Chapter 9, Problem 9.31P

To determine

The expression for the steady state voltage v_o (t)for a full wave rectifier.

The steady stat response for the given fullwave rectifier is given by,

Given: The sinusoidal voltage waveform of a fullwave rectifier

FigureP9.31

Fourier series approximation and is given by

Fourier series approximation = v_s (t) =

Transfer function = Where R = 600 and C

Concept Used:

We first calculate magnitude of the given transfer function, phase angle, bandwidth and magnitude of phase angles of respective frequencies and finally calculate the expression for steady state response of the full wave rectifier.

Calculation:

The Fourier series approximation is given by,

v_s (t) =

The transfer function of series RC circuit is given by,

The expression for magnitude of transfer function of the given full wave rectifier is

(1)

Substituting for R = 600 and C in equation (1) we get,

(2)

The phase angle for the given fullwave rectifier is given by

.... (3)

Substituting for R = 600 and C in equation (3) we get,

.... (4)

The bandwidth for the given system should lie between 0 and

(5)

Substituting for R = 600 and C in equation (5) we get,

1666.67 rad/s

As is greater than 1666.67 rad/s which is outside the required bandwidth, we consider only 0, 240 and 480 only for frequency values.

The magnitude value for the frequencies 0, 240 and 480 is,

From equation (2) we know that

Substituting for 0, 240 and 480 respectively we get

(6)

On simplifying we get

0.9111.... (7)

On simplifying we get

(8)

From equation (4) we have

Now calculating the phase angles for corresponding frequencies 0, 240 and 480 respectively we get,

The steady state voltage for the given full-wave rectifier with Fourier series,

v_s (t is given by

Conclusion:

Therefore, the steady state response for the given fullwave rectifier is given by,