8-1

Switch-Mode DC-AC

Converters

EE 442/642

8-2

Some Applications: AC Motor Drives & PV Inverters

8-3

Switch-Mode DC-AC Inverter

Four quadrants of operation.

8-4

Half-Bridge Inverter:

1. Capacitors provide the mid-point.

2. The transistors TA+ and TA- are switched

using pulse-width-modulation (PWM).

8-5

Synthesis of a Sinusoidal Output by PWM

,,1f

fm

V

Vm s

f

tri

controla

Amplitude and frequency modulation ratios:

1,2

1)ˆ( 1 adaAo mforVmV

Peak value of fundamental voltage:

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.

For small values of mf ( e.g., ≤ 21), the two

signals must be synchronized to avoid

sub-harmonics.

8-6

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.

8-7

Fundamental Voltage as a Function of ma

1. Note the linear and the over-modulation regions; with square-

wave operation in the limit.

1,2

)ˆ(2

11 adAod mforVVV

8-8

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).

8-9

Square-Wave Mode of Operation

...7,5,3,2

)ˆ(

,2

)ˆ( 1

hVh

V

VV

dhAo

dAo

Fundamental and harmonic voltages:

8-10

Single-Phase Full-Bridge DC-AC Inverter

1. No need for capacitor mid-point.

2. The output voltage now switches between +Vd and -Vd.

8-11

PWM to Synthesize Sinusoidal Output: Bipolar Switching

Peak value of fundamental voltage: 1,ˆ1

adao mforVmV

1,4ˆ

1 adod mforVVV

8-12

Analysis with Ideal Filters

d

ood

D

ood

ddd

oodd

oo

oo

V

IVI

V

IVI

where

tIIti

titvtiV

tIti

tVtv

2),cos(

)2cos(2...)(

),()()(

)sin(2)(

),sin(2)(

2

12

*

*

1

1

8-13

PWM Unipolar Voltage Switching

1,ˆ1

adao mforVmV

1,4ˆ

1 adod mforVVV

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.

Legs A and B are controlled separately:

8-14

DC-Side Current with PWM Unipolar Switching

The ripple content is significantly less than when using

bipolar switching.

8-15

Sinusoidal Synthesis by Voltage Shift (Modified Square Wave)

...7,5,3,1),sin(4

)ˆ( hhVh

V dho

8-16

Fundamental and Ripple in Inverter Output

Active and Reactive Power: L

EEVQ

L

EVP oooo

1

2

01

1

1 )cos(),sin(

δ

8-17

Square-Wave versus PWM Operation

PWM results in much smaller ripple current.

8-18

Push-Pull Inverter (requires transformer with center tap)

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.

1,/ˆ1

adao mfornVmV

1,4ˆ

1 a

do

d mforn

VV

n

V

8-19

Three-Phase Inverter

1. Three inverter legs;

2. No mid-capacitor point is required.

8-20

Three-Phase PWM Waveforms

Legs A, B and C are controlled separately:

1,612.022

3ˆ1 adadaLL mforVmVmV

1,6ˆ

22

31 adLLd mforVVV

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.

8-21

Three-Phase Inverter Harmonics

8-22

Three-Phase Inverter Output

8-23

DC-Side Current in a Three-Phase Inverter

The current consists of a dc component and the

switching-frequency related harmonics.

8-24

Three-Phase Inverter: Fundamental Frequency

),cos(3

...)(

),()()()()()()(

*

*

d

oodd

CCnBBnAAndd

V

IVIti

titvtitvtitvtiV

(DC quantity only)

8-25

Three-Phase Inverter: Square-Wave Mode

8-26

Square-Wave Operation

8-27

Square-Wave and PWM Operation

PWM results in much smaller ripple current

8-28

PWM Operation: Short-Circuit States

8-29

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 cross-

conduction through the leg.

Impact on output voltage:

8-30

Effect of Blanking Time on Voltage

(during current zero crossing)

8-31

Programmed Harmonic Elimination

The notch angles are based on the desired output.

8-32

Current Control: Tolerance-Band Current Control

Variable switching frequency which depends on the load inductance,

motor back emf, and DC voltage.

8-33

Fixed-Frequency Operation

8-34

Transition from Inverter to Rectifier Mode