Switching rules Either A+ or A– is always closed, but never at the same time * Either B+ or B– is always closed, but never at the same time * *same time.

Switching rules

•Either A+ or A– is always closed, but never at the same time *

•Either B+ or B– is always closed, but never at the same time *

*same time closing would cause a short circuit from Vdc to ground

Corresponding values of Va and Vb

• A+ closed, Va = Vdc

• A– closed, Va = 0

• B+ closed, Vb = Vdc

• B– closed, Vb = 0

H BRIDGE

Vdc

Load

A+ B+

A– B–

Va Vb

Corresponding values of Vab

•A+ closed and B– closed, Vab = Vdc

•A+ closed and B+ closed, Vab = 0

•B+ closed and A– closed, Vab = –Vdc

•B– closed and A– closed, Vab = 0

•The free wheeling diodes permit current to flow even if all switches did open

•These diodes also permit lagging currents to flow in inductive loads

H BRIDGE

Vdc

Load

A+ B+

A– B–

Va Vb

Figure 1. Vcont , –Vcont , and Vtri

Vcont –VcontVtri

But is a square wave output good enough? Not for us! Sinusoidal load voltage is usually the most desirable. But how do we approximate a

sinusoidal output with only three states (+Vdc, –Vdc, 0) ?

The answer: Unipolar PWM modulation

Vcont > Vtri , close switch A+, open switch A– , so voltage Va = Vdc

Vcont < Vtri , open switch A+, close switch A– , so voltage Va = 0

–Vcont > Vtri , close switch B+, open switch B– , so voltage Vb = Vdc

–Vcont < Vtri , open switch B+, close switch B– , so voltage Vb = 0

A+ closed, A– open, so Va in Figure 2 = Vdc. Else A– closed, A+ open, so Va = 0.

B+ closed, B– open, so Vb in Figure 2 = Vdc. Else B– closed, B+ open, so Vb = 0.

Vdc

Idealized Load Voltage (Va – Vb) Waveform–Vdc

0

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1

1.5

ma = 0.50

(linear region)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1.5

-1

-0.5

0

0.5

1

1.5

ma = 1.5

(overmodulation region)

Figure 6. Variation of RMS value of no-load fundamental inverteroutput voltage (V1rms

) with ma

ma0 1

V1rms

linear overmodulation saturation

asymptotic to square wave value2

4 dcV

2dcV

2mf cluster

4mf cluster

2dcVTable 1. Load voltage harmonic RMS magnitudes with respect to (for large mf )

Harmonicma = 0.2

ma = 0.4

ma = 0.6

ma = 0.8

ma = 1.0

1 (fundamental) 0.200 0.400 0.600 0.800 1.000

2mf ± 1 0.190 0.326 0.370 0.314 0.181

2mf ± 3 0.024 0.071 0.139 0.212

2mf ± 5 0.013 0.033

4mf ± 1 0.163 0.157 0.008 0.105 0.068

4mf ± 3 0.012 0.070 0.132 0.115 0.009

4mf ± 5 0.034 0.084 0.119

4mf ± 7 0.017 0.050

(For control electronics wiring with solid #22 wire, use green for ground, red for

+12Vdc, violet for –12Vdc, and blue for all others)

Figure 7. PWM inverter control circuit(note – be sure to use the wiring color code to

make troubleshooting easier)

8 5

Op Amp1 4

0.01µF(freq. control)

500Ωtrimmer

7 1

Waveform Gen.8 14

1kΩ

1kΩ0.01µF 100kΩ

Approx 22kHztriangle wave

Filtered and buffered

triangle wave

High-pass filter to block DC

8 5

Comp1 4

1.5kΩ, ½W

270kΩ

1.5kΩ, ½W

1kΩ

1kΩ

270kΩ

+12Vdc regulated from 2W, DC-DC converter output

–12Vdc regulated from 2W, DC-DC

converter output

V(A+,A–) V(B+,B–)

Vcont

Vcont

red

green

blue

blue

blue

violet

blue

violet

violet violet

green

red

red

green

The IC is upside down to minimize wiring clutter

These ½W resistors can get hot - keep them off the surface of the protoboard

10kΩ8.2kΩ

5kΩtrimmer

–Vcont

blue

Vcont

60Hz AC signal from AC wall wart and 500Ω potentiometer

Protoboard common connected to common of2W, DC-DC converter outputSee Appendix for IC pin configurations

4”

Jack for AC wall

wart

Jack for DC wall

wart

–12Vdc isolated rail

+12Vdc isolated rail

2W, DC-DC converter

500Ω pot for adjusting Vcont

Protoboard common(i.e., the green wires)

Figure 8a. The 10” long piece of 1” x 6” wood piece with inverter control circuit mounted in the lower 4”

You will build this part the following

week

Figure 8b. Zoom-in of protoboardMount triangle wave generator IC upside down to minimize

wiring clutter

2W, DC-DC converter

+12Vdc isolated rail (red)

–12Vdc isolated rail (violet) Protoboard common (i.e., the green wires)

Input from 12Vdc

regulated wall wart

Isolated outputs from 2W, DC-DC converter (red = +12V, violet = –12V,

green = common)

Zoom-in of DC-DC converter

Triangle wave generator

Dual Op Amp

Dual Comparator

Figure 10. Rise and fall times of the triangle wave

Approx. equal rise and fall times

Figure 12. Output control voltages V(A+,A–) and V(B+,B–), with respect to protoboard common, with Vcont = 0 (i.e., the ma = 0 case)

Figure 15. Idealized Vload, with ma just into the overmodulation region

Figure 16. Idealized Vload observed in the scope averaging mode, with ma in the linear region

Figure 17. Idealized Vload observed in the scope averaging mode, with ma just into the overmodulation region

Figure 18. Idealized Vload observed in the scope averaging mode, with ma almost into the saturation (i.e., square wave) region

Figure 19. FFT of idealized Vload in the linear region with ma ≈ 1.0, where the frequency span and center frequency are set to 100kHz and 50kHz, respectively

2mf cluster (46kHz)4mf cluster (92kHz)

60Hz component

Figure 23. Near saturation, the 3rd harmonic magnitude is 0.30 of the fundamental

Figure 24. Near saturation, the 5th harmonic magnitude is 0.13 of the fundamental

One firing circuit for each MOSFET, with each firing circuit mounted on a separate protoboard. A– and B– can share a power supply and ground. A+ and B+ must each use separate power supplies and grounds. Do not connect any of these grounds to the ground of the control circuit.

O+ O–

(see Figure 2 for connections)Powered by +12Vdc regulated supply

(isolated from control circuit)

10kΩ

0.1µF10Ω1.2kΩ

MOSFET

G D S

100kΩ

5 4

Opto

8 1

5 4

Driver

8 1

Figure 1. Isolated firing circuit with optocoupler

and gate driver

Outline of protoboard

A+ and B+ use inverting drivers. A– and B– use non-inverting drivers. The optocouplers provide an additional inversion.

green

green

green

blue for A+,B+,violet for A–,B–

blue

blue

red

blue

Grounds (isolated from control circuit)

Wait until next week

Figure 2. Physical layout of firing circuits(A+ opto and driver are powered by a 12Vdc isolated DC-DC

converter. Likewise, B+ has a 12Vdc isolated DC-DC converter. A– and B– are powered by the DC wall wart.)

Individual protoboard for each firing circuit

Optically-isolated firing circuits. Mount drivers near the MOSFETs

A+

FiringA–

FiringB+

FiringB–

Firing

Control Circuit from Previous Lab

Jack for DC wall

wart

O+ O– O+ O– O+ O– O+ O–

V(A+,A–) V(B+,B–)

–12Vdcregulated

blue

blue blue

violet violet

Jack for AC wall

wart

8”

Figure 3. Layout of inverter control circuit and isolated firing circuits

Figure 4. Zoom-in view of A+ and A– isolated

firing circuits

DC-DC converter for A+

Pin configuration for 6N136 optocoupler

Input from 12Vdc wall wart

Isolated output

V(A+,A–) – V(B+,B–) with control circuit driving optos

V(A+,A–)

Opto A+ output

V(A+,A–)

Opto A– output

We want the opto output waveforms to look identical in this test in order to preserve symmetry in firing

Opto A+ output

Opto A– output

V(A+,A–)

A+ driver output

V(A+,A–)

A– driver output

A+ driver output

A– driver output

We want no overlap in driver “on” times, so there will be no idling current

After finishing A+ and A-, perform same checkout for B+ and B-

Figure 1. Physical layout of inverter

MOSFETA+

MOSFETA–

MOSFETB+

MOSFETB–

H-Bridge and Filters

Individual heat sink for each MOSFET

–Vdc

+

–Vac (Output)+

b

a

A+

FiringA–

FiringB+

FiringB–

Firing

Control Circuit from Previous Lab

Jack for DC wall

wart

O+ O– O+ O– O+ O– O+ O–

V(A+,A–) V(B+,B–)

–12Vdcregulated

blue

blue blue

violet violet

Jack for AC wall

wart

Vdc Input Power

10µF, 50V, high-frequency capacitor

–

Vdc

+

Figure 2. Zoom-in of filter details for Vdc input and Vac output sections of Figure 1(points “a” and “b” correspond to the two sides of the inverter output)

10µF, 50V, bipolar, high-frequency capacitor

100µH, 9A or 10A inductor

–

Vac

+

Point “a” in H-bridge

Point “b” in H-bridge

Figure 3. H-Bridge wiring color scheme (using #16 stranded)(note – wire crossings are not connected)

A+ A– B+ B–

G D S G D S G D S G D S

–

Vdc

+

–

Vac

+

red

orange

blue

black

VGS of A+

VGS of A–

blanking time toeliminate overlap

actual MOSFETturn on

+VDS of A+

–

–VDS of A–

+

A+ off

A– on

A+

on

A–

off

+VDS of B+

–

–VDS of B–

+

B+ off

B– on

B+

on

B–

off

Note - the added vertical bars show slight overlap in “on” times, but only during the transitions.

Vac, without and with filter

Vac with Vcont near saturation