STEPPED PULSE- WIDTH MODULATION USING MATLAB

To generate Output pulses by varying modulating index (ma) and to find the THD and FFT analysis.

Software Used: MATLAB R2018a

Theory:

As its name suggests, pulse width modulation is used for the speed control that works by driving the motor with a series of “ON-OFF” pulses and varying the duty cycle, the fraction of time that the output voltage is “ON” compared to when it is “OFF”, of the pulses while keeping the frequency constant. In this, it is done by considering the reference pulse as our Stepped wave with 4 step pulse.

MATLAB Code:

clc; %clear the command window

clear all; %clear the workspace

close all; %close all previous figure window

f=50; %Frequency

w=2*pi*f;

t=0:0.000001 :1/f; %range of time period

tri=asin(sin(w*t));

ref1=square(w*t); %Reference Square Wave

car=(((asin(sin((w*2)*t+(pi/2))))*(2/pi))+1).*ref1; %Carrier wave

car1=(((asin(sin((5*w*2)*t+(pi/2))))*(2/pi))+1).*ref1; %Carrier wave

car2=asin(sin(10*w*t+(pi/2)))*(1.333);

% car=(((2*asin(sin((w*2)*t+(pi/2)))))).*ref1;

sq=(ref1>=0 & car>=0 & ref1<=car)-(ref1<=0 & car<=0 & ref1>=car)

 

sq1=sq+ref1

out=(sq1>=0 & sq1>=car)-(sq1<=0 & sq1<=car);

 

ref2=1.6*ref1;

out1=(ref2>=car)-(ref2<=car);

%plot(out1)

o1=out+out1;

% plot(t,o1)

ref3=0.78*ref1;

out2=(ref3>=car)-(ref3<=car);

%plot(out2)

o2=out+out1+out2;

% plot(t,o2)

ref4=0.39*ref1;

out3=(ref4>=0 & ref4>=car)-(ref4<=0 & ref4<=car);

% plot(out3)

o3=out+out1+out2+out3;

o4=(1/4)*(o3)

 

 ma=0.01:0.01:1

 for(i=1:max(size(ma)))

   sq2=ma(i)*o4; 

    plot(t,sq2);

    hold all

    C(i,:)=(o4>=0 & sq2>=car2)-(o4<=0 & sq2<=car2);

    plot(t,C)

    N=max(size(C(i,:)));

    y(i,:)=(2/N)*abs(fft(C(i,:),N));%FFT analysis formula

    C1(i,:)=sum(y(i,:).^2);  %Sum of the harmonic components in the output signal

    C2(i,:)=sqrt(C1(i,:)-y(i,2).^2);    %Square root of (sum of hormonic components-First hormonic component)

    C3(i,:)=C2(i,:)/y(i,2); % Finding Total hormonic distortion(THD)

 end

figure()

plot(t,C(50,:))%Plot of Output signal with modulation index=0.5

figure()     %To plot separate figure

bar(ma,C3(:,1))

axis([0 .1 -1 11])

figure()

plot(ma,y(:,2:2:8)); % Plot of Modulation index vs THD

set(gca,'Xdir','reverse');

Waveforms:

Fig 4.1: Comparison of Reference with Carrier wave

Fig 4.2: Different ma and the Reference signal

Fig 4.3: Output Pulse Single PWM for ma=0.50

Fig 4.4: Harmonics Profile of Single Pulse -Width Modulation

Fig 4.5: FFT Analysis

Observation:

1.     There is a difference in the THD and ma plot of Stepped and Staircase waveform so we can say both are not the same also the staircase has 3 levels whereas in my stepped wave it has 4 level reference signals.

2.     As the modulation index increases, the THD of the Output Pulse decreases but at a slower pace. As it is in starting at 2 and reach to approximately 1.7 whereas in the case of the staircase it was coming 8 and reaches 2. So, we can say stepped is better than the stair-case as it has less value of THD at the start.

Result: In the above experiment we can say that ma is varied from 0 to 1 and output pulse generation is shown in fig 4.3 for ma = 0.50. THD and FFT analysis is also done for the same ma.