TRAPEZOIDAL PULSE- WIDTH MODULATION using MATLAB

TRAPEZOIDAL PULSE- WIDTH MODULATION

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

Software Used: MATLAB R2018a

Theory:

Trapezoidal wave is suitable for the modulating signal of the microcomputer-based pulse-width modulation (PWM) inverter for the use of motor drives because the switching patterns can be generated by means of on-line computation. The waveform is changed from a rectangular to a triangular wave. We can get the output pulse by using a single pulse width and multiple pulses width modulation and can vary the amplitude with the help of modulation index of the reference pulse which is Trapezoidal in this case.

TRAPEZOIDAL SINGLE PULSE- WIDTH MODULATION

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=0:0.00001 :1/f; %range of time period

 

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

tri=asin(sin(w*t)); %Triangle wave

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

sq1=(ref>=0 & tri>=0 & ref>=tri )-(ref<=0 & tri<=0 & ref<=tri); %Square Wave logic for trapezoidal wave

sq2=(ref>=0 & tri>=0 & ref<=tri )-(ref<=0 & tri<=0 & ref>=tri); %Square Wave logic for trapezoidal wave

trap1=sq1.*tri;

new=trap1.*ref;

trap2=new+sq2; % trapezoidal wave reference wave

 

 

ma=0.01:0.01:1; %range of ma

for i=1:max(size(ma))

trap3=ma(i).*trap2;

Vo(i,:)=((trap3>=0)&(car>=0)&(trap3>=car))-((0>=trap3)&(0>=car)&(car>=trap3)); %output pulse

plot(t,trap3)

hold on

 

subplot(2,1,1)

plot(t,car)

hold on

plot(t,trap2)

subplot(2,1,2)

plot(t,Vo(i,:))

 

N=max(size(Vo(i,:)));

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

B1(i,:)=sum(y(i,:).^2); % To find THD

B2(i,:)=sqrt(B1(i,1)-y(i,2).^2);

B3(i,:)=B2(i,1)/y(i,2);

end

figure()

plot(Vo(40,:))%Plot of Output signal with modulation index=0.4

figure()             %To plot separate figure

bar(ma,B3(:,1))

axis([0 .1 -1 11])

figure()

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

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

 

 

Waveforms:

Fig3.1.1: Comparison of Trapezoidal  Reference with  Carrier wave

Fig3.1.2: Different ma and Trapezoidal Reference signal

Fig3.1.3: Trapezoidal Single PWM for ma=0.40

Fig3.1.4: Harmonics Profile of Trapezoidal Single Pulse -Width Modulation

Fig3.1.5: FFT Analysis

 

 

TRAPEZOIDAL MULTIPLE PULSE- WIDTH MODULATION

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=0:0.00001 :1/f; %range of time period

 

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

tri=asin(sin(w*t)); %Triangle wave

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

sq1=(ref>=0 & tri>=0 & ref>=tri )-(ref<=0 & tri<=0 & ref<=tri); %Square Wave logic for trapezoidal wave

sq2=(ref>=0 & tri>=0 & ref<=tri )-(ref<=0 & tri<=0 & ref>=tri); %Square Wave logic for trapezoidal wave

trap1=sq1.*tri;

new=trap1.*ref;

trap2=new+sq2; % trapezoidal wave reference wave

 

 

ma=0.01:0.01:1; %range of ma

for i=1:max(size(ma))

trap3=ma(i).*trap2;

Vo(i,:)=((trap3>=0)&(car>=0)&(trap3>=car))-((0>=trap3)&(0>=car)&(car>=trap3)); %output pulse

plot(t,trap3)

hold on

 

subplot(2,1,1)

plot(t,car)

hold on

plot(t,trap2)

subplot(2,1,2)

plot(t,Vo(i,:))

 

N=max(size(Vo(i,:)));

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

B1(i,:)=sum(y(i,:).^2); % To find THD

B2(i,:)=sqrt(B1(i,1)-y(i,2).^2);

B3(i,:)=B2(i,1)/y(i,2);

end

figure()

plot(t,Vo(40,:))       %  Plot of Output signal with modulation index=0.40

figure()             %To plot separate figure

bar(ma,B3(:,1))

axis([0 .1 -1 11])

figure()

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

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

 

 

 Waveforms:

Fig3.2.1: Comparison of Trapezoidal Reference with Carrier wave

Fig3.2.2: Different ma and Trapezoidal Reference signal

Fig3.2.3: Trapezoidal Multiple PWM for ma=0.40

Fig3.2.4: Harmonics Profile of Trapezoidal Multiple Pulse -Width Modulation

 

Fig3.2.5: FFT Analysis

Observations:

1.     As the modulation index increases, the Total Harmonic Distortion decreases at a faster rate in case of Trapezoidal Single PWM.

2.     In the Harmonics Profile of Trapezoidal Multiple Pulse -Width Modulation, the fundamental has a major component and rest are almost close to zero only whereas for Single Pulse-Width Modulation it has all fundamental, 3^rd, 5^th and 7^th all components with considerable values.

Result:

By the above experiment we can say that if ma is varied from 0 to 1 and output of Trapezoidal single pulse generation and Multiple pulse generation is shown in fig 3.1.3 and fig 3.2.3 for ma = 0.40 THD and FFT analysis is also done for the same ma.