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1
ENEL371S2
Power Electronics 1
Lecture 2 PWMPulse Width Modulation
Department of ECE
University of Canterbury
2012
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Pulse Width Modulation(PWM) for DC-DC
Conversion- How to switch to convert DC power
from one level to another level
Read Chapter 7.1-7.2, Mohan etc.
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Switch-Mode Converter
t
kT T
SwitchON
Switch
OFF
kis duty cycle/ratio,0
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Switch-Mode Synthesis
Average value of voi
- DC Component:
Chopped voltage voi 0 0
1 1T kT
oi oi d d avv v dt v dt kv
T T
Single Pole Double Throw Switch
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Switch-Mode Synthesis
oi dav
v kv
DC Component:
oi oi rippleavd ripple
v v vkv v
That is, DC component(voi)av + high frequencyharmonics vripple
at nfs
We can define voi:
T=1/fs
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Switching Strategies
TT T 4T
on
off
on
off
on
off
on
off
t
How to generate duty-ratio-controllablerectangular pulse train
to switch ON/OFF?
1. Constant switching frequency with variable ONtime and OFF
time (i.e. variable duty ratio)
:
:
on off
on on
on off
switching period T t t
t tduty ratio k
t t T
This is called pulse-width-modulation
(PWM)
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Why PWM is Popular ?
Read Spectral_analysis.pdf
Fourier analysis shows that the
frequency spectrum of any PWM signalfor DC-DC conversion
contains DCcomponent (average value)+ switchingfrequency harmonics
(nf
s). A low pass
filter can easily remove harmonics. Theoutput voltage can be
convenientlyregulated by tuning duty ratio k.
If switching frequency varies with dutyratio, it is hard to
design filter toremove harmonics (ripples), and is
difficult to choose power switch too.
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How to Get PWM Switching ?
Double-edge Modulation:
Both edges of PWMsignal move
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Generating PWM Signal
11
( )
1 1:
: , 0 1
son of
control
carrier peak
f
on
switching frequency fT t t
tduty ra
V
Vtio k k
T
One-edge Modulation:
One edge of PWMsignal move
PWM Signal:
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Generating PWM Signal
Why carrier signal usually chose trianglesignal or sawtooth
signal, because
DC component (average value) of PWM isproportional to the of
control signal Vcontrol, i.e.output can be regulated linearly.
Switching frequencyfs of DC-DC converters isusually choose to be
10~100kHz.
High switching frequency means less filtering isneeded.
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Signal Analysis
0
1/2
2
0
22
0 0
/ :
/ :
:
1
1
1 1
T
avg
T
rms
T Trms
Average voltage current
RMS voltage current
Output average powe
e edt T
e e dt T
vvP vidt dt
T T R R
r
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Lecture 2 - Summary
PWMVariable Duty-RatioFixed Frequency SwitchingStrategy for
DC-DC conversion
PWM actually can be extendedfor DC-AC conversion, which will
be referred as Sinusoidal PWM(SPWM) in the late Lectures.
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Homework #2
Download homework #2 questions for
Lecture 2 fromLearn/ENEL371/Term3/Lecture2
Calculate voltage/current RMS value
Find additional readings for Lecture 2
from Learn/ENEL371/Term3/Lecture2
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Contact Information:
Dr. Keliang ZhouOffice: Electrical A512
Email: [email protected]
Phone: 3642240 Ext.6240
