ECET 307 Analog Network Signal Processing

Fall 2006

 

Prof. Paul Lin

 

Week 4

Waveform Analysis

 

 

 

Half-Wave Rectifier

 

 

The Half-wave Rectifier Circuit (without filter circuit)

 

 

 

 

 

 

Vout Calculation

 

 

Vdc or Vavg

 

We then compute the average voltage (dc voltage) Vavg or Vdc for one complete cycle

 

MATLAB Solution

% halfwave_rect.m

% 9/10/2006

% Paul Lin

f = 60;

T = 1/f;

Vacrms = 12;

Vm = Vacrms*1.414;

dt = T/100;

t = 0: dt: T;

vt = Vm*sin(2*pi*f*t);

vt_half = zeros(size(vt));

for n = 1: length(t)

if vt(n) >= 0

vt_half(n) = vt(n);

else

vt_half(n) = 0.0;

end

end

row = 2;

col = 1;

figure(1), subplot(row, col, 1), plot(t, vt), grid on, title('AC input')

xlabel('time'), ylabel('volts')

subplot(row, col, 2), plot(t, vt_half), grid on, title('Half-wave Rectified')

xlabel('time'), ylabel('volts')

% MATLAB Numerical Integration

% Trapezoidal Integration: split the area under the curve into rectangles.

% If the rectangles are fine enough, the sum of these areas gives the

% approximate value of the integral.

%

% _pi

% / |pi

% / sinx dx = -cos x| = cos 0 - cos pi = 1- (-1) = 2

% / |0

% -0

%

x = linspace(0, pi,10); % 1.9797, gives 1 percent error

y = sin(x);

trapz(x,y)

x = linspace(0, pi,100); %1.9998 gives 0.1 percent error

y = sin(x);

trapz(x,y)

x = linspace(0, pi,1000); %2.0000

y = sin(x);

trapz(x,y)

%vt_hal

% Exact Integration to obtain

% Vdc = 0.45*Vrms = 5.4 Volts

% Vdc = 0.318*Vm = 5.4 Volts

% Numerical Integration

% Vdc = 5.394 volt

w = 2*pi*f;

theta = w*t;

Vdc = trapz(theta(1:50), vt_half(1:50))/(2*pi)

 

Vrms at the Load Resistance

 

 

 

 

 


Compute Ripple Factor

 

Ripple Factor = RMS value of the AC component/DC value of the component

 

 

Efficiency

 

η = (dc output power/ac input power) x 100%

 

 

Form Factor

 

FF = rms value / average value = (Vm/2)/(Vm/π)= π/2 = 1.57

 

Peak Factor

 

Peak value / rms value = Vm/(Vm/2) = 2


 

Filter Capacitor Design

 

Regulator

 

Zener Diode Regulator

 

IC Voltage Regulator

 

 

Lab Design 2

 

Lab Note

Lab Report

Circuit Diagram

Lab Pictures

Scope Measurement

MS Equation Editor

 

Half-Wave Rectifier

Full-Wave Rectifier

Power-on indicator - LED

Filter Circuits

IC Regulator

Applications

 

EWB simulation

MATLAB simulation

Lab Measurement

 

Lab Measurement