ELG4139: DC to AC Converters
Converts DC to AC power by
switching the DC input voltage (or
current) in a pre-determined
sequence so as to generate AC
voltage (or current) output.
IDC
+
VDC

Iac
+
Vac

Square Wave Converter
S1,S2 ON; S3,S4 OFF
SQUARE-WAVE
INVERTER
for t1 < t < t2
vO
T3
T1
D1
+ VO -
VDC
S1
D3
VDC
+ vO 
IO
T4
T2
D2
t1
S4
D4
VDC
S3
S2
S3,S4 ON ; S1,S2 OFF
for t2 < t < t3
EQUIVALENT
CIRCUIT
S1
vO
S3
S1
VDC
S4
t
t2
S3
t2
+ vO 
S2
S4
S2
-VDC
t3
t
Harmonics Filtering
DC SUPPLY
INVERTER
(LOW PASS) FILTER
LOAD
L
+
vO 1

BEFORE FILTERING
vO 1
+
C
vO 2

AFTER FILTERING
vO 2
Output of the inverter is “chopped AC voltage with zero DC component”. It
contain harmonics. An LC section low-pass filter is normally fitted at the
inverter output to reduce the high frequency harmonics. In some applications
such as UPS, “high purity” sine wave output is required. Good filtering is a must.
In some applications such as AC motor drive, filtering may not required.
Fourier Series for Harmonics Analysis
Fourier Series
ao 
an 
bn 
1

1
Harmonics of Square Wave
2
 f ( v ) d
(" DC" term)
0
2
f (v) cosn d

 0
1

Vdc
(" cos" term)

=t
-Vdc
2
 f (v) sinn d
2
(" sin" term)
0
Inverse Fourier
ao

1
f (v)  ao   an cos n  bn sin n 
2
n 1
where   t
an
2

1 
   Vdc d    Vdc d   0
  0


2

Vdc 

  cosn d   cosn d   0
  0


2

Vdc 
bn 
 sin n d   sin n d 
  0


Half-Bridge Inverter
S1 ON
Vdc S2 OFF
+
Vdc
2
S1
VC1
-
V +
o
0
G
+
VC2
-
t
RL
S2

Vdc
2
S1 OFF
S2 ON
Also known as the Inverter Leg!
Both capacitors have the same value. Thus the DC link is equally
spilt into two. The top and bottom switch has to be complementary.
Meaning, If the top switch is closed (ON), the bottom must be OFF,
and vice-versa.
Single Phase Full Bridge
LEG R
VRG
Vdc
2
LEG R'

2
t

2
t

2
t
+
Vdc
2
+
S1
-
Vdc
G
R
S3
 Vo -
R'
VR 'G
Vdc
2

Vdc
2
+
Vdc
2

S4
S2
Vdc
2
Vo
Vdc
Vo  V RG  VR 'G
G is " virtual groumd"
 Vdc
Single phase full bridge is built from two half-bridge leg. The switching in the
second leg is delayed by 180 degrees from the first leg.
Three Phase Inverter
+Vdc
+
Vdc/2
G
S1
S3
S5

+
Vdc/2
R
Y
iR
iY
S4
B
iB
S6
S2

ia
ZR
ib
ZY
N
ZB
Each leg is
delayed by 120
degrees
Pulse Width Modulation
h( x)  if ( k ( x)  c ( x)  1  if ( k ( x)  c ( x)  1  0) )
1
t1 t2
Modulating Waveform
1
M1
Sinusoidal modulating
waveform, vm(t)
Carrier, vc(t)
Carrier waveform
2

0
t
1
Regular sampling waveform, vs (t )
Vdc
2
0

t'1
t0 t1 t 2
t3 t 4 t 5
t'2
v pwm
t
Vdc
2
Regular sampling PWM
Triangulation method (Natural sampling). Amplitudes of the triangular wave
(carrier) and sine wave (modulating) are compared to obtain PWM
waveform. Analogue comparator may be used. Basically an analogue
method. Its digital version, known as REGULAR sampling is widely used in
industry.
Typical Configuration with 3-Wire DC Source
Load current may not reverse at the
same instants as does the load
voltage.
Current may lead or lag the output
voltage due to the presence of
capacitance and/or inductance in
the load circuit.
Diodes D1 and D2 in antiparallel
with each transistors permit load
current to flow if necessary.
For positive voltage we should turn
on the transistor connected to the
positive half, and for negative
voltage we should turn on the
transistor connected to the negative
half.
In the leading current case, the
output current reverses its direction
at tx. Output voltage reverses its
direction at T/2. Therefore, from tx
to T/2 the output current will flow
through D1.
In the lagging current case, the
output current reverses its direction
at tY. Output voltage reverses its
direction at T/2. Therefore, from T/2
to tY the output current will flow
through D2.
From the curves, it may be seen that the thyristors may start to conduct
at different instants in the half cycle, depending on the nature of the
load. To ensure that the thyristors will begin to conduct when required,
each must be gated continuously throughout the half
cycle.
Single-Phase Half-Bridge Inverter
(Rashid, Prentice Hall)
3-wire DC source
•
•
•
•
Consists of 2 choppers, 3-wire DC source
Transistors switched on and off alternately
Need to isolate the gate signal for Q1 (upper device)
Each provides opposite polarity of Vs/2 across the load
Q1 on, Q2 off, vo = Vs/2
Peak Reverse Voltage of Q2 = Vs
Q1 off, Q2 on, vo = -Vs/2
Waveforms with Resistive Load
Output Voltage
rms value of the output voltage, Vo

2
Vo  
 To

1
2

V
Vs

0 4 dt   2


To
2
2
s
Fourier Series of the Instantaneous Output Voltage
ao 
vo     an cos(nt )  bn sin(nt ) 
2 n 1
ao , an  0
0


Vs
1  Vs
bn   
sin(nt )d (t )   sin( nt ) d (t ) 
   2
2
0

2Vs
bn 
 n  1,3,5,...
n

2Vs
vo  
sin(nt )
n 1,3,5,.. n
Load Current for a Highly Inductive Load
Transistors are only switched on for a quarter-cycle, or 90
Performance Parameters
• Harmonic factor of the nth harmonic (HFn)
Von
HFn 
Vo1
for n>1
Von = rms value of the nth harmonic component
V01 = rms value of the fundamental component
• Total Harmonic Distortion (THD): Measures the “closeness” in
shape between a waveform and its fundamental component
1

1
THD 
(  Von2 ) 2
Vo1 n 2,3,...
Performance Parameters
• Distortion Factor (DF): Indicates the amount of HD
that remains in a particular waveform after the
harmonics have been subjected to second-order
attenuation.
1
2
1    Von   2
DF 
   2  
Vo1  n  2,3,...  n  
DFn 
Von
Vo1n 2
for n>1
• Lowest order harmonic (LOH): The harmonic
component whose frequency is closest to the
fundamental, and its amplitude is greater than or equal
to 3% of the amplitude of the fundamental component.
Single-Phase Full-Bridge Inverter
•
•
•
•
Consists of 4 choppers and a 3-wire DC source
Q1-Q2 and Q3-Q4 switched on and off alternately
Need to isolate the gate signal for Q1 and Q3 (upper)
Each pair provide opposite polarity of Vs across the load
Q1-Q2 on, Q3-Q4 off, vo = Vs
+ Vs -
Q3-Q4 on, Q1-Q2 off, vo = -Vs
- Vs +
When the Load is Highly Inductive
Turn Q1-Q2 off – Q3-Q4 off
Turn Q3-Q4 off – Q1-Q2 Off
Load Current for a Highly Inductive Load
Three-Phase Inverter
Design Constraints of a Pure Sine wave Inverter
Quantity
Details
Voltage
Convert 12VDC to 120 VAC
Power
Provide 300 W continuous
Efficiency
> 90% efficiency
Waveform
Pure 60 Hz sinusoidal
Total Harmonic
Distortion
< 5% THD
Physical Dimensions
8” x 4.75” x 2.5”
Cost
$175.00
Required Components for Design
12 V DC Input
from vehicle battery)
PWM Control
Circuit
Half-bridge
Converter
Transformer
Low-pass
Filter
Full-bridge
Inverter
Sinusoidal PWM
Controller
120 VAC,
60 Hz, 300 W
Output
PWM Controller
• Produces two complementary
pulses to control half-bridge
transistors.
• Problem:
– Voltage may drop when
the input voltage is
decreased.
• Solution:
– A feedback network may
be added for voltage
regulation.
Half-Bridge Converter
• Chops the 12 VDC to produce
a 12 V, 100 kHz, square pulse
• Problem:
– IRF740A MOSFETs has an
Rds(on) = 0.55Ω, resulting in
high power losses.
• Solution:
– Choose IRF530 MOSFETs
with an Rds(on) = 0.16 Ω
Full-bridge Inverter
• Converts 170 VDC to a
120 Vrms, 60 Hz, sine
wave
• IRF740A MOSFETs
– Vdss = 400 V
– Id = 10 A
– Rds(on) = 0.55 Ω
Software Flow Diagram
(Dr. Yaroslav Koshka)
Initialize all
variables
no
Count0 = 300 (300 duty cycles)
yes
300 duty cycle
values?
Output 1 = high, Output 2 = low
duty cycle table (increment pointer)
Output 1 = low, Output 2 = high
Decrement Count0 by 1
Duty cycle and sampling period timer
no
no
Has duty cycle been
reached?
yes
One Sampling
Period?
ye
s
Low-pass Filter
• 2nd order L-C filter
– Filters to retain a 60
Hz fundamental
frequency
– Few components
– Handle current
– Wind inductor (fine
tune)
PCB Layout
Case Study: Solar System Using Inverters
Stand Alone; Simple Grid Tied; Grid Tie with Battery
Solar Schoolhouse and San Mateo College
Simple Grid-Connected System
Utility
Solar Array
Inverter
Distribution
Panel
Subpanel
Solar AC in from
Inverter
Lightning surge
arrestor
Stand Alone Residential System
Solar Array
Charge
Controller
Battery
DC to AC Inverter
Distribution Panel
AC
Distribution Panel
DC
Small Stand
Alone
System
(to power an
office)
Solar Array
Charge
Control
Storage:
Battery
“Fuel Gauge”
Inverter DC to
AC