Chapter 9, Problem 9.32P

To determine

The expression for the steady state voltage v_o (t).

The steady state response for the given function is given by,

Given:

The square wave input for the given circuit is given as,

Fourier series approximation and is given by

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.

Calculation:

The Fourier series approximation is given by,

The transfer function of series RC circuit is given by,

The expression for magnitude of transfer function of the given system is,

(1)

Substituting for R = 10³ and C = in equation (1) we get,

The phase angle is given by

.... (3)

Substituting for R = 10³ and C = in equation (3) we get,

.... (4)

The bandwidth for the given system should lie between 0 and

(5)

Substituting R = 10³ and C = in equation (5) we get,

1000 rad/s

As is greater than 1000 rad/s which is outside the required bandwidth, we consider only 0 and 120 for frequency values.

The magnitude value for the frequencies 0and 120 is,

From equation (2) we know that

Substituting for 0 and 120 respectively we get,

(6)

On simplifying we get

0.9357.... (7)

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 Fourier series,

is given by,

Conclusion:

Therefore, the steady stat response for the given function is given by