ECE 442 Power Electronics 1
Single-phase half-bridge inverter
ECE 442 Power Electronics 2
Operational Details
• 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
3-wire DC source
ECE 442 Power Electronics 3
Q1 on, Q2 off, vo = Vs/2
Peak Reverse Voltage of Q2 = Vs
ECE 442 Power Electronics 4
Q1 off, Q2 on, vo = -Vs/2
ECE 442 Power Electronics 5
Waveforms with resistive load
ECE 442 Power Electronics 6
Look at the output voltage
1
222
0
2
4 2
oT
s so
o
V VV dt
T
rms value of the output voltage, Vo
ECE 442 Power Electronics 7
Fourier Series of the instantaneous output voltage
1
0
0
1,3,5,..
cos( ) sin( )2
, 0
1sin( ) ( ) sin( ) ( )
2 2
21,3,5,...
2sin( )
oo n n
n
o n
s sn
sn
so
n
av a n t b n t
a a
V Vb n t d t n t d t
Vb n
nV
v n tn
ECE 442 Power Electronics 8
rms value of the fundamental component
1,3,5,..
1
1
2sin
21
20.45
so
n
so
o s
Vv n t
n
VV
V V
ECE 442 Power Electronics 9
When the load is highly inductive
ECE 442 Power Electronics 10
Turn off Q1 at t = To/2Current falls to 0 via D2, L, Vs/2 lower
+
Vs/2
-
+
Vs/2
-
ECE 442 Power Electronics 11
Turn off Q2 at t = To
Current falls to 0 via D1, L, Vs/2 upper
+
Vs/2
-
+
Vs/2
-
ECE 442 Power Electronics 12
Load Current for a highly inductive load
Transistors are only switched on for a quarter-cycle, or 90
ECE 442 Power Electronics 13
Fourier Series of the output current for an RL load
2 21,3,5,...
1
2sin( )
( )
tan ( )
o o so n
n
n
v v Vi n t
Z R jn L n R n L
n L
R
ECE 442 Power Electronics 14
Fundamental Output PowerIn most cases, the useful power
21 1 1 1 1
2
1 2 2
cos
2
2 ( )
o o o o
so
P V I I R
VP R
R L
ECE 442 Power Electronics 15
DC Supply Current
• If the inverter is lossless, average power absorbed by the load equals the average power supplied by the dc source.
• For an inductive load, the current is approximately sinusoidal and the fundamental component of the output voltage supplies the power to the load. Also, the dc supply voltage remains essentially at Vs.
0 0
( ) ( ) ( ) ( )T T
s s o ov t i t dt v t i t dt
ECE 442 Power Electronics 16
1 1
0 0
11
1( ) 2 sin( ) 2 sin( )
cos( )
T T
s o o ss
os o
s
i t dt V t I t dt IV
VI I
V
DC Supply Current (continued)
ECE 442 Power Electronics 17
Performance Parameters
• Harmonic factor of the nth harmonic (HFn)
1
onn
o
VHF
V for n>1
Von = rms value of the nth harmonic component
V01 = rms value of the fundamental component
ECE 442 Power Electronics 18
Performance Parameters (continued)
• Total Harmonic Distortion (THD)• Measures the “closeness” in shape between a
waveform and its fundamental component
12 2
2,3,...1
1( )onno
THD VV
ECE 442 Power Electronics 19
Performance Parameters (continued)
• Distortion Factor (DF)• Indicates the amount of HD that remains in a
particular waveform after the harmonics have been subjected to second-order attenuation.
12 2
22,3,...1
21
1 on
no
onn
o
VDF
V n
VDF
V n
for n>1
ECE 442 Power Electronics 20
Performance Parameters (continued)
• 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.
ECE 442 Power Electronics 21
Single-phase full-bridge inverter
ECE 442 Power Electronics 22
Operational Details
• 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 Vsacross the load
ECE 442 Power Electronics 23
Q1-Q2 on, Q3-Q4 off, vo = Vs
+ Vs -
ECE 442 Power Electronics 24
Q3-Q4 on, Q1-Q2 off, vo = -Vs
- Vs +
ECE 442 Power Electronics 25
When the load is highly inductiveTurn Q1-Q2 off – Q3-Q4 off
ECE 442 Power Electronics 26
Turn Q3-Q4 off – Q1-Q2 off
ECE 442 Power Electronics 27
Load current for a highly inductive load
ECE 442 Power Electronics 28
Example 6.3 – MultiSim7
Q11 V 0 V
Q21 V 0 V
Q31 V 0 V
Q41 V 0 V
D1DIODE_VIRTUAL
D2DIODE_VIRTUAL
D3DIODE_VIRTUAL
D4DIODE_VIRTUAL
R
10 Ohm
L
31.5mH
C
112uF
XFG1
C11000uF
C21000uF
ECE 442 Power Electronics 29
Example 6.3 using the scope
Vs220 V
Q11 V 0 V
Q21 V 0 V
Q31 V 0 V
Q41 V 0 V
D1DIODE_VIRTUAL
D2DIODE_VIRTUAL
D3DIODE_VIRTUAL
D4DIODE_VIRTUAL
R
9 Ohm
L
31.5mH
C
112uF
XFG1
C11000uF
C21000uF
XSC1
A B
G
T
Rs
1 Ohm
ECE 442 Power Electronics 30
Fourier Analysis of load current