In het geval van een algemene belasting (RL) volgt dat de uitgangsstroom is
i0 =
<latexit sha1_base64="nYoqGMy7RCSCN71DX0SsWEbXt2M=">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</latexit>
• Met
1
X
n=1,3,5,...
n⇡
p
4Vs
R2
✓n = arctan(n!L/R)
<latexit sha1_base64="Z9AF+SD7B8mcAQ9st2CfQshVNgw=">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</latexit>
+
(n!L)2
sin(n!t
✓n )
Ingangsstroom DC bron
• Zonder verliezen wordt de (instantane) vermogensbalans gegeven door
vs (t)is (t) = v0 (t)i0 (t)
<latexit sha1_base64="lpYcJIEwDUa+TyaQehAYiBJLB6w=">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</latexit>
• Voor inductieve belastingen en relatief hoge schakelfrequenties kan de
uitgangsspanning en stroom sinusvormig zijn
p
1p
is (t) =
2V01 sin(n!t) 2Io sin(!t
Vs
✓1 )
<latexit sha1_base64="QHvgJng+4UPkcryUrsBsVLyHxSs=">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</latexit>
• Dit kan worden vereenvoudigd tot
Vo1
is (t) =
Io cos(✓1 )
Vs
Vo1
Io cos(2!t ✓1 )
Vs
• Hierin is Vo1 de fundamentele rms spanning en Io de rms stroom. ✓1 is de
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impedantiehoek bij de fundamentele frequentie
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en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
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Vs = 48 V
Vs
2
Vs
+
Vs
2
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i1
+
C1
Q1
i3
D1
a
0
C2
Q4
D4
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R
i4
• Bereken:
• De RMS uitgangsspanning bij de
fundamentele frequentie Vo1
• Het uitgangsvermogen Po
• De gemiddelde stroom door de transistoren
• De piekstroom door de transistoren
• De peak reverse blocking spanning van elke transistor VBR
• De gemiddelde ingangsstroom Is
• De total harmonic distortion T HD
• De distortion factor DF
• De harmonic factor HF
• De lowest order harmonic LOH
<latexit sha1_base64="wPaHJFBrIlZBPRO4HmVr7ej+Q/Q=">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</latexit>
Q3
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
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i1
+
Vs
2
Vs
Vs = 48 V
+
Vs
2
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• Bereken:
• De RMS uitgangsspanning bij de
fundamentele frequentie Vo1
• Het uitgangsvermogen Po
C1
Q1
i3
D1
a
0
Q3
R
i4
C2
Q4
D4
Q2
<latexit sha1_base64="STXvgDZGW/I5vwOAx605N/gWz5w=">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</latexit>
<latexit sha1_base64="bKSl30W5oxDbqoxHXKjOF/qJQoI=">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</latexit>
• Antwoord
• Uit de formule Vo1 = 0.9Vs volgt
<latexit sha1_base64="+JXSkvsucHyRfBnRwZ1onUxSNho=">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</latexit>
Vo1 = 0.9 ⇥ 48 = 43.2 V
<latexit sha1_base64="w1mlR/Hkf5clTgZz7COZIRpB8zs=">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</latexit>
• Het uitgangsvermogen kan worden bepaald uit Vo = Vs = 48 V
<latexit sha1_base64="+YUXDjAdc8qdUCEgnmGsvpqFdZ8=">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</latexit>
Po = Vs2 /R = 482 /2.4 = 960 W
<latexit sha1_base64="XDKmR2qZG3vALD3mWceFmhPKdtE=">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</latexit>
D3
io (t) b
i2
D2
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
i1
+
Vs
2
Vs
Vs = 48 V
+
Vs
2
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De gemiddelde en de piekstroom
door de transistoren
Q1
C1
i3
D1
a
0
Q3
R
i4
Q4
C2
D4
Q2
D3
io (t) b
i2
D2
• Antwoord
• De piekstroom door de transistor is Ip = 48/2.4 = 20 A
<latexit sha1_base64="DigmhUYpW/O75Cyw85K0YEVN9nU=">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</latexit>
• De gemiddelde stroom bij een 50% duty cycle is IQ = 0.5 ⇥ 20 = 10 A
<latexit sha1_base64="hoQrqeNFysvl0WF/dLiNycBtA/4=">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</latexit>
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">AAAFIHichVTLbtNAFHVJgFJeLSzZWLSVUlH8GDt1NkYFqipISH2oTStlEmvijBOrfgTPGBFZ/hQ2/AobFiAEO/garuNpSd0KRkpyc86Ze8+9Y89gEviMa9qvhRu1+s1btxfvLN29d//Bw+WVRx0Wp4lLj904iJPTAWE08CN6zH0e0NNJQkk4COjJ4Ox1wZ+8pwnz4+iITye0F5JR5Hu+SzhAzkptax13Ow6zzRbm9APP5E6Oe0u4e2gjxRTQGt4L6YisFcxMnsV6bmuK2cTcDykzWzbSla35BEKW25BbRZAdvpBZUew7MfBxH6lQzYQfKAmBJmQnQvbGmQA6I/Vz7uUFdwBGhA9ds5sVHky8OsxRySOz0uYsAbPBh1rMAEqr0Ms1Oc77BdU5NrYxe5fwDLM0dLLINjabm9amoih5H/uRx6dysS/K+ygXyo6j9dHzMluBagrSrerUjto7dqNkoNiG2hBlN8C6YogJ4nWh/o8FHFCPN7CXEDcr3eRZBKVx4o/GfOOvtarQAKExL3xWVTRB0fynwgKFdVnhDmPOisY1ZF6Mcmf3ApjrtqkYLVTptnRmlxNUjRJs7zqGXTIqnGKmwVHpqmEbhmIYlQQ7hbb0KXZAk8KfKo5ZV5FlG4qlVWf9dq8t6sB/Z3kVTM+WfDXQRbAqibXvLP/Ew9hNQxpxNyCMdXVtwnsZSbjvBjRfwimjE+KekRHtQhgReF572ewFz+V1QIayFyfwibg8Q+d3ZCRkbBoOQBkSPmZVrgCv47op91q9zI8mKaeRWxby0kDmsVzcFvLQT6jLgykExE188Cq7YwInzOFOKYagV1u+GnSQomuKfoBWt1+IcSxKT6SnUkPSJUvaltrSvnQsubWPtc+1r7Vv9U/1L/Xv9R+l9MaC2PNYurTqv/8AiXGanA==</latexit>
Vs = 48 V
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De peak reverse blocking
spanning van elke transistor VBR
• De gemiddelde ingangsstroom Is
i1
+
Vs
2
Vs
+
C1
Q1
D1
a
0
Vs
2
i3
R
i4
C2
Q4
D4
<latexit sha1_base64="gfXaU9T+0mIcKAJvoeDenjX4gZs=">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</latexit>
<latexit sha1_base64="wPaHJFBrIlZBPRO4HmVr7ej+Q/Q=">AAAFSnichVTLbtNAFHVJCqW8WliysWgrpaL4MXZINkYFqiqVkPpQ61bKJGbiTBKrfuGZICLL38eGFTs+gg0LEGLDdTxNU7cCS0luzjkz99wz1vRi32Nc074t3KpUF2/fWbq7fO/+g4ePVlYf2ywaJy49cSM/Ss56hFHfC+kJ97hPz+KEkqDn09Pe+ducP/1IE+ZF4TGfxLQTkGHoDTyXcICc1cr7Ddy2HWaZTczpJ57KdoY7ywAeWUgxBbaO9wM6JOuCsp000kV94EQz8M1RDuL2nsPmhZammHXMvYAys2khXXlZapXLMgtcqAh8wBcySwroAnzURSrYMuEHvEGhCdmpkO05MaBTUr/gXs+4QzAifOiaVS/xhX9U8Mi8HghMZYEPNU8LWqswyw17XMxrX2YwsjD7kPAUs3HgpKFlbNW3GluKomRd7IUDPpHzdWHWRZlQ2o7WRS+K3XJUU5DeKKd23NqxagUDzTbVmmi7CdYVQySIN4T6PxawTwe8hgcJcdPCTZaG0Bon3nDENy+tlYUGCI154fOyog6K+j8VDVA0rircfsRZPriGzFmUO7szYG7aumI0UWnawplVJKgaBdjadQyrYFQ4xVSDo9JVwzIMxTBKG+zk2sKnWAFDCn+qOGZdRQ3LUBpaOet3+y3RB/47K2tgevrI1wtdFGuSeA6cla+4H7njgIbc9QljbV2LeSclCfdcn2bLeMxoTNxzMqRtKEMC72snnV4FmbwBSF8eRAl8Qi5P0fkVKQkYmwQ9UAaEj1iZy8GbuPaYD5qd1AvjMaehWzQajH2ZR3J+r8h9L6Eu9ydQEDfxwKvsjgicMIfbJw9BL498vbCRomuKfojWtl+JOJakp9IzqSbpUkPallrSgXQiuZXPle+Vn5Vf1S/VH9Xf1T+F9NaCWPNEuvIsVv8CBQ2ohA==</latexit>
• Antwoord
• De peak reverse blocking spanning van elke transistor is
VBR = 48 V
<latexit sha1_base64="mvJZAEsSLG3YsbezSix+KM75eJM=">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</latexit>
• De gemiddelde ingangsstroom kan worden bepaald met Is
<latexit sha1_base64="wPaHJFBrIlZBPRO4HmVr7ej+Q/Q=">AAAFSnichVTLbtNAFHVJCqW8WliysWgrpaL4MXZINkYFqiqVkPpQ61bKJGbiTBKrfuGZICLL38eGFTs+gg0LEGLDdTxNU7cCS0luzjkz99wz1vRi32Nc074t3KpUF2/fWbq7fO/+g4ePVlYf2ywaJy49cSM/Ss56hFHfC+kJ97hPz+KEkqDn09Pe+ducP/1IE+ZF4TGfxLQTkGHoDTyXcICc1cr7Ddy2HWaZTczpJ57KdoY7ywAeWUgxBbaO9wM6JOuCsp000kV94EQz8M1RDuL2nsPmhZammHXMvYAys2khXXlZapXLMgtcqAh8wBcySwroAnzURSrYMuEHvEGhCdmpkO05MaBTUr/gXs+4QzAifOiaVS/xhX9U8Mi8HghMZYEPNU8LWqswyw17XMxrX2YwsjD7kPAUs3HgpKFlbNW3GluKomRd7IUDPpHzdWHWRZlQ2o7WRS+K3XJUU5DeKKd23NqxagUDzTbVmmi7CdYVQySIN4T6PxawTwe8hgcJcdPCTZaG0Bon3nDENy+tlYUGCI154fOyog6K+j8VDVA0rircfsRZPriGzFmUO7szYG7aumI0UWnawplVJKgaBdjadQyrYFQ4xVSDo9JVwzIMxTBKG+zk2sKnWAFDCn+qOGZdRQ3LUBpaOet3+y3RB/47K2tgevrI1wtdFGuSeA6cla+4H7njgIbc9QljbV2LeSclCfdcn2bLeMxoTNxzMqRtKEMC72snnV4FmbwBSF8eRAl8Qi5P0fkVKQkYmwQ9UAaEj1iZy8GbuPaYD5qd1AvjMaehWzQajH2ZR3J+r8h9L6Eu9ydQEDfxwKvsjgicMIfbJw9BL498vbCRomuKfojWtl+JOJakp9IzqSbpUkPallrSgXQiuZXPle+Vn5Vf1S/VH9Xf1T+F9NaCWPNEuvIsVv8CBQ2ohA==</latexit>
Is = Po /Vs = 960/48 = 20 A
<latexit sha1_base64="+IuwObjgNXKnjIUvF6cbZamKMho=">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</latexit>
Q3
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
i1
+
Vs
2
Vs
Vs = 48 V
C1
+
• Bereken:
• De total harmonic distortion T HD
D1
a
0
Vs
2
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
Q1
i3
Q3
R
i4
C2
Q4
D4
D3
io (t) b
i2
Q2
<latexit sha1_base64="i1L+c169oaOQsgodHivOuDxUFg8=">AAAFU3ichVTLbtNAFHWbBEqhkMKSjUVbKRXFj7FDsjEqUFVBQupDrVspk1gTZ5JY9SN4xojI8j8iJBb8CBsWcB1PQ+pWYCnJzTln5p57xprB1PcY17QfK6uVau3e/bUH6w8fbTx+Ut98arMoiV167kZ+FF8OCKO+F9Jz7nGfXk5jSoKBTy8GV+9z/uIzjZkXhWd8NqW9gIxDb+S5hAPkbFa8Hdy1HWaZbczpF57KdoZ76wCeWkgxBbaNjwI6JtuCsp000kV97EQL8N2pAD84DArcPescLK+wNMVsYu4FlJltC+nK61LPXJZZYEdFYAi+kFlSQDvgoz5SwZ8JP2ASCk3ILhYGpoDOSf2ae7vgTsCI8KFrVrPEF4Oggkfm7WRgOgt8qHls0FqFWe7Y43pee57FHJtYmH2KeYpZEjhpaBl7zb3WnqIoWR974YjP5HxdmPVRJpS2o/XRq2K3HNUUpLfKqUHKVqNgoNmu2hBtd8G6YogE8Y5Q/8cC9umIN/AoJm5auMnSEFrj2BtP+O5fa2WhAUJjWfiyrGiCovlPRQsUrZsKdxhxlg+uIXMR5cHhAliatqkYbVSatnBmFQmqRgF2Dh3DKhgVTjHV4Kh01bAMQzGM0gYHubbwKVbAkMKfKo5ZV1HLMpSWVs7641FH9IH/Tn0LTM8f+Xahi2JLEs+xU/+Gh5GbBDTkrk8Y6+ralPdSEnPP9Wm2jhNGp8S9ImPahTIk8L720vmdkMk7gAzlURTDJ+TyHF1ekZKAsVkwAGVA+ISVuRy8i+smfNTupV44TTgN3aLRKPFlHsn5BSMPvZi63J9BQdzYA6+yOyFwwhyuoTwEvTzy7cJGiq4p+gna2n8j4liTnksvpIakSy1pX+pIx9K55Fa+Vn5Wflel6vfqr9pqrVpIV1fEmmfSjae28QdqPahg</latexit>
• Antwoord
• De RMS waarde van de som van de harmonischen 3,5,7,… kan is
v
u
u
Vh = t
<latexit sha1_base64="bfIOKmHZOUbOxLnnFWxqZeCXj+A=">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</latexit>
1
X
2 =
Von
n=3,5,7,...
q
V02
2 = 0.4359V
Vo1
s
• De total harmonic distortion T HD daarna kan berekend worden met
<latexit sha1_base64="i1L+c169oaOQsgodHivOuDxUFg8=">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</latexit>
T HD = (0.4359Vs )/(0.9Vs ) = 48.34%
<latexit sha1_base64="TxhmfBVXp/03Ku+6Jp1lNOyd8xM=">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</latexit>
D2
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
Vs = 48 V
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De distortion factor DF
i1
+
Vs
2
Vs
+
Vs
2
C1
Q1
i3
D1
a
0
Q3
R
i4
C2
Q4
D4
Q2
D3
io (t) b
i2
D2
<latexit sha1_base64="szA/gXdLGyfEdYMEy8jx2slWtss=">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</latexit>
• Antwoord
• De distortion factor kan worden bepaald met
v
u X
✓
◆2 s✓
◆2 ✓
◆2 ✓
◆2
1
u
Von
Vo3
Vo5
Vo7
t
=
+
+
+ · · · = 0.048Vs
2
2
2
2
n
3
5
7
n=3,5,7,...
<latexit sha1_base64="1oHWzhPJFoTFf7Znpv9ija5n6VQ=">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</latexit>
• Waarna volgt
DF = 0.048Vs /(0.9Vs ) = 5.333%
<latexit sha1_base64="C6AQlNF8Q1QfbsB8i6o3UQrySGA=">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</latexit>
en
am
nt
Te
Parameters van de
Single-Phase Full-Bridge Inverter
• De single-phase half-bridge inverter
heeft een belastingweerstand en DC
ingangsspanning van
R = 2.4 ⌦
<latexit sha1_base64="iULU8U6dBWmJVV0bILmA2N/DDbw=">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</latexit>
i1
+
Vs
2
Vs
Vs = 48 V
+
Vs
2
<latexit sha1_base64="jNj1sStBKO7TQOayhX0WJqb9b8E=">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</latexit>
• Bereken:
• De harmonic factor HF
• De lowest order harmonic LOH
C1
D1
a
0
Q3
R
i4
C2
<latexit sha1_base64="CuQY/JKoVxLXdtqnD/fzTyQZLWM=">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</latexit>
<latexit sha1_base64="OpgzDJoZzKF7p81E7CQuSxGtNeE=">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</latexit>
• Antwoord
• De LOH is de derde harmonische Vo3 = Vo1 /3
<latexit sha1_base64="OpgzDJoZzKF7p81E7CQuSxGtNeE=">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</latexit>
<latexit sha1_base64="K2ALoWtMcb4U2xxRzcql8hgMUGE=">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</latexit>
HF3 = Vo3 /V01 = 1/3 = 33.33%
<latexit sha1_base64="igdRYd4jZ42WAB3yEa0sJAnXQEU=">AAAFU3ichVRNb9NAEHWbBEqh0MKRi0VbKRXFH2uH5LKoQFUFCakfat1K2cTaOJvEqj+Cd4OILP9HhMSBP8KFA4zjbWjdClayPX7vjefNrLX9SeBzYRg/lpYr1dq9+ysPVh8+Wnv8ZH3jqcPjaeKxMy8O4uSiTzkL/IidCV8E7GKSMBr2A3bev3yf8+efWcL9ODoVswnrhnQU+UPfowIgd6Pib5OO43Jst4hgX0SqOhnprgJ4gpFmS2yLHIZsRLck5bhpbMr4yI0X4LsTCX5weRF8PGxfT8GGZjeI8EPG7RZGpva6VDSXZRj86AgcwQ3ZJQXUAz7uIR0M2vAAlxAYUna+cDABdE6aV9zbBXcMRqQP08CNEl90glEhQPbt2UB/GIzo+eCgtg7N3PGRq4adq2k47hgT/ikRKeHT0E0jbO02dpu7mqZlPeJHQzFT87wo66FMKh3X6KFXxddy1NCQ2SyP7bS9j+sFA8V29LosuwPWNUuOkGxL9X8skIANRZ0ME+qlhZssjaA0SfzRWOz8tVYWWiC0rgtflhUNUDT+qWiConlT4Q1iwfPGDWQvRrl/sACuddvQrBYqdVs4w8UEdQtA0mkfuBYuCNjD1ICNMnULW5ZmWaX0/VxauJQJ0KJ0p8tNNnXUxJbWNMqTht9floF3d30TLM+XejswZbCpyHXkrn8jg9ibhiwSXkA575jGRHRTmgjfC1i2SqacTah3SUesA2FE4W/tpvMzIVO3ARmowziBKxLqHL2ekdKQ81nYB2VIxZiXuRy8i+tMxbDVTf1oMhUs8opCw2mgiljNDxh14CfME8EMAuolPnhVvTGF/RVwDOVDMMst3w4cpJmGZh6jzb03chwrynPlhVJXTKWp7Clt5Ug5U7zK18rPyu+qUv1e/VVbrlUL6fKSzHmm3Fi1tT/qzqhx</latexit>
• De distortion factor van de derde harmonische is
DF3 = Vo3 /32 /Vo1 = 1/27 = 3.704%
<latexit sha1_base64="sSw8+bwQ0b6cGEFhMSdnA45t97s=">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</latexit>
Q1
i3
Q4
D4
Q2
D3
io (t) b
i2
D2
DEEL 7
Single-Phase Full-Bridge Inverter met RLC load
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
Q3
D1
R
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<latexit sha1_base64="QrrmLNB4l7/eJxcaAroMFP8XDWA=">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</latexit>
L = 31.5 mH
C = 112 µF
Vs
+
Vs
2
a
0
i4
C2
Q4
Q2
D4
D3
io (t) b
i2
D2
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A.
B.
C.
D.
E.
Druk de uitgangsstroom io (t) uit in een Fourier reeks
Bepaal de RMS uitgangsstroom van de fundamentele component Io1
Bepaal de THD van de uitgangsstroom
Bepaal het vermogen dat wordt opgenomen door de belasting Po
Bepaal de fundamentele component van het vermogen dat wordt opgenomen
door de belasting Po1
F. Bepaal de gemiddelde stroom van de DC bron Is
G. Bepaal de RMS en piek-stroom door de transistoren
H. Plot de fundamentele uitgangsstroom en geef aan waar de transistoren en
dioden geleiden
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en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
a
0
Vs
2
Q4
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I. Bereken de tijd waarover de transistoren in geleiding zijn
J. Bereken de tijd waarover de transistoren in geleiding zijn
K. Bereken de e ectieve hoek van de belasting ✓
ff
R
i4
C2
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<latexit
Q3
D4
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
Vs
2
a
0
C2
Q4
D4
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A. Druk de uitgangsstroom io (t) uit in een Fourier reeks
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• De capacitieve reactantie van de n-de harmonische is
j106
=
2n⇡ ⇥ 60 ⇥ 112
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sha1_base64="6wN0+a9onylPIK9hH0uGUxDjOg8=">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</latexit>
• Hierin is
f0 = 60 Hz
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R
i4
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j
XC =
=
n!C
Q3
j23.68
⌦
n
! = 2⇡ ⇥ 60 = 377 rad/s
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
a
0
Vs
2
C2
Q4
D4
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A. Druk de uitgangsstroom io (t) uit in een Fourier reeks
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• De inductieve reactantie van de n-de harmonische is
XL = jn!L = j2n⇡ ⇥ 60 ⇥ 31.5 ⇥ 10
3
= j11.87n ⌦
• Hierin is
f0 = 60 Hz
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R
i4
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Q3
! = 2⇡ ⇥ 60 = 377 rad/s
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
i1
+
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
Vs
2
C1
Q1
i3
D1
<latexit sha1_base64="oIYRp0l3o4XuYXeF/WQY/AMUkmQ=">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</latexit>
Vs
<latexit sha1_base64="N0TyBFyuBDgyii+UfJS2mWAN+vY=">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</latexit>
+
Vs
2
<latexit sha1_base64="QrrmLNB4l7/eJxcaAroMFP8XDWA=">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</latexit>
L = 31.5 mH
C = 112 µF
a
0
Q3
R
i4
C2
Q4
D4
D3
io (t) b
i2
Q2
D2
<latexit sha1_base64="U02A08oFC2x6Z08gZku7J6+8+cQ=">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</latexit>
<latexit sha1_base64="lHBVJ/jihzmHydQTD9YVkt0GxcQ=">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</latexit>
A. Druk de uitgangsstroom io (t) uit in een Fourier reeks
<latexit sha1_base64="GuVncfiIif6vZR5Ynq/F78psI+0=">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</latexit>
• In totaal is de impedantie bij de n-de harmonische
|Zn | =
<latexit sha1_base64="Erao3VGZzhw0p71asH5YpmSVHQY=">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</latexit>
s
✓
R2 + n!L
• Hierin is
1
n!C
◆2
p
= 102 + (11.87n
f0 = 60 Hz ! = 2⇡ ⇥ 60 = 377 rad/s
11.87n 23.68/n
✓n = arctan
= arctan (1.187n
10
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23.68/n)2
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2.368/n)
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
Vs
2
a
0
Q3
R
i4
C2
Q4
D4
D3
io (t) b
i2
Q2
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A. Druk de uitgangsstroom io (t) uit in een Fourier reeks
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1
X
4Vs
• De uitgangsspanning wordt dan v0 =
sin n!t
n⇡
n=1,3,5,...
• En dus
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= 0 voor n = 2, 4, ...
v0 (t) =280.1 sin(377t) + 93.4 sin(3 ⇥ 377t) + 56.02 sin(5 ⇥ 377t)
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+ 40.02 sin(7 ⇥ 377t) + 31.12 sin(9 ⇥ 377t) + ...
D2
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i0 (t) =18.1 sin(377t + 49.72o ) + 3.17 sin(3 ⇥ 377t 70.17o ) + sin(5 ⇥ 377t
+ 0.5 sin(7 ⇥ 377t 82.85o ) + 0.3 sin(9 ⇥ 377t 84.52o ) + ...
<latexit
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<latexit
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<latexit
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<latexit
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
• Met
• Volgt dan
i0 =
n=1,3,5,...
1
X
n⇡
p
+
Vs
2
Vs
L = 31.5 mH
C = 112 µF
R2
+
+
Vs
2
C1
C2
Q1
0
Q4
4Vs
(n!L-(1/nwC))2
D1
a
D4
R
i4
sin(n!t
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
i1
i3
Q3
D3
io (t) b
i2
Q2
D2
A. Druk de uitgangsstroom io (t) uit in een Fourier reeks
✓n )
79.63o )
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
Vs
2
a
0
Q3
R
i4
C2
Q4
D4
D3
io (t) b
i2
Q2
D2
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B. Bepaal de RMS uitgangsstroom van de fundamentele component Io1
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• Uit
i0 (t) =18.1 sin(377t + 49.72o ) + 3.17 sin(3 ⇥ 377t
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+ 0.5 sin(7 ⇥ 377t
• Volgt dat
82.85o ) + 0.3 sin(9 ⇥ 377t
Im1 = 18.1 A
p
Io1 = 18.1/ 2 = 12.8 A
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70.17o ) + sin(5 ⇥ 377t
84.52o ) + ...
79.63o )
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
i1
+
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
Vs
2
C1
Q1
i3
D1
<latexit sha1_base64="oIYRp0l3o4XuYXeF/WQY/AMUkmQ=">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</latexit>
Vs
<latexit sha1_base64="N0TyBFyuBDgyii+UfJS2mWAN+vY=">AAAIl3icfVVtb9s2EFa7rfGyt3Tbl2FfiCUt7BqiRSq25AHaOqQoUiDAkqB5waxYoGXaUasXT6KLZqp+0v7Mvu3f7EjRsRO7E2CbvnvuuefI42k0i6NCWNa/Dx5+8ulnj7Yan29/8eVXX3+z8/jb8yKb5yE/C7M4yy9HrOBxlPIzEYmYX85yzpJRzC9Gbw+k/+Idz4soS1+Lmxm/Stg0jSZRyASYgseP/n7iD86DwqPU8gV/L0p0XvlX2/5gElheb2E7/EsaAXrqkYVtz/894VO2pz1Hnk1wV/uSQ2098AihtwHJfO+ldmym9zNJ6VF/FvkiSniBehbykO04GpmzcadQYAm/DI48f5KzsHxTlWkdjA4qz9RGYg17VUlRioAQLRn1CqRVOt58Q23cc4Gl2lyeH/OJ+PBHkPp5NL0WHzy/+DMX5emQtpWruUh/hHR2siqpjmoNZUIVCNJou0kIdp3UVLk7qXTrbOKaCxakns/yULBUM95BV8BR3QKUBoKJAmBbAnROyYj8EZ9GacniaJo+q94FVlO0vKfUtTDxiyhtwg6LVrtv4/36r94hMCOwd3vYokh5uksPUPtA/bS9b4FbeZ27cdARRMf1Vz2o1cYYS1k8HS9EramMtErirohs7/exQ4cZkGPirIs1HSjJkf41uabTxz0bXFq2Be26Jtp0KXa7Mt7C9gblpruPuyr/5goGr4IyIZWnRNed9FtVH4F0ZdrVqbsA2oFAvnVgsmgTwEKjyFrhh2DZNaBbfduymwCwvyHRte7rmgX4htSslUFQVS6yV3dgiguAddI7MGgpx+3fz/P68MX/56mXi56vm1T3ssxVqfqWl8MkywoyD9g6t7sk4SubZsuOu6fmGGKUY0gXF9zySK+/GEoXS6A6h/o4hhShU3UKK2Ewc0jPhpz3Q1/BqIQ8HTkyJXUH5qbnYGf9BGZS/8eOpzwJymbC3rcqKSO7LRPCOlQXS70+XqtRDxQB05O4lqkuAxRtYeoOM41RTmWq64HZ12kCetnHLRi9Nlkdy0V1Gzz2JNisGVofp6C2RTdSnAcZ1OSHWVGPMSR3TPvUa0Zy6BNU5CtIpM5L17qwdW3s2Kq8YGcXZo160PqC6MWuoZ/jYOcff5yF84SnIoxZUQyINRNXJctFFMa82vbnBZ+x8C2b8gEsUwZ6rkr1Xq3QE7CM0STL4ZMKpKyrESVLiuImGQEyYeK6uO+Txk2+wVxM3KsySmdzwdOwTjSZx0hkSL6k0TjKeSjiG1iwMI9AKwqvGVwbAa9yuQnkfsnri3OKCYzCE7r7/Be9HQ3jR+Mno2kQwzGeG4fGsXFmhFvfb/28dbD1ovFD49fGy8ZhDX34QMd8Z9x5Gif/ATrUn+0=</latexit>
+
Vs
2
<latexit sha1_base64="QrrmLNB4l7/eJxcaAroMFP8XDWA=">AAAIl3icfVVtb9s2EFa7rfGyt3Tbl2FfiCUt7BqiRSq25AHaOqQoUiDAkqJ5waxYoGXaUasXT6KLZqp+0v7Mvu3f7EjRsRM7E2CbvnvuuefI42k0i6NCWNa/Dx5+8ulnj7Yan29/8eVXX3+z8/jbsyKb5yE/DbM4yy9GrOBxlPJTEYmYX8xyzpJRzM9H7w6k//w9z4soS9+I6xm/TNg0jSZRyASYgseP/n7iD86CwqPU8gX/IEp0VvmX22CdBJbXWxgP/5JWf/DaIwvTnv97wqdsT8OPPJvgrvYlh9p64BFCbwKS+d7L+9nB6meS0qP+LPJFlPAC9SzkIdtxNDJn406hwBJ+ERx5/iRnYfm2KtM6GB1UnqmNxBr2qpKiFAEhWjLqFUirdLz5ltq45wJLtbk8P+YT8fGPIPXzaHolPnp+8WcuytdD2lau5iL9EdLZyaqkOqo1lAlVIEij7SYh2HVSU+XupNKts4krLliQej7LQ8FSzXgLXQFHdQNQGggmCoBtCdA5JSPyR3wapSWLo2n6rHofWE3R8p5S18LEL6K0CTssWu2+jffrv3qHwIzA3u1hiyLl6S49QO0D9dP2vgVu5XVux0FHEB3XX/WgVhtjLGXxdLwQtaYy0iqJuyKyvd/HDh1mQI6Jsy7WdKAkR/rX5JpOH/dscGnZFrTrmmjTpdjtyngL2xuUm+4+7qr8mysYvArKhFSeEl130m9VfQTSlWlXp+4CaAcC+daByaJNAAuNImuFH4Jl14Bu9W3LbgLA/oZEV7qvaxbgG1KzVgZBVbnIXt2CKS4A1klvwaClHLd/N8+bwxf/n6deLnq+blLdyzJXpepbXg6TLCvIPGDr3OyShK9smi077o6aY4hRjiFdXHDLI73+YiidL4HqHOrjGFKEXqtTWAmDmUN6NuS8G/oKRiXk6ciRKak7MDc9BzvrJzCT+u87nvIkKJsJ+9CqpIzspkwI61BdLPX6eK1GPVAETE/iWqa6DFC0hak7zDRGOZWprgdmX6cJ6GUft2D02mR1LBfVTfDYk2CzZmjdT0Fti26kOAsyqMkPs6IeY0jumPap14zk0CeoyFeQSJ2XrnVh69rYsVV5wc4uzBr1oPUF0YtdQz/Hwc4//jgL5wlPRRizohgQayYuS5aLKIx5te3PCz5j4Ts25QNYpgz0XJbqvVqhJ2AZo0mWwycVSFlXI0qWFMV1MgJkwsRVcdcnjZt8g7mYuJdllM7mgqdhnWgyj5HIkHxJo3GU81DE17BgYR6BVhReMbg2Al7lchPI3ZLXF2cUExiFJ3T3+S96OxrGj8ZPRtMghmM8Nw6NY+PUCLe+3/p562DrReOHxq+Nl43DGvrwgY75zrj1NE7+AzbQn+0=</latexit>
L = 31.5 mH
C = 112 µF
a
0
Q3
R
i4
C2
Q4
D4
Q2
D3
io (t) b
i2
D2
<latexit sha1_base64="U02A08oFC2x6Z08gZku7J6+8+cQ=">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</latexit>
<latexit sha1_base64="lHBVJ/jihzmHydQTD9YVkt0GxcQ=">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</latexit>
C. Bepaal de THD van de uitgangsstroom
• Als we componenten tot de 9de harmonische meenemen dan volgt dat de
peilstroom door de belasting wordt
Im =
<latexit sha1_base64="VUV0CCsK4oEPw64UGIMYMkFw4iM=">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</latexit>
p
18.12 + 3.172 + 1.02 + 0.52 + 0.32 = 18.41 A
• De rms waarde van de stroom van de hogere harmonischen is
Ih =
<latexit sha1_base64="NdhYt6pqhsTx7DkxgPG2uCIXS3I=">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</latexit>
p
2
Im1
2
Im
p
2
=
p
18.412
p
18.12
2
= 2.3789 A
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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<latexit sha1_base64="QrrmLNB4l7/eJxcaAroMFP8XDWA=">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</latexit>
L = 31.5 mH
C = 112 µF
Vs
+
Vs
2
a
0
C2
Q4
D4
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C. Bepaal de THD van de uitgangsstroom
• De THD volgt dan uit
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R
i4
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s✓
p
◆2
2
2
Im Im1
18.41
T HD =
=
Im1
18.1
Q3
1 = 18.59%
Q2
D3
io (t) b
i2
D2
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
Q3
D1
R
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<latexit sha1_base64="QrrmLNB4l7/eJxcaAroMFP8XDWA=">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</latexit>
L = 31.5 mH
C = 112 µF
Vs
+
a
0
Vs
2
i4
C2
Q4
Q2
D4
D3
io (t) b
i2
D2
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<latexit sha1_base64="lHBVJ/jihzmHydQTD9YVkt0GxcQ=">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</latexit>
D. Bepaal het vermogen dat wordt opgenomen door de belasting Po
E. Bepaal de fundamentele component van het vermogen dat wordt opgenomen
door de belastingPo1
<latexit sha1_base64="7gTJW46ApxU16RGknGj2/ICbZRs=">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</latexit>
p
p
Io = Im / 2 = 18.41/ 2 = 13.02 A
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sha1_base64="OhsREV1msDgxBIRBTRvX81znzjQ=">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</latexit>
Po = 13.022 ⇥ 10 = 1695 W
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2
Po1 = Io1
R = 12.82 ⇥ 10 = 1638.4 W
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en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 10 ⌦
i1
+
Vs
2
C1
Q1
i3
D1
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L = 31.5 mH
C = 112 µF
Vs
+
a
0
Vs
2
Q3
R
i4
C2
Q4
D4
Q2
D3
io (t) b
i2
D2
<latexit sha1_base64="U02A08oFC2x6Z08gZku7J6+8+cQ=">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</latexit>
<latexit sha1_base64="lHBVJ/jihzmHydQTD9YVkt0GxcQ=">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</latexit>
F. Bepaal de gemiddelde stroom van de DC bron
Is = Po /Vs = 1695/220 = 7.7 A
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G. Bepaal de RMS en piek-stroom door de transistoren
Ip = Im = 18.41 A
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H. Plot de fundamentele uitgangsstroom en geef aan waar de transistoren en
dioden geleiden
IQ(max)
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p
= Io / 2 = Ip /2 = 18.41/2 = 9.2 A
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
H. Plot de fundamentele uitgangsstroom en geef aan waar de transistoren en
dioden geleiden
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
i1
+
Vs
2
Vs
• Bereken:
•
Vs
2
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!t0 = 180
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Q1
D1
a
0
Q3
R
i4
C2
Q4
D4
Q2
49.72 = 130.28o
t0 = 130.28 ⇥ ⇡/(180 ⇥ 377) = 6031 µs
td = (180
<latexit sha1_base64="V2UEr3nfO9pmPspnUu5rPgXJZmg=">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</latexit>
Vo Io cos ✓ = Po
<latexit sha1_base64="jO9BkCQuupx6hlRuXzE6hv5R5T8=">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</latexit>
+
C1
i3
130.28) ⇥ ⇡/(180 ⇥ 377) = 2302 µs
D3
io (t) b
i2
D2
en
am
nt
Te
Single-Phase Full-Bridge Inverter met RLC load
i1
+
Vs
2
Vs
• Bereken:
•
+
Vs
2
220 ⇥ 13.02 ⇥ cos ✓ = 1695
<latexit sha1_base64="pS53f9+SJanCGCP/PsaBseXQ/D0=">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</latexit>
✓ = 53.73o
<latexit sha1_base64="ufK30asPlCP7gBVPXighwJxc/uI=">AAAIlHicfVVtb9s2EFa7rfGylyYbsC/7QixpYc8QLVKxJQPTkCLbkALBlhbNCxbZAi3Tjlq9eBJdNFP1h/Zz9m3/ZkeKduw4rQDb9N1zzz1HHk+jWRwVwrL+e/Dwk08/e7TV+Hz7iy+/+vrxzu4350U2z0N+FmZxll+OWMHjKOVnIhIxv5zlnCWjmF+M3hxJ/8VbnhdRlr4SNzM+SNg0jSZRyASYgt1H/zzxr86DwqPU8gV/J0p0XvmDbbBOAsvrLYzHf2vrS48sbPv+Hwmfsn3tOfFsgrvalxxr65FHCF0GJPP93z5K72eS0qP+LPJFlPAC9SzkIdtxNDJn406hwBJ+GZx4/iRnYfm6KtM6GB1VnqmNxBr2qpKiFAEhumXUK5BW6XjzNbVxzwWW6v7y/JhPxPs/g9TPo+m1eO/5xV+5KF8OaVu5mov0J0hnJ6uS6qjWUCZUgSCNtpuEYNdJTZW7k0q3ziauuWBB6vksDwVLNeMaugKOaglQGggmCoBtCdA5JSPyR3wapSWLo2n6Y/U2sJqi5T2lroWJX0RpE3ZYtNp9Gx/Uf/UOgRmBvdvDFkXK0731ALUP1E/bBxa4lddZj4OOIDquv+pBrTbGWMri6XghakNlpFUSd0Vk+6CPHTrMgBwTZ1Os6UBJjvRvyDWdPu7Z4NKyLWjXDdGmS7HblfEWtu9RbroHuKvy31eBf/U8KBNSeUpz3UjP9JmCJ9OeTt0D0AwEsq3hkAQmiyYBLLSJrBR+CJY9A6rVty17CQAHZDP+Wnd1zQJ8Q2rWwiCoKhfZqzWY4gJgnXQNBg3luP27eV4d//LxPPVy0fF1i+pOlrkqVd/t1TDJcqcyD8g6y02S6JU9s2W73RFzCjHKMaSL2215pNdfTKSLW6A6hvo0hhShl+oQVsJg4JCeDTnvhj6HQQl5OnJgSuoOTE3Pwc7mAcyk/g+dTvkiKJsJe9eqpIxsWSaEdagulnp9vFGjniYCRidxLVPdBCjawtQdZhqjnMpU1wODr9ME9G0Tt2Du2mR1JhfVMnjsSbBZM7Q+TEFti95LcR5kUJMfZkU9w5DcMe1TLxnJoU9Qka8gkTqvwTZaDEAwdW3s2Kq6YGcP5ox60OaC6MWeoZ/TYOdff5yF84SnIoxZUVwRayYGJctFFMa82vbnBZ+x8A2b8itYpgzkDEr1Uq3QE7CM0STL4ZMKpKyrESVLiuImGQEyYeK6uOuTxvt8V3MxcQdllM7mgqdhnWgyj5HIkHxDo3GU81DEN7BgYR6BVhReM7g0At7jchPI3ZI3F+cUExiDL+je4c96OxrG98YPRtMghmMcGsfGqXFmhFu7W87W4dazxneNnxpHjV9r6MMHOuZbY+1p/P4/bPufbw==</latexit>
C1
Q1
i3
D1
a
0
Q3
R
i4
C2
Q4
D4
Q2
D3
io (t) b
i2
D2
Vermogenselektronica 2
Jan van Hulzen
September 2018 version 1.0
Inverters
3
Lesprogramma
Lesweek week dag
datum
1
36 wo 05/09/2018
2
37 wo 12/09/2018
3
38 wo 19/09/2018
4
39 wo 26/09/2018
5
40 wo 03/10/2018
6
41 wo 10/10/2018
7
42 wo 10/10/2018
van
11:00
15:00
11:00
15:00
15:00
15:00
15:00
• NB Lokaal moet nog worden aangepast
tot
12:30
16:30
12:30
16:30
16:30
16:30
16:30
duur
01:30
01:30
01:30
01:30
01:30
01:30
01:30
lokaal
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
L0-30B
Programma van vandaag
• Introductie
• Literatuur
• Single-phase Full-bridge inverters
• Karakteriseren van prestaties van inverters
• Single-phase half-bridge inverters ohmse belasting
• Single-phase half-bridge inverters met RLC load
• Voorbeeld opgave inverters
Aanbevolen Literatuur (niet verplicht)
• Deze presentatie is gebaseerd op
Hoofdstuk 6 van het boek;
• Power Electronics: Circuits, Devices &
Applications (4th Edition) 4th Edition
• Muhammad H. Rashid
• ISBN-13: 978-0133125900
• ISBN-10: 0133125904
DEEL 8
De three-phase Full-bridge inverter
Three-Phase Inverters
• Three-Phase inverters
worden gebruikt voor
toepassingen met hoge
vermogens
• Drie half/full-bridge
inverters kunnen parallel
worden geschakeld
• Aanstuur signalen van de
single-phase inverters
moeten 120o ten opzichten
van elkaar verschoven zijn
• De primaire zijden van
transformatoren moeten
worden gescheiden
Full-Bridge Three-Phase Inverters
fi
• De secundaire zijde van
de transformatoren
kunnen worden
gekoppeld in een ster of
een driehoek con guratie
Half-Bridge Three-Phase Inverters : 180o geleiding
• Control signaal kan met 120o en
180o verschuiving worden
aangebracht
• 180o verschuiving maakt beter
gebruik van de schakelaars en
wordt bij voorkeur toegepast
Half-Bridge Three-Phase Inverters : 180o geleiding
• Drie transistoren zijn tegelijk in
geleiding
• Als Q1 aan is dan is punt a
verbonden aan de positieve
aansluiting van Vs
• Als Q4 aan is dan is punt a
verbonden aan de negatieve
aansluiting van Vs
• Golfvormen van g1-g6 zijn
60o in fase verschoven
• Q1-Q4, Q3-Q6, Q2-Q5
kunnen niet gelijktijdig aan
zijn (kortsluiting)
• Q1-Q4, Q3-Q6, Q2-Q5
kunnen niet gelijktijdig uit
zijn (ongede nieerd)
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
fi
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
Half-Bridge Three-Phase Inverters : Switch states
Half-Bridge Three-Phase Inverters : 180o geleiding
• Een belasting kan worden
aangesloten in ster of driehoek
Half-Bridge Three-Phase Inverters : State 1
• Een belasting kan worden
aangesloten in ster of driehoek
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
1
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
Half-Bridge Three-Phase Inverters : State 2
• Een belasting kan worden
aangesloten in ster of driehoek
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
2
Half-Bridge Three-Phase Inverters : State 3
• Een belasting kan worden
aangesloten in ster of driehoek
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">AAAOhHiczVdbb9s2FFbareuy2k27x70QC4LZcOzoksQdMBcF9rICxtAZi1vMtAVKph2tsuRIdLFA0B/Zz9rb/s0ObwodO126FlgE2KIOv3P5ziEPpWAZRzmz7b937t3/7PMHXzz8cverR7X6470nT4d5uspCehamcZq9CUhO4yihZyxiMX2zzChZBDF9Hbz9kc+/fkezPEqTX9nlko4XZJ5EsygkDET+k0d/HuCRjWN6gdMFnRPEfsDL6MjD410EMwO/oBdlb9DCs4yExaAs3LInx554ULjId5R46OdlIdU00hUywAP4AOHRO78gSdmDW5hoDBgwjUsNQyEAZJuDFKBtIgAigzZpuJoHt3AbHoKGezsaiJNWPEBpsA65Fvca0TaHG+4NIojruNuZaJ63IoI4E++/FCQwCuK9tyChLIhXFcTkvquyE2h14tvcWAvnq4VfJD2nnOAombFLIDpjDeInOExzJJ8SzRxn0fycNVsBTOdRcsO0vsmVCFjl0ykLSFwplEbgjfkFZjLWEz5RnJblRIu0wCwKJBO8bneKpg0tQc3WmvUN2yfrxj/MtpSNFafjIegmglalLmeEkJtV2dg67ZXrydI10lU59A5PDjudTlUd5dT/RF55ETVAMVQLWaXIDE9toPD/ja9txOca8cFuVBuB3IkAuxsZFP1i6PchuouMFWrrgzMRB1+x9kQ8oCOvhAgnrrHwmuV1Na/koJ7deeacnsBItYKhX/T9qmtIplLTLRFsWTDPTfHdu87IUHdMdSTAp/YkNQxJM3an2/2+i0zny6o/9TXcq/pcpa5aExg47jrHlQHV+n42CritcNrspyqg7Ei32geL5Rbx2Ag+uBPBb98kNwaPdPThXYr++g56T+7x6Dc4gn9HunP3q1OXbOsFhSSmj6It/HRccNALyWDitqpzod+caJLjj02CIvFxy7CN2Tll/NBey4mW9jDJQkaSKwJHg2b15pA3WDMS/z15/IhnAv8t2e4jP1AP0FrFZNhgzSrDQrM64XkWBQNc4IDOo6QgWUYuyyIuOV41AOgyqSNSd9XgMIsWNK8gL/10bV5zdJoIY8RtMfoHK5C4+IvMjZbbjgvN61/tC9SGF/QBftzj2/gRqCs/nAlNpipNSFYQ63b8Ejq8pzsq9ygzzI3C+1mjstKuFu4WbN/AIgBXtvVR5JWIW6xOAM5MY7iYC6FD+3v7dscWF9ocOGqwb6nrlb/3F56m4WpBExbGJM9Hjr1kY6DKojCm5S5e5XRJwrdkTkcwTAgkblyIj6gSHYBkimZpBr+EISE1NQqyyPPLRQDIBWHn+fU5Ltw2N1qx2bNxESXLFaNJKB3NVjFiKeJfZGgaZTRk8SUMSJhFECsKzwmklcF32y4kwblOeXMwdDuO3XF+cfdfPFfpeGh9Y31rNSzH6lovrJ+sV9aZFdZ2at/V7JpTf1A/rHv1Ewm9t6N0vrbWrvrzfwCnDCaI</latexit>
Vs
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
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Vs
3
Half-Bridge Three-Phase Inverters : State 4
• Een belasting kan worden
aangesloten in ster of driehoek
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
Vs
4
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
Vs
Half-Bridge Three-Phase Inverters : State 5
• Een belasting kan worden
aangesloten in ster of driehoek
5
Vs
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
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Vs
Half-Bridge Three-Phase Inverters : State 6
• Een belasting kan worden
aangesloten in ster of driehoek
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
Vs
Vs
<latexit sha1_base64="sV+B1k85TwLVkOb8Qj7Ir2msJo8=">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</latexit>
<latexit sha1_base64="PoKb7zAPDaIQAAUuA35rZcPFKog=">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</latexit>
Vs
6
Half-Bridge Three-Phase Inverters : Ster
Half-Bridge Three-Phase Inverters : lijnspanning
• Gedurende 0  !t < 13 ⇡ zijn Q1,
Q5 en Q6 in geleiding
<latexit sha1_base64="G0txhSPHjEr4Kq1n/eo/FGYl8KI=">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</latexit>
• Weerstand van het netwerk is
Req
<latexit sha1_base64="ODrBngN5Anvw833UY9bUpCXfYF8=">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</latexit>
R
3R
=R+
=
2
2
• De stroom door het netwerk is
Vs
2Vs
i1 =
=
Req
3R
<latexit sha1_base64="dXx+KodET20gjKQN/5heuPQx9Bk=">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</latexit>
• De spanningen tussen a,b,c en n zijn
i1 R
Vs
van = vcn =
=
2
3
Vs
vbn = i1 R =
3
<latexit sha1_base64="F/obewp4X9QHomdBCHqUBUBW1mM=">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</latexit>
<latexit sha1_base64="V4qDHGEyVZcj52MbpXmQ+KZMng0=">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</latexit>
Half-Bridge Three-Phase Inverters : lijnspanning
1
2
• Gedurende 3 ⇡  !t < 3 ⇡ zijn Q1,
Q5 en Q6 in geleiding
<latexit sha1_base64="wkWjoH9DbvdSpKdbJJrrMlnXbWc=">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</latexit>
sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit>
sha1_base64="meDGVbAkmDtpnExoIFVQNcIQfyA=">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</latexit>
sha1_base64="kgOXyt1OPPZfbFTgpIrS6mQkiNk=">AAAOrniczVdbb9s2FFbbXbqs8dL1cS/EggA2HDu6JHEHzEOBvayAMbTG4hY1bYGSaUerLDkSXSwQ9O/2C/a2f7PDm0xf0qVrgUWALerwO5fvHPJQChZxlDPb/vve/Qefff7Flw+/2vv60X7tm4PH3w7ydJmF9CJM4zR7HZCcxlFCL1jEYvp6kVEyD2L6Knj7M59/9Y5meZQmv7HrBR3NySyJplFIGIj8x4/+PMJDG8f0CqdzOiOI/YgX0YmHR3sIZvp+Qa/Kbr+JpxkJi35ZuGVXjj3xoHCR7yjxwM/LQqpppCtkgAfwEcLDd35BkrILtzDRGDBgGpcahkIAyBYHKUDLRABEBm3ScDUPbuE2PAQN93Y0ECeteIBSfx2yEfca0RaHG+4NIojruLuZaJ63IoI4E++/FCQwCuK9tyChLIhXFcTkvqeyE2h14tvcWBPny7lfJF2nHOMombJrIDpldeInOExzJJ8SzRxn0eySNZoBTOdRcsO0vsmVCFjl0ykLSFwplIbgjfkFZjLWMz5RnJflWIu0wCwKJBO87naKJnUtQY3mmvUt22frxj/MtpSNFKfTAegmglalLmeEkJtV2dg57ZXrydI10lU59o7PjtvtdlUd5dT/RF55ETVAMVQLWaXIDE9toPD/ja9lxOca8cFuVBuB3IkAO1sZFP1i4PcguquMFWrrgzMRB1+x9lg8oBOvhAjHrrHwGuWmmldyUNduP3XOz2CkWsHAL3p+1TUkU6nplgi2LJjnpvjuXWdkqDumOhLgc3ucGoakGbvd6fzQQabzRdWfehruVX2uUletCQycdpzTyoBqfb8aBdxVOG32UxVQdqRb7YP5Yod4ZAQf3Ingd2+SG4NHOvrwLkW/uYPek3s8fANH8O9Id+5edeqSXb2gkMT0UbSDn44LDnoh6Y/dZnUu9BpjTXL0sUlQJD5uGbYwu6SMH9prOdHSLiZZyEiyInDSb1RvDnmdNSLx35XHj3gm8N+U7T7yA/UArVVMhnXWqDIsNKsTnmdRMMAFDugsSgqSZeS6LOKS41UDgC6TOiJ1qwaHWTSneQV57qdr85qj00AYI26L0T9YgcTFX2RutNxyXGhe/2pfoLa8oA/w457exo9ArfxwJjSZqDQhWUGs2/Fz6PCe7qjco8wwNwrvZ/XKSqtauDuwPQOLAFzZ1keRVyJusToBODON4WK+lHSBwQVsCngdRqsPFLY6k5B4N/YPDu22LS60PXDU4NBS1wv/4C88ScPlnCYsjEmeDx17wUaQFBaFMS338DKnCxK+JTM6hGFCIMWjQnxulegIJBM0TTP4JQwJqalRkHmeX88DQM4Ju8w357hw19xwyaZPR0WULJaMJqF0NF3GiKWIf7uhSZTRkMXXMCBhFkGsKLwkkAsGX3h7kARnk/L2YOC2HbvtvLQPn/2k0vHQ+s763qpbjtWxnlm/WC+sCyvcb+6/3H+zP6zZtUFtVPMl9P49pfPEWrtql/8A3vo4AA==</latexit>
• Weerstand van het netwerk is
Req
<latexit sha1_base64="JPMRJBqNiGheGGg4tXDDHU9j+ds=">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</latexit>
R
3R
=R+
=
2
2
• De stroom door het netwerk is
Vs
2Vs
i2 =
=
Req
3R
<latexit sha1_base64="MMLanEBoxxbv64DNmwA4cAvaEcI=">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</latexit>
• De spanningen tussen a,b,c en n zijn
van
<latexit sha1_base64="6w3B9D+SrpcN5JCQLKzyehke7NE=">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</latexit>
vbn
<latexit sha1_base64="GF011i6cjXKG5g8jFUP3B7zqvkY=">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</latexit>
2Vs
= i2 R =
3
i2 R
= vcn =
=
2
Vs
3
Half-Bridge Three-Phase Inverters : lijnspanning
2
• Gedurende 3 ⇡  !t < ⇡ zijn Q1, Q5
en Q6 in geleiding
<latexit sha1_base64="dFF6jgipu51vx7SpjlP04LrU3bQ=">AAAOoXiczVdbb9s2FFa7W5fVXro9DhiIBQFsOHZ0SeIOmIcC28MCeEVmLG4x0xYomXa0ypIj0cUCQb9r/2Nv+zc7vCl04nTuWmARYIs6/M7lO4c8lIJlHOXMtv9+8PCDDz/6+JNHn+589rhW/3z3yRfDPF1lIT0P0zjNXgYkp3GU0HMWsZi+XGaULIKYvghe/cDnX7ymWR6lya/saknHCzJPolkUEgYi/8njP/fxyMYxvcTpgs4JYt/hZXTo4fEOgpmBX9DLsjdo4VlGwmJQFm7Zk2NPPChc5DtKPPTzspBqGukKGeABvI/w6LVfkKTswS1MNAYMmMalhqEQALLNQQrQNhEAkUGbNFzNg1vYhoeg4W5HA3HSigcoDdYhN+JeI9rmcMO9QQRxHXczE81zKyKIM/H+S0ECoyDeGwsSyoJ4VUFM7jsqO4FWJ77NjbVwvlr4RdJzygmOkhm7AqIz1iB+gsM0R/Ip0cxxFs0vWLMVwHQeJXdM65tciYBVPp2ygMSVQmkE3phfYCZjPeYTxUlZTrRIC8yiQDLB62anaNrQEtRsrVm/Zft43fjb2ZayseJ0NATdRNCq1OWMEHKzKhsbp71yPVm6RroqB97B8UGn06mqo5z678krL6IGKIZqIasUmeGpDRT+v/G1jfhcIz7YjWojkHsRYPdWBkW/GPp9iO4yY4Xa+uBMxMFXrD0RD+jQKyHCiWssvGZ5U80rOahnd546J8cwUq1g6Bd9v+oakqnUdEsEWxbMc1N8964zMtQdUx0J8Ik9SQ1D0ozd6Xa/7SLT+bLqT30N96o+V6mr1gQGjrrOUWVAtb7nRgE3FU6bfV8FlB1pq32wWG4Qj43gg3sR/OZNcmfwSEcf3qfob+6gN+Qej36DI/h3pDt3vzp1yaZeUEhi+ijawE/HBQe9kAwmbqs6F/rNiSY5ftckKBLvtgzbmF1Qxg/ttZxoaQ+TLGQkuSZwOGhWbw55gzUj8d+Tx494JvDfku0+8gP1AK1VTIYN1qwyLDSrE55nUTDABQ7oPEoKkmXkqizikuNVA4AukzoiddcNDrNoQfMKcuqna/Oao9NEGCNui9E/WIHExV9k7rTcdlxoXv9qX6BueUFv4cc92saPQF374UxoMlVpQrKCWLfjU+jwnu6o3KPMMDcK72eNykq7WrgbsH0DiwBc2dZHkVcibrE6ATgzjeFivpSujx2+KeB1GJkfKHjs7+7ZHVtc6PbAUYM9S11n/u5feJqGqwVNWBiTPB859pKNIQ8sCmNa7uBVTpckfEXmdATDhEBWx4X4wirRPkimaJZm8EsYElJToyCLPL9aBIBcEHaR35zjwk1zoxWbPR0XUbJcMZqE0tFsFSOWIv65hqZRRkMWX8GAhFkEsaLwgkBuGHzU7UASnJuUbw+GbsexO84v7t6z71U6HllfWd9YDcuxutYz6yfrzDq3wtrXtR9rP9ee1/fqp/Wz+kBCHz5QOl9aa1d99A9N0jKg</latexit>
• Weerstand van het netwerk is
Req
<latexit sha1_base64="96GlfoaJJJqYQD+F2Rf/Y4+DgTw=">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</latexit>
R
3R
=R+
=
2
2
• De stroom door het netwerk is
Vs
2Vs
i3 =
=
Req
3R
<latexit sha1_base64="qMDY+vnVaQDFvtgJTebyG1T1RiA=">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</latexit>
• De spanningen tussen a,b,c en n zijn
i3 R
Vs
van = vbn =
=
2
3
2Vs
vcn = i3 R =
3
<latexit sha1_base64="j4s9aQAOR41AOyMwSAk4wN/g1fM=">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</latexit>
<latexit sha1_base64="t5ruXCSE0d+IxkpnQccYOQ2aWsI=">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</latexit>
Half-Bridge Three-Phase Inverters : lijnspanning
<latexit sha1_base64="/A6MPv20aOfkX5MJHhGGw3+XNP0=">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</latexit>
⇡
6
• De lijnspanning vab kan worden uitgedrukt in de Fourier reeks:
1
a0 X
vab =
+
(an cos (n!t) + bn sin (n!t))
2
n=1
<latexit sha1_base64="KZ1+C3TjbPqOfWq/SIw2VygcDGc=">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</latexit>
<latexit sha1_base64="rTT4/fortFRhm8OaQtCng79tqUw=">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</latexit>
⇡
6
• Door de symmetrie eigenschappen rondom !t =
<latexit sha1_base64="QxGb0SA2SYWhb+ueFjtZDEOAABg=">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</latexit>
bn =
<latexit sha1_base64="vk5BrD7TZ9BWoFJxw5LcXTRG3Tw=">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</latexit>
2
14
⇡
Z
⇡
6
5⇡
6
Vs sin (n!t) d(!t) +
⇣ n⇡ ⌘
⇣ n⇡ ⌘
4Vs
=
sin
sin
n⇡
2
3
Z
5⇡
6
⇡
6
volgt a0 = 0, an = 0
<latexit sha1_base64="E8KrmKiZ0iTxcLLcBKsmS+V40m4=">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</latexit>
3
Vs sin (n!t) d(!t)5
Half-Bridge Three-Phase Inverters : lijnspanning
• Met
vab
<latexit sha1_base64="rTT4/fortFRhm8OaQtCng79tqUw=">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</latexit>
1
a0 X
=
+
(an cos (n!t) + bn sin (n!t))
2
n=1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
4Vs
a0 = 0, an = 0
bn =
sin
sin
n⇡
2
3
<latexit sha1_base64="E8KrmKiZ0iTxcLLcBKsmS+V40m4=">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</latexit>
<latexit sha1_base64="lBDV16zzx1yify+NjuKnAkJcOLw=">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</latexit>
• Volgt
vab
<latexit sha1_base64="UiEdtW6p2DyI2T+C7PTvLLI79Sw=">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</latexit>
⇣ n⇡ ⌘
⇣ n⇡ ⌘
⇣
4Vs
⇡⌘
=
sin
sin
sin n !t +
n⇡
2
3
6
n=1,3,5,...
1
X
• Waarna met een verschuiving van 120o ( 46 ⇡) volgt
1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
⇣
X
4Vs
vbc =
sin
sin
sin n !t
n⇡
2
3
n=1,3,5,...
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<latexit sha1_base64="X6r+ZfGmWd8gGpPJL80XuS5jKbU=">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</latexit>
vca
<latexit sha1_base64="Q+QZ9Jdac1+cLpdf+VrOo+uqXgE=">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</latexit>
✓
⇣ n⇡ ⌘
⇣ n⇡ ⌘
4Vs
=
sin
sin
sin n !t
n⇡
2
3
n=1,3,5,...
1
X
• Merk op dat n=3,9,15,… een lijnspanning van 0 oplevert
⇡⌘
2
7⇡
6
◆
Half-Bridge Three-Phase Inverters : lijnspanning
• De RMS waarde van de lijn-naar-lijn spanning is te berekenen met
VL =
s
2
2⇡
<latexit sha1_base64="oky0vFv6WpjuCRarL6CtUHOfBVs=">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</latexit>
Z
2⇡/3
0
Vs2 d(!t) =
r
2
Vs = 0.8165Vs
3
• De RMS waarde van 1e en de n-de harmonische van de lijn-naar-lijn
spanning is te berekenen met
VL 1
<latexit sha1_base64="4+w77iWUrS/tIvzyGE7TQjbzsXE=">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</latexit>
4Vs sin 60o
p
=
= 0.7797Vs
2⇡
VL n
<latexit sha1_base64="bOHpD6vSdk3qtkm7V83Cl72ZFFU=">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</latexit>
4Vs
n⇡
p
=
= sin
3
2n⇡
• De RMS waarde van de lijn-naar-neutraal spanning is te bereken met
VL
Vp = p =
3
<latexit sha1_base64="Ut37asJ6H+1YzfZCBAYxNNUciqg=">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</latexit>
p
2Vs
= 0.4714Vs
3
Half-Bridge Three-Phase Inverters : RL load
a
<latexit sha1_base64="R2h0Y8aiP+VDNu5Wu45xxiBXpRs=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu16bBac+vuEmSTeAWpQYHWsPo1GCUsi1EaJqjWfc9NTZBTZTgTOK8MMo0pZVM6xr6lksaog3x56JxcWWVEokTZkoYs1d8TOY21nsWh7Yypmeh1byH+5/UzE90GOZdpZlCy1aIoE8QkZPE1GXGFzIiZJZQpbm8lbEIVZcZmU7EheOsvb5JOo+65da/dqDUbRRxluIBLuAYPbqAJ99ACHxggPMMrvDmPzovz7nysWktOMXMOf+B8/gC97YzT</latexit>
<latexit
R
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
R
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="ewA9rTDnDuj5vP4E2zYZHhrMgy0=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu1w2G15tbdJcgm8QpSgwKtYfVrMEpYFqM0TFCt+56bmiCnynAmcF4ZZBpTyqZ0jH1LJY1RB/ny0Dm5ssqIRImyJQ1Zqr8nchprPYtD2xlTM9Hr3kL8z+tnJroNci7TzKBkq0VRJohJyOJrMuIKmREzSyhT3N5K2IQqyozNpmJD8NZf3iSdRt1z6167UWs2ijjKcAGXcA0e3EAT7qEFPjBAeIZXeHMenRfn3flYtZacYuYc/sD5/AG/cYzU</latexit>
<latexit
b
c
R
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="rB/uEJa6rsqz3qu8+qz1XEnB5zk=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu12bBac+vuEmSTeAWpQYHWsPo1GCUsi1EaJqjWfc9NTZBTZTgTOK8MMo0pZVM6xr6lksaog3x56JxcWWVEokTZkoYs1d8TOY21nsWh7Yypmeh1byH+5/UzE90GOZdpZlCy1aIoE8QkZPE1GXGFzIiZJZQpbm8lbEIVZcZmU7EheOsvb5JOo+65da/dqDUbRRxluIBLuAYPbqAJ99ACHxggPMMrvDmPzovz7nysWktOMXMOf+B8/gDA9YzV</latexit>
<latexit
• Voor een belasting is ster con guratie geldt van
<latexit sha1_base64="IJpWsdRqzJHpCHvjZWK3PIG4ji8=">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</latexit>
vab
= p en dus
3
1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
h ⇣
X
4Vs
⇡⌘ ⇡i
p
vaN =
sin
sin
sin n !t +
⌥
2
3
6
6
3n⇡
n=1
1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
h ⇣
X
4Vs
⇡⌘ ⇡i
p
vbN =
sin
sin
sin n !t
⌥
2
3
2
6
3n⇡
n=1
 ✓
◆
1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
X
4Vs
7⇡
⇡
p
vcN =
sin
sin
sin n !t
⌥
2
3
6
6
3n⇡
n=1
<latexit sha1_base64="ZL3bSjaFzGHQhWZN9HWcHSrUASA=">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</latexit>
<latexit sha1_base64="vEfKVf7B6cIiqRs2ZFjdb3/6tU8=">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</latexit>
fi
<latexit sha1_base64="HGpyMQLYCXp75eHUAu05C3aJy+0=">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</latexit>
Half-Bridge Three-Phase Inverters : RL load
a
<latexit sha1_base64="R2h0Y8aiP+VDNu5Wu45xxiBXpRs=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu16bBac+vuEmSTeAWpQYHWsPo1GCUsi1EaJqjWfc9NTZBTZTgTOK8MMo0pZVM6xr6lksaog3x56JxcWWVEokTZkoYs1d8TOY21nsWh7Yypmeh1byH+5/UzE90GOZdpZlCy1aIoE8QkZPE1GXGFzIiZJZQpbm8lbEIVZcZmU7EheOsvb5JOo+65da/dqDUbRRxluIBLuAYPbqAJ99ACHxggPMMrvDmPzovz7nysWktOMXMOf+B8/gC97YzT</latexit>
<latexit
R
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
R
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="ewA9rTDnDuj5vP4E2zYZHhrMgy0=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu1w2G15tbdJcgm8QpSgwKtYfVrMEpYFqM0TFCt+56bmiCnynAmcF4ZZBpTyqZ0jH1LJY1RB/ny0Dm5ssqIRImyJQ1Zqr8nchprPYtD2xlTM9Hr3kL8z+tnJroNci7TzKBkq0VRJohJyOJrMuIKmREzSyhT3N5K2IQqyozNpmJD8NZf3iSdRt1z6167UWs2ijjKcAGXcA0e3EAT7qEFPjBAeIZXeHMenRfn3flYtZacYuYc/sD5/AG/cYzU</latexit>
<latexit
b
c
R
<latexit sha1_base64="FZOle5V+opQyYIUVXpR06IvMJpg=">AAAB6HicbVA9TwJBEJ3DL8Qv1NJmIzGxInc0UpLYWIKRjwQuZG+Zg5W9vcvungm58AtsLDTG1p9k579xgSsUfMkkL+/NZGZekAiujet+O4Wt7Z3dveJ+6eDw6PikfHrW0XGqGLZZLGLVC6hGwSW2DTcCe4lCGgUCu8H0duF3n1BpHssHM0vQj+hY8pAzaqzUuh+WK27VXYJsEi8nFcjRHJa/BqOYpRFKwwTVuu+5ifEzqgxnAuelQaoxoWxKx9i3VNIItZ8tD52TK6uMSBgrW9KQpfp7IqOR1rMosJ0RNRO97i3E/7x+asK6n3GZpAYlWy0KU0FMTBZfkxFXyIyYWUKZ4vZWwiZUUWZsNiUbgrf+8ibp1KqeW/VatUqjlsdRhAu4hGvw4AYacAdNaAMDhGd4hTfn0Xlx3p2PVWvByWfO4Q+czx+nMYzE</latexit>
<latexit
L
<latexit sha1_base64="NxLlf26uibbHdConaZ5Yd1tX3JE=">AAAB6HicbVA9SwNBEJ2LXzF+RS1tFoNgFe7SmDJgY2GRgPmA5Ah7m7lkzd7esbsnhCO/wMZCEVt/kp3/xk1yhSY+GHi8N8PMvCARXBvX/XYKW9s7u3vF/dLB4dHxSfn0rKPjVDFss1jEqhdQjYJLbBtuBPYShTQKBHaD6e3C7z6h0jyWD2aWoB/RseQhZ9RYqXU/LFfcqrsE2SReTiqQozksfw1GMUsjlIYJqnXfcxPjZ1QZzgTOS4NUY0LZlI6xb6mkEWo/Wx46J1dWGZEwVrakIUv190RGI61nUWA7I2omet1biP95/dSEdT/jMkkNSrZaFKaCmJgsviYjrpAZMbOEMsXtrYRNqKLM2GxKNgRv/eVN0qlVPbfqtWqVRi2PowgXcAnX4MENNOAOmtAGBgjP8ApvzqPz4rw7H6vWgpPPnMMfOJ8/nhmMvg==</latexit>
<latexit
<latexit sha1_base64="rB/uEJa6rsqz3qu8+qz1XEnB5zk=">AAAB6HicbVBNT8JAEJ3iF+IX6tHLRmLiibRc9EjixSMkFkigIdtlCivbbbO7NSENv8CLB43x6k/y5r9xgR4UfMkkL+/NZGZemAqujet+O6Wt7Z3dvfJ+5eDw6PikenrW0UmmGPosEYnqhVSj4BJ9w43AXqqQxqHAbji9W/jdJ1SaJ/LBzFIMYjqWPOKMGiu12bBac+vuEmSTeAWpQYHWsPo1GCUsi1EaJqjWfc9NTZBTZTgTOK8MMo0pZVM6xr6lksaog3x56JxcWWVEokTZkoYs1d8TOY21nsWh7Yypmeh1byH+5/UzE90GOZdpZlCy1aIoE8QkZPE1GXGFzIiZJZQpbm8lbEIVZcZmU7EheOsvb5JOo+65da/dqDUbRRxluIBLuAYPbqAJ99ACHxggPMMrvDmPzovz7nysWktOMXMOf+B8/gDA9YzV</latexit>
<latexit
• Met een belasting Z = R + jn!L volgt
<latexit sha1_base64="MlepcsrISR84n6p0LRzoWEaqnp0=">AAAOfHiczVdbb9s2FFbbXbosTtPucQ8jlgWw4djRJYk7YB4K7GUFjKEzFreYaQuUTCdaZcmR6GKBoD+xn7a3/ZS9DDu8KXSsbOlaYBFgizr8zuU7hzyUgmUc5cy2/7h3/8EHH3708cNPtj7dbuw82n38ZJSnqyykp2Eap9mrgOQ0jhJ6yiIW01fLjJJFENOXwevv+PzLNzTLozT5iV0u6WRBzpJoHoWEgch/vP3bPh7bOKYXOF3QM4LYN3gZHXp4soVgZugX9KLsD9t4npGwGJaFW/bl2BMPChf5jhKP/LwspJpGukIGeADvIzx+4xckKftwCxONAQOmcalhKASA7HCQAnRMBEBk0CYNV/PgFm7DQ9Bwb0cDcdKKBygN1yHX4l4j2uFww71BBHEdt56J5nkrIogz8f5LQQKjIN4/FiSUBfGqgpjct1R2Aq1OfJsba+N8tfCLpO+UUxwlc3YJROesSfwEh2mO5FOimeMsOjtnrXYA03mU3DCtb3IlAlb5dMoCElcKpTF4Y36BmYz1mE8UJ2U51SItMIsCyQSv9U7RrKklqNVes75h+3jd+NvZlrKJ4nQ0At1E0KrU5YwQcrMqG7XTXrmeLF0jXZUD7+D4oNvtVtVRTv335JUXUQMUQ7WQVYrM8NQGCv/f+DpGfK4RH+xGtRHInQiwt5FB0S9G/gCiu8hYobY+OBNx8BVrT8UDOvRKiHDqGguvVV5X80oO6tvdp87JMYxUKxj5xcCvuoZkKjXdEsGWBfPcFN+964wMdcdURwJ8Yk9Tw5A0Y3d7va97yHS+rPrTQMO9qs9V6qo1gYGjnnNUGVCt7wejgHWF02bfVwFlR7rVPlgsa8QTI/jgTgRfv0luDB7p6MO7FP31HXRz+Hj8M5zAvyDduAfVoUvqWkEheemTqIaeDgvOeSEZTt12dSwMWlPNcfKuOVAc3m0VdjA7p4yf2cZyhFcwJe1jkoWMJFcEDoet6sUhb7JWJP778vQRzwT+27LbR36gHqCzismwyVpVhoVmdcDzLAoGuMABPYuSgmQZuSyLuOR4tf+hyaSOSN1Vf8MsWtC8gjz307V5zdFpIYwRt8Xor6xA4uLvMTda7jgu9K5/tS9QG17QW/hxj27jR6Cu/HAmNJmpNCFZQay78XNo8J5uqNyjzDA3Cq9nzcpKp1q4NdiBgUUArmzrk8grEbdYHQCcmcZwsb+7Z3dtcaHNgaMGe5a6Xvi7v+NZGq4WNGFhTPJ87NhLNgGOLApjWm7hVU6XJHxNzugYhgmBjE0K8fFUon2QzNA8zeCXMCSkpkZBFnl+uQgAuSDsPL8+x4V1c+MVmz+dFFGyXDGahNLRfBUjliL+JYZmUUZDFl/CgIRZBLGi8JxAPhl8r/EkONcpbw5Gbtexu86P7t6zb1U6HlqfW19aTcuxetYz63vrhXVqhdt/Nr5oNButxl87X+20dzoSev+e0vnMWrt2Tv4GJFYleQ==</latexit>
ia =
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1
X
2
4p h p
i sin
3 n⇡ R2 + (n!L)2
n=1,3,5,...
✓n = arctan(n!L/R)
<latexit sha1_base64="5dKyIhl1UC3d/2HVswqbGVZpHWg=">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</latexit>
4Vs
⇣ n⇡ ⌘
2
sin
⇣ n⇡ ⌘
3
3
h ⇣
⌘ ⇡
⇡
5 sin n !t +
⌥
6
6
✓n
i
Half-Bridge Three-Phase Inverters : ingangsstroom
• De ingangsstroom kan bepaald worden door het vermogen te analyseren
• Aanname is dat er geen verliezen zijn
• Het vermogen is dan vs (t)is (t) = vab (t)ia (t) + vbc ib (t) + vca (t)ic (t)
<latexit sha1_base64="IFgS/QofKaGBtmGVNNlS95u6RaM=">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</latexit>
• Waaruit volgt
p
8 p
9
2Vpo1 sin(!t) ⇥ 2Io sin(!tp ✓1 )
<
=
1
is (t) =
+ p2Vo1 sin(!t 120o ) ⇥ p2Io sin(!t 120o ✓1 )
;
Vs :
o
o
+ 2Vo1 sin(!t 240 ) ⇥ 2Io sin(!t 240
✓1 )
p
• Met daarin de RMS load lijnstroom IL = 3Io ,de RMS load fase stroom Io
en de fase spanning Vo1
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DEEL 9
Three-Phase Full-Bridge Inverter met RL load
en
am
nt
Te
Three-Phase Bridge Inverter met RL load
a
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<latexit
R
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<latexit
L
R
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<latexit
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<latexit
L
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<latexit
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<latexit
b
c
R
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<latexit
L
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<latexit
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<latexit
• Een Three-Phase Bridge inverter heeft een RL belasting aangesloten in een
ster con guratie.
• De volgende gegevens zijn bekend
• Ingangsspanning Vs = 220 V
• Inverter frequentie f0 = 60 Hz
• Belasting R = 5 ⌦ L = 23 mH
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fi
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en
am
nt
Te
Three-Phase Bridge Inverter met RL load
a
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<latexit
R
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<latexit
L
R
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L
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<latexit
b
c
L
R
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<latexit
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
Druk de line-to-line spanning vab (t) en line stroom ia (t) uit in een Fourier reeks
Bepaal de RMS lijnspanning VL
Bepaal de RMS fasespanning Vp
Bepaal de RMS lijnspanning VL1 bij de fundamentele frequentie
Bepaal de RMS fasespanning Vp1 bij de fundamentele frequentie
Bepaal de total harmonic distortion THD
Bepaal de distortion factor DF
Bepaal de Harmonic Factor HF en de Distortion Factor DF van de LOH
Bepaal de load power Po
Bepaal de gemiddelde waarde en de RMS waarde van de transistorstroom
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Three-Phase Bridge Inverter met RL load
A. Druk de line-to-line spanning vab (t) en line stroom ia (t) uit in een Fourier reeks
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• Met behulp van Vs = 220 V , f0 = 60 Hz en ! = 2⇡ ⇥ 60 = 377 rad/s
volgt
1
⇣ n⇡ ⌘
⇣ n⇡ ⌘
⇣
X
4Vs
⇡⌘
vab =
sin
sin
sin n !t +
n⇡
2
3
6
n=1,3,5,...
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• Waarna volgt
vab (t) = 242.58 sin(377t + 30o ) 48.52 sin 5(377t + 30o )
34.66 sin 7(377t + 30o ) + 22.05 sin 11(377t + 30o )
+18.66 sin 13(377t + 30o ) 14.27 sin 17(377t + 30o ) + ...
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• Waarna de stroom kan worden bepaald…
en
am
nt
Te
Three-Phase Bridge Inverter met RL load
A. Druk de line-to-line spanning vab (t) en line stroom ia (t) uit in een Fourier reeks
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• Met behulp van Vs = 220 V , f0 = 60 Hz en ! = 2⇡ ⇥ 60 = 377 rad/s
volgt
2
3
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ia =
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1
X
4Vs
4p h p
i sin
3 n⇡ R2 + (n!L)2
n=1,3,5,...
⇣ n⇡ ⌘
2
sin
⇣ n⇡ ⌘
3
h ⇣
⌘ ⇡
⇡
5 sin n !t +
⌥
6
6
✓n
i
✓n = arctan(n!L/R)
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sha1_base64="5dKyIhl1UC3d/2HVswqbGVZpHWg=">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</latexit>
• Waarna met R = 5 ⌦ en L = 23 mH volgt
p
p
2
2
ZL = R + (n!L) \ arctan(n!L/R) = 52 + (8.67n/5)2 \ arctan(8.67n/5)
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<latexit sha1_base64="hR9C05bBRZ+8trlfN9duHUzwrvU=">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</latexit>
• Waarna de stroom kan worden bepaald
ia (t) = 14 sin(377t 60o ) 0.64 sin 5(377t + 36.6o )
0.33 sin(7 ⇥ 377t + 94.7o ) + 0.13 sin(11 ⇥ 377t + 213o )
+0.1 sin(13 ⇥ 377t + 272.5o ) 0.06 sin(17 ⇥ 377t + 391.9o ) + ...
Vermogenselektronica 2
Jan van Hulzen
September 2018 version 1.0
Voltage control of Inverters
5
Programma van vandaag
• Voltage control of single phase inverters
• Uniform pulse-width modulation
• Sinusoidal pulse-width modulation
• Modi ed sinusoidal pulse-width modulation
• Phase Displacement control
fi
• Voltage control of tree phase inverters
DEEL 10
Voltage Control van Single-Phase Inverters
Voltage Control van Single-Phase Inverters
i1
+
Vs
2
Q1
C1
L
Vs
+
Vs
2
0
R
a
i2
io (t)
C2
D1
Q2
D2
• In veel applicaties is het sturen van de amplitude van het uitgangssignaal
noodzakelijk
• Variatie in DC ingangsspanning
• Constant houden uitgangsspaning onder invloed van wisselende
belasting
• Spanning- en frequentieregeling
Voltage Control van Single-Phase Inverters
i1
+
Vs
2
Q1
C1
L
Vs
+
0
Vs
2
R
Q2
• Technieken zijn:
• Single-pulse-width modulation
• Multiple-pulse-width modulation
• Sinusodial pulse-width modulation
• Modi ed sinusodial pulse-width modulation
fi
• Phase displacement control
a
i2
io (t)
C2
D1
D2
DEEL 11
Voltage Control van Single-Phase Inverters
uniform pulse-width modulation
Voltage Control van Single-Phase Inverters
• De modulatie index is een maat
voor de uitgangsspaning
• Het aantal pulsen per half cycle kan
worden gevonden met
P =
fc
mf
=
2fo
2
• Waarin mf = fc /fo de frequentie
modulatie index wordt genoemd
• Deze modulatie methode heet ook
wel uniform pulse-width modulation
Voltage Control van Single-Phase Inverters
• Beschouwen we een signaal met een positieve puls, startend op ↵m en
eindigend op ↵m + en een negatieve puls startend op ⇡ + ↵m en
eindigend op ⇡ + ↵m + dan kan deze puls beschreven worden met
1
a0 X
v(t) =
+
(an cos (n!t) + bn sin (n!t))
2
n=1
• Hierin is a0 = 0 omdat het signaal symmetrisch is in de x as en an = 0
omdat het signaal keer symmetrisch is in de y-as
• Het signaal
1
a0 X
v(t) =
+
(an cos (n!t) + bn sin (n!t))
2
n=1
• heeft alleen termen bn welke kunnen worden bepaald met
1
bn =
⇡
Z
↵m +
1
⇡
sin (n!t) d(!t)
↵m
Z
⇡+↵m +
sin (n!t) d(!t)
⇡+↵m
• oplossen van de integraal levert
bn =

1
cos (n!t)
n⇡
↵m +
↵m

1
cos (n!t)
n⇡
⇡+↵m +
⇡+↵m
fo
In
Voltage Control van Single-Phase Inverters
fo
In
Voltage Control van Single-Phase Inverters
• De uitdrukking
bn =

1
cos (n!t)
n⇡

↵m +
↵m
1
cos (n!t)
n⇡
⇡+↵m +
⇡+↵m
• kunnen we uitwerken tot
bn =
1
[cos n (↵m + )
n⇡
cos n (↵m ) + cos n (⇡ + ↵m )
cos n (⇡ + ↵m + )]
• De cosinus termen kunnen worden omgezet met behulp van
cos ↵
cos
↵+
= 2 sin
2
sin
↵
2
• waarmee volgt
bn =

✓
1
2 sin n sin n ↵m +
n⇡
2
2
◆
✓
+ 2 sin ( n ) sin n ⇡ + ↵m +
2
◆
fo
In
Voltage Control van Single-Phase Inverters
• Halen we de term met
buiten haakjes dan volgt dat

✓
1
bn =
2 sin n sin n ↵m +
n⇡
2
2
◆
✓
+ 2 sin ( n ) sin n ⇡ + ↵m +
• wordt omgezet naar
bn =

✓
2
sin n sin n ↵m +
n⇡
2
2
• vervolgens volgt met sin ↵

sin
2
bn =
sin n 2 cos n
n⇡
2
✓
◆
= 2 cos
✓
sin n ⇡ + ↵m +
↵+
2
◆
⇡
+ ↵m +
2
2
sin
sin n
↵
2
⇣⇡⌘
2
2
◆
dat
2
◆
fo
In
Voltage Control van Single-Phase Inverters
• Uiteindelijk volgt dat

2
bn =
sin n 2 cos n
n⇡
2
• met cos(↵ + ) = sin ↵ cos
worden omgezet naar
✓
⇡
+ ↵m +
2
2
+ cos ↵ sin

✓
◆
sin n
⇣⇡⌘
2
1
en cos( 2 ⇡ + ) = cos
4
bn =
sin n sin n ↵m +
n⇡
2
2
◆
• Waarmee we de Fourier serie kunnen opzetten voor een enkele puls
kan
Voltage Control van Single-Phase Inverters
• Breiden we de beschouwing uit naar een puls trein met p pulsen per halve
periode dan volgt
Bm

✓
◆
2p
X
4Vs
n
=
sin
sin n ↵m +
n⇡
2
2
m=1
Voltage Control van Single-Phase Inverters
• De uitgangsspanning wordt nu
vo (t) =
1
X
Bn sin n!t
n=1,3,5,...
• met
Bm

✓
◆
2p
X
4Vs
n
=
sin
sin n ↵m +
n⇡
2
2
m=1
• en de RMS waarde van de uitgangsspanning volgt nu uit
Vo =
s
2p
2⇡
Z
(⇡/p+ )/2
(⇡/p
)/2
Vs2 d(!t)
= Vs
r
p
⇡
Voltage Control van Single-Phase Inverters
Voltage Control van Single-Phase Inverters
Voltage Control van Single-Phase Inverters
• Variëren we nu de modulatie
index M = Ar /Acr dan volgt
• waarmee we de verhouding
tussen de harmonischen en de
DC voedingsspanning kunnen
bepalen
DEEL 12
Voltage Control van Single-Phase Inverters
sinusoidal pulse-width modulation
Voltage Control van Single-Phase Inverters
• bij sinusoidal PWM wordt de
breedte van de pulsen
gevarieerd
• De DF en LOH worden
gereduceerd t.o.v. UWPM
• De RMS spanning wordt
dan
v
u 2p
uX
Vo = V s t
m=1
m
⇡
Voltage Control van Single-Phase Inverters
UPWM
SPWM
DEEL 13
Voltage Control van Single-Phase Inverters
fi
modi ed sinusoidal pulse-width modulation
Voltage Control van Single-Phase Inverters
Voltage Control van Single-Phase Inverters
Voltage Control van Single-Phase Inverters
SPWM
MSPWM
DEEL 14
Voltage Control van Single-Phase Inverters
phase displacement control
Voltage Control van Single-Phase Inverters
i1
+
Vs
2
Vs
+
Vs
2
C1
Q1
i3
D1
a
0
Q3
R
i4
C2
Q4
D4
D3
io (t) b
i2
Q2
D2
• Een full bridge inverter is eigenlijk
een optelsom van twee halfbridge inverters (a-c)
• We kunnen een trap b in fase
verschuiven t.o.v. trap a (d-e)
• we kunnen de aansturing ook zo
schuiven dat symmetrie t.o.v. de
y-as ontstaat (f)
Vermogenselektronica 2
Jan van Hulzen
September 2018 version 1.0
Voltage control of Inverters
5
Programma van vandaag
• Voltage control of three phase inverters
• Uniform pulse-width modulation
• Sinusoidal pulse-width modulation
• Modi ed sinusoidal pulse-width modulation
• Phase Displacement control
fi
• Voltage control of tree phase inverters
Aanbevolen Literatuur (niet verplicht)
• Deze presentatie is gebaseerd op
Hoofdstuk 6 van het boek;
• Power Electronics: Circuits, Devices &
Applications (4th Edition) 4th Edition
• Muhammad H. Rashid
• ISBN-13: 978-0133125900
• ISBN-10: 0133125904
DEEL 15
Voltage Control van three-Phase Inverters
Voltage Control van Three-Phase Inverters
• Technieken voor single-phase inverters kunnen ook worden toegepast op
drie-fase inverters.
• De meest gebruikte technieken zijn
• Sinusoidal PWM
• Third Harmonic PWM
• 60-deg PWM
• Space vector modulation
Voltage Control van Three-Phase Inverters
• Sinusoidal PWM voor drie-fase
inverter
• Elk signaal is 120 graden
verschoven t.o.v origineel
Voltage Control van Three-Phase Inverters
• Sinusoidal PWM voor drie-fase
inverter
• Elk signaal is 120 graden
verschoven t.o.v origineel
Voltage Control van Three-Phase Inverters
• Sinusoidal PWM voor drie-fase
inverter
• Elk signaal is 120 graden
verschoven t.o.v origineel
Voltage Control van Three-Phase Inverters
• Sinusoidal PWM voor drie-fase
inverter
• Elk signaal is 120 graden
verschoven t.o.v origineel
Voltage Control van Three-Phase Inverters
• Sinusoidal PWM voor drie-fase
inverter
• Elk signaal is 120 graden
verschoven t.o.v origineel
Voltage Control van Three-Phase Inverters
• De amplitude van het modulerende
signaal kan ook hoger gekozen
worden dan 1 zodat overmodulatie
ontstaat.
Voltage Control van Three-Phase Inverters
• Bij 60o PWM wordt een gedeelte
van de golfvorm afgeplat.
• De afplatting vindt plaats tussen
60o en 120o en 240o en 300o
• De power devices worden op 1/3
van de cycle vastgehouden en
hebben lage schakelverliezen
• De fundamentele golfvorm heeft
een hogere amplitude dan bij
sinusoidal PWM
Voltage Control van Three-Phase Inverters
• Bij third Harmonic PWM worden
harmonischen in het sinuvormige
signaal geïnjecteerd
• De referentie golfvorm is niet
sinusvormig maar is een combinatie
van de fundamentele frequentie en de
derde harmonische
• Omdat de derde harmonische in elk
van de drie fasen aanwezig is komt
deze niet voor in het uitgangssignaal
•
Voltage Control van Three-Phase Inverters
• Space vector modulatie
• Bij PWM modulatie genereert
elke push-pull driver stage een
golfvorm onafhankelijk van de
andere fasen
• Bij space vector modulatie
wordt de gehele inverter als
een enkele unit beschouwd
• De inverter kan in 8
verschillende states worden
gestuurd zodanig dat
ua (t) + ub (t) + uc (t) = 0
<latexit sha1_base64="bonkBWkrXcwIraMZAc9b6cvujEc=">AAACA3icbVDLSsNAFJ3UV62vqDvdDBahIpSkG90IRTcuK9gHJCFMppN26GQS5iGUUHDjr7hxoYhbf8Kdf+O0zUJbDwz3cM693LknyhiVynG+rdLK6tr6RnmzsrW9s7tn7x90ZKoFJm2cslT0IiQJo5y0FVWM9DJBUBIx0o1GN1O/+0CEpCm/V+OMBAkacBpTjJSRQvvI93SIaursXIfRvGBTrhw/CO2qU3dmgMvELUgVFGiF9pffT7FOCFeYISk918lUkCOhKGZkUvG1JBnCIzQgnqEcJUQG+eyGCTw1Sh/GqTCPKzhTf0/kKJFynESmM0FqKBe9qfif52kVXwY55ZlWhOP5olgzqFI4DQT2qSBYsbEhCAtq/grxEAmElYmtYkJwF09eJp1G3XXq7l2j2rwu4iiDY3ACasAFF6AJbkELtAEGj+AZvII368l6sd6tj3lrySpmDsEfWJ8/BsiV0Q==</latexit>
Voltage Control van Three-Phase Inverters
• De mogelijke states van de inverter zijn 23 standen van drie wisselschakelaars
• We kunnen de space vector bepalen met behulp van
u(t) =
<latexit sha1_base64="H6aTfuvMr/ylWMNBCroiUfm2zVk=">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</latexit>
2
3
h
ua + ub ej(2/3)⇡ + uc e
j(2/3)⇡
i
Voltage Control van Three-Phase Inverters
• De uitdrukking
h
u(t) = 23 ua + ub ej(2/3)⇡ + uc e
j(2/3)⇡
<latexit sha1_base64="H6aTfuvMr/ylWMNBCroiUfm2zVk=">AAACMXicbZDLSsNAFIYn3q23qks3wSJUxJrUhW4E0Y1LBatCEsNketKOnVyYOSOUkFdy45uIGxeKuPUlnNaC1x8Gfr5zDmfOH+WCK3ScJ2tsfGJyanpmtjI3v7C4VF1euVCZlgxaLBOZvIqoAsFTaCFHAVe5BJpEAi6j3vGgfnkLUvEsPcd+DkFCOymPOaNoUFg98T1dx80DH2NJWdEsi93SFxCjp0O6pcMIroubenNnd9PPeWkAM2D7i/iSd7oY+EFYrTkNZyj7r3FHpkZGOg2rD347YzqBFJmgSnmuk2NQUImcCSgrvlaQU9ajHfCMTWkCKiiGF5f2hiFtO86keSnaQ/p9oqCJUv0kMp0Jxa76XRvA/2qexng/KHiaa4SUfS6KtbAxswfx2W0ugaHoG0OZ5OavNutSEx2akCsmBPf3yX/NRbPhOg33rFk7PBrFMUPWyDqpE5fskUNyQk5JizByRx7JM3mx7q0n69V6+2wds0Yzq+SHrPcPPF2o/Q==</latexit>
i
• Kan in een complex getal worden uitgedrukt
u(t) = ux + juy
<latexit sha1_base64="ExgL/KswrcCeIc8Ui/4p4/84o2s=">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</latexit>
• Als we de spacevector omzetten van een
drie assig stelsel (a,b,c) naar een (x,y) stelsel
dan kan dit worden gedaan met

<latexit sha1_base64="ycZHMuH2jSmJO+BGd9pn7WuW16I=">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</latexit>
ux
uy
2
=
3

1
0
1
2
1
p2
3
1
2
1
2
p
3
2
3
ua
4 ub 5
uc
Voltage Control van Three-Phase Inverters
• De uitdrukking

2
=
3
ux
uy

1
0
1
2
1
p2
1
2
3
1
2
p
3
<latexit sha1_base64="ycZHMuH2jSmJO+BGd9pn7WuW16I=">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</latexit>
2
3
ua
4 ub 5
uc
• Komt overeen met
ux =
<latexit sha1_base64="Dlf19GCtnE1WlI6XYeDXfw04AFE=">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</latexit>
uy =
<latexit sha1_base64="A+EICGgRsOH/kMk4TpgL9mnYeco=">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</latexit>
2
3
2
3
⇥
va
h p
1
2
1
2 vb
3vb
1
2 vc
p
1
2
⇤
3vc
i
• We kunnen dit assenstelsel weer omzetten naar
een draaiend assenstelsel ( ↵
stelsel)
<latexit sha1_base64="HcMHfaY1mT3J36N/Pv+3JteAJZk=">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</latexit>
Voltage Control van Three-Phase Inverters

<latexit sha1_base64="lu2EeGH2PfM4RKWZvzq9SujeK6U=">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</latexit>
u↵
u
=
2
3

cos(!t)
sin(!t)
cos(!t +
sin(!t +
⇡
2)
⇡
2)

ux
uy