Switch-Mode DC-AC
Converters
EE 442/642
8-1
Some Applications: AC Motor Drives & PV Inverters
8-2
Switch-Mode DC-AC Inverter
Four quadrants of operation.
8-3
Half-Bridge Inverter:
1. Capacitors provide the mid-point.
2. The transistors TA+ and TA- are switched
using pulse-width-modulation (PWM).
8-4
Synthesis of a Sinusoidal Output by PWM
Amplitude and frequency modulation ratios:
ma 
Vcontrol
f
, mf  s ,
Vtri
f1
For small values of mf ( e.g., ≤ 21), the two
signals must be synchronized to avoid
sub-harmonics.
Peak value of fundamental voltage:
1
ˆ
(VAo )1  maVd ,
2
for
ma  1
The harmonics in the inverter output
appear as sidebands around mf, 2mf,
3mf, …,kmf,…
Only odd harmonics are present in
the output voltage waveform →mf
should be an odd integer value.
8-5
Harmonics in the DC-AC Inverter Output Voltage
1. The fundamental voltage is proportional to the amplitude modulation index.
2. Some harmonics can be larger than the fundamental component.
8-6
Fundamental Voltage as a Function of ma
1. Note the linear and the over-modulation regions; with squarewave operation in the limit.
1
2
ˆ
Vd  (VAo )1  Vd ,
2

for
ma  1
8-7
Harmonics in the Over-Modulation Region
The side bands start to spread out to a point where all the integer harmonics
appear in the frequency spectrum (including the low-order harmonics which
are hard to filter).
8-8
Square-Wave Mode of Operation
Fundamental and harmonic voltages:
2
ˆ
(VAo )1  Vd ,

2
ˆ
(VAo ) h  Vd , h  3,5,7...
h
8-9
Single-Phase Full-Bridge DC-AC Inverter
1. No need for capacitor mid-point.
2. The output voltage now switches between +Vd and -Vd.
8-10
PWM to Synthesize Sinusoidal Output: Bipolar Switching
Peak value of fundamental voltage:
Vˆo1  maVd ,
for
4
ˆ
Vd  Vo1  Vd ,

ma  1
for
ma  1
8-11
Analysis with Ideal Filters
vo (t )  2Vo sin(1t ),
io (t )  2 I o sin(1t   )
Vd id* (t )  vo (t )io (t ),
 id* (t )  ...  I d  2 I d 2 cos(21t   )
where
VI
VI
I d  o o cos( ), I d 2  o o
VD
2Vd
8-12
PWM Unipolar Voltage Switching
Legs A and B are controlled separately:
Vˆo1  maVd ,
for
4
ˆ
Vd  Vo1  Vd ,

ma  1
for
ma  1
The harmonics in the inverter output
appear as sidebands around 2mf,
4mf, 6mf, …
Note the harmonics at and around
mf, 3mf, 5mf, … are absent → lower
harmonic content.
Note also only odd harmonics are
present.
8-13
DC-Side Current with PWM Unipolar Switching
The ripple content is significantly less than when using
bipolar switching.
8-14
Sinusoidal Synthesis by Voltage Shift (Modified Square Wave)
4
ˆ
(Vo ) h  Vd sin(h ), h  1,3,5,7...
h
8-15
Fundamental and Ripple in Inverter Output
δ
Vo1Eo
V01Eo cos( )  Eo2
sin( ), Q 
Active and Reactive Power: P 
1L
1L
8-16
Square-Wave versus PWM Operation
PWM results in much smaller ripple current.
8-17
Push-Pull Inverter (requires transformer with center tap)
Vˆo1  maVd / n,
Vd ˆ
4 Vd
 Vo1 
,
n
 n
for
for
ma  1
ma  1
1. vo switches between Vd/n and –Vd/n where n is the transformer turn
ratio.
2. Advantage: no more than one switch conducts at any time → less
voltage drop. Also the control drives have the same ground.
3. Difficulty: strong magnetic coupling between the two half windings is
required to reduce the energy associated with the leakage inductance.
8-18
Three-Phase Inverter
1. Three inverter legs;
2. No mid-capacitor point is required.
8-19
Three-Phase PWM Waveforms
Legs A, B and C are controlled separately:
VˆLL1 
3
maVd  0.612maVd ,
2 2
3
6
ˆ
Vd  VLL1 
Vd ,

2 2
for
for
ma  1
ma  1
The frequency modulation index, mf, should be
an odd number that is a multiple of 3 to cancel
out the most dominant harmonics
See harmonic content of line voltage during
linear modulation in the next slide.
8-20
Three-Phase Inverter Harmonics
8-21
Three-Phase Inverter Output
8-22
DC-Side Current in a Three-Phase Inverter
The current consists of a dc component and the
switching-frequency related harmonics.
8-23
Three-Phase Inverter: Fundamental Frequency
Vd id* (t )  v An (t )i A (t )  vBn (t )iB (t )  vCn (t )iC (t ),
3Vo I o
 i (t )  ...  I d 
cos( ),
Vd
*
d
(DC quantity only)
8-24
Three-Phase Inverter: Square-Wave Mode
8-25
Square-Wave Operation
8-26
Square-Wave and PWM Operation
PWM results in much smaller ripple current
8-27
PWM Operation: Short-Circuit States
8-28
Blanking Time: Non-Ideal switches
Instantaneous switching from ON
to OFF and vice versa.
In practice, the turn-on and turn-off
times are finite (non-zero). Blanking
Time is chosen to avoid crossconduction through the leg.
Impact on output voltage:
8-29
Effect of Blanking Time on Voltage
(during current zero crossing)
8-30
Programmed Harmonic Elimination
The notch angles are based on the desired output.
8-31
Current Control: Tolerance-Band Current Control
Variable switching frequency which depends on the load inductance,
motor back emf, and DC voltage.
8-32
Fixed-Frequency Operation
8-33
Transition from Inverter to Rectifier Mode
8-34