Examination Aid Sheet
Faculty of Applied Science & Engineering
CONST
-
12
=
50 8.857-12
=
light
Equivalentckt
line
Candidate’s signature:_________________
h
4TLE-7ITm/A?
-bu9 G
of n 15P
3E8 [m/3]
=
Vcc&-Ucc
to
+
I
Vo
openloop hain
I
Gain Vout.
-V
=
Lynne
parallel
41 12
+
222
C + cr
C
+
V Tr
=
-V L
i 10
2
v Vo
=
i
C2
=
=
t/EUdt
+
I/
=
c onnect
not
DiffiV+&V->
to
Current Divider
input.(105-100;As
loop gain K
in
Closed
Wit ILi2
=
+
=
VoltageDivider in series;Vi 1,
limitval
to
>
R, R2
R1 +R2
↳ 2
41 +22
R1 + R2
resistor
Linductor
·Ccapacitor
inverting
Un
Lynne
series
·R
Up for noninverting input
Un for
input
·+U
Up
(Kailing (in
Candidate’s name:____________________
IC2/Nm2]3 N
Op-Amp
I
Energy -> Work
E-19[C?
e 1.6
Mo=
=
P
K 8.99 E9 [Nm2/C1
=
ECE212
Subject:___________________________
1eV 1.602E-19]
Both sides of the sheet may be used;
must be printed on 8.5” x 11” paper.
WcIt)
idt
PR2
=
ICV2
IS} *ise
VToT
RRM2 [ToT
parallel:ii=
Source Transformation
Vs is
I
IVin
noninvert
R2
RI
I
I
vi.
E
+
No
I
Therein & Norton
e
vo m
=
-
by superposition
-Vo
Vo
kVp=cK/I1/RK) ,
=
follower Buffere
voltage
Me
Difference Amp
m
·
i
D
=
a
m
II
C
vo
+Va
I
I
Vo
-
v,
I
Va
V2
E
is
ovo
I
=
-
RC
comparator
And &dep
Isc;Rth for volt-> short,
Voc
=>
or
Dep => *terminal
if
if
V2 then Vo
v,
<
V, then Vo =-Vcc
=
test src(vol/cur);call,I
EworIE:Rth=Utest/Itest, equ cktY
FARth. Rth so, supply power.
sinusoid
X(t) Xmsin Lt
=
XmSincwt)
=
XmCos(rt
=
XmCos(Wt-5112)
-
XmSin(Wt+Tzs
Xmsin(wt XmSin(Wt1T2)
=
=
f 117,
W
=
:.T 2T/r
=
ctime
Xmsin (Wt
=
Ve-charge Vm(1-2
XmSin(Wt+4)
&GTO 180
sin (2
B1 bin2Cos
+
=
Impedance
+
Cob2Sin
z V/1
=
=
z
+
Magnetically Coupled
=
[m].
·
z(W) 4(w)
=
+
=
VLOz
j X (w)
z0z R+jX
+
no
=
=
-
=
=
+
Impedence in series:270l=Izi
supermeshTT) atBut Er
parallel:1/Ext [(1/Ei)
Admittence:
y zt, y ymL0y G jB2n
in
EFIE
Currentsource)super
mesh) kVL, #9)currentsuc eqa.
Steps:
is mesh
2)
analysis, every
+
=
C: Conductance
=
B:
+
voltage
3) solve
susceptance
12
its
or
I
KVL> redraw the ckt;
rep induced voltage;
E2 + FAE mutual x3 FEDi
=
func.
>
"I complex II"
Can use
=
=
I
voltage rise (-)voltage MAE
Frequency mutual voltage (jwM)1
Time Domain mutual
d(R x )
=
For resistor:E R creal
node
self-inductance -> L: Mutual
It57/,i3RK)Et NetEEA,
voltage drop for current's direction;
=
z
Networks
otherwise,
·
imaginary parts
part,
ZITA vol sourceI
For inductor:z (WL);w o, z o, short cky
mesh ij. I
every mesh & dir (br-CCW/CW) For
capacitor:z -1/(WCjs w-o, z xy, open ct
sourceEY), volt rise" ":A KUL
supernode zEref
=
(ob(2 B) C032cos-binnsin
=
Ume= Vm<lOU-Dis
S
-
by 4 Vc-discharge Vm(2-**)
by
4
-
=
-
-t-to
=
periods
delays
RC
VCt= Voe
25f
21T
=
Xmsin (Wt+1) leads Xmsin(Wte
invertingCob(Wt+O)
Circuit
B
At
RC
XmCoS (WH XmCoS(WtITL)
-
-t- to
I
analysis
open
=
+Vcc
Currentt o Volt Converter
Vo= Ris
curi-
Isc: Rth Voc/1sc
(openloop hairs
>
Vop/152;
=
HESrc, Rth=
Beq
or
=>
d
V.
Rth
*
Ind Voc
differentiator
·voit
I
E
R3
time,
=
=>
+
noninvert summer
vo
#
+
=
ERth/Rx
(2V, Ev2 5Vs)
src each
Isc:IN ISC
RL short
t
Vo
power
Vsrc, Ibr4.
Linearity of linear ckt
Effic, max 50%
RopenEiVop:Vth=Uop
↑max 0.54s;
=
2 FM/GainD*/-
+
One
=
**SrC,
=
invert summer
It
I
Gain=
1+R2/R,
Vin
H
Superposition
Vth2 /4Rth= 4IN2Rth
only reali Pmax=
Ps Vth2 / 2Rth; Total P in ckt
Total P =
amp
·Vo= (1 R2/R1) Vin
t
EcktR Th/N,F
Rth RL.
Gain=- R2/RI
n
m r-
=
=
Vo
E
I
vin
Vo =-(R2/R1> Vin
O
(for DC)
MaxP transfer RL= Rth
inverting amp
R2
is Vs/Req
xReq
=
nu
Energy
·
if both currents flows
(t)
in/out dot;1->
Analysis:
if
one out, one in.
·
I4ct
Wit
=
+
IL2 is it I
Mit TzIt);
(M = b(h1(2))
Complingefficienttoe
·
k0
=
k
=
1
zero
=
coupling
perfectcoupling
:
(20.99)
-
M
ckt
2nd
power in
Voltaa
me
Vs (t)
I
instantaneous
canatte
=
sedgYEts Radars
+
3b xc
32
+
+
N
+ Vct
vs
=
5
0
=
2!
S+ 23 WoS
3
-
I
3 1
=
3
<
damped
over
x+(t)
x (t)
under
x (
x(t) x + (t)
=
Solve IVP
by
+
C,
=
RNs values Xrms
Max
power
=
=
VmImCoS(Or-DiC=UrmsIrmscos(Or-Oil
d5Sx2dt:Urms
-
5Vm, Irms= 5 Im
transfer, when z=Eth*
=
Wo
freq
eSt+ Crest
+
e2t(C,sint+CrCost)
(31.2
=
IVclOts
in 104 i2
Vcl0-3
=
Naturalresponseof charega
2
=
Bis
Vc'Ot) iclOts/C
=
=
X'CO)
0
=
+
22bit 2 + @sit
=
+
Xss(t)
+
Xc0),
+ pct dt
=
0
+
wo:natural
critically
1
=
=
3 (1/RC) / (2 Wo>
ratio
damping
c
pCt V(iCt VmCoS (Wt+Ov).ImCoS (Wt+Oi)
(W1
=
=
3
3
+
3 (R/L) / (2 Wo)
Power
average Power (NCP I1
Vi ( (di/dt);ic c (dv/dt);kCL;kVL
=
Sinusoidal steady state
;
10);in 'COts
=
VclOt)/L
Forced
resp
Alsteady state resp;particular
bol
of
CE.
First-order ckt
IEr*
RC circuit
Mickt*
BR at
is
0-Rtckt=>L
short, I
O+EtcKt=>
current arc,
1
ReatU=Vs e
open,
a ticte-is tr
4(2510/ CAVo-
C voltsrc, Vot=V-
Itx10t)
t
#
->
btckt,L.C,Calt= RthC, I L/ Rth
=
It - betckt,L
*
short,
Copen,
cal
X(P)
[brc1.
t/t
X (t) x(0) [X10+) -X(b)1e=
inverse
Transformer
Ideal
1
+
(V2/Vi3
otherwise
=
-
N1/N2).
N2 is with load.
1
(
ki
(N2/ Nis
Partial
=
=>
FIs)
(A2/Ni) Since dotat both "+" or both"-"
=
(12/11) (N1/N2) since same
2)
hip fite=[kepit
polarity;otherwise
sp.
=
13
=
-
full power
kn
-
pn
firse oitease...an
=
fraction expansion
lessorDamisinserveso
=
delivered to the
+-+3
Final value this
Yi M2)zu
=
3
+
Pic xF(s) 1s pi
-
inputimpedance:EI
krePrt+... + knePut]. rct)
+
primary winding
mfit=msFcs: mfile=hmsFix
Complex Power
Sinusoidal Response
VE UrmsIFrms=1rms/12ms/cOr-Oic=P+ jR
complex power IVAIS=Irmsz
iupH xc XACoS(rt+4,
b 1s1= 1Vrms/1I*ms) /CP2+O
apparent power IVAI
steady state output Yss(t) XAlTjns/cos(wt +4
=
=
=
=
=
=
real/average power IWIP ReS33= cos(Or-Dic
Site
Power factor
minimum
=
reactive
power
Leading
Lagging
A
IVARI R
Im533= bbinCOU-Dic
=
pf=P/>=Cob(Or-0ic
Or-Oi c0, Q
Or-0; >0,0
=
inputvoltage
Cob(02)
heg (cap)
pob
(inde
Itt2Hvoltagecurrent YRMS:PHEREY power PACEEY
=
Power factor correction, real power, reactive
power -40.
c
Ko
Imx
↳
↓Ov-0i
Re
-
I
+
poles,
a leads
lok, EB(H 0,
=
"Gusjus
w>
"Gusjus
for
-
case:So
(I/).
=
X:
w
WCE, H1 0dB,W I,3 less, overshootbig,
wit, slope 140dB/decade. I
11800,
W lot, LH 0,w> h, H
=
=
=
12 Ws t, 3Ablope;W=1/2, 4H 190
e, FE 2H I90N,
=
freq:
Wo= 1/dE2 ;
=
we
slope
W=1/2, GH
"Gusjus
"Gusjus
I20d/decade
=
45" N
=
necess in South one
a
1
High-pass
normal
=
=
s
is const
0)
+
impedence Im EBot 0, Fiks, 92) xj, w
↓TERRe.
=
--
=
w
1
=
plot
1H1 20log,o(ko) E:CH 00
aclags
>
↳
Bode
23(jW2 15W2,02361
+
(p
Resonance
FN55slopesDoNddecadeFeteit,
I
y Ou-Dip
1
As=
jw,*7zeros, is
PctanOorig -tan Ofinal YO
=
WUrms
impulses
1
=
0
frequencies
2 d(+to]
We I
=
=
+
1B)
Ispc+/[I)"+c1
Quality factor
0
Wo/B d(/c)/R BI
=
=
R(((/) +1
Band-stop
WLOWOWH2
corner
=
-
>w
i
22f:
=
>W