Question

For the low-pass filter circuit shown in Fig 2 200mH 3k Ω out in Fig 2 (i) (ii) (iii) Write an expression for the transfer function of the circuit State the value of the dc gain of the filter circuit in dB Calculate the cutoff frequency of the filter b. Sketch the frequency response of the voltage gain and phase shift for the filter shown in Fig 2. Show all the values and required information in both graphs Magnitude Frequency Hz

Answer 1

transfer function, T(s) = v_out (s) /v_in (s) = (R_2/R_1 + R_2 + sL) = R_2/(R_1 + R_2) [1/S(L/R_1 + R_2) + 1] = (1/1 + 3) [1/S (0.2 times 4 times 10^3) + 1] = (0.25/1 + s/2000) = (5000/s + 20,000) d.c gain, T(0) = lim_s rightarrow 0 [0.25/1 + (s/20,000)] = 0.25 d.c gain (in dB) = 20 log_10 (T(0)) = 20 log_10 (0.25) = -12.041 dB. T(s) = 0.25/(1 + s/20,000) out off frequency, w_0 = 20, 000 rad/s. f_0 = (w_0/2 pi) = 3183.1 Hz \r\n he bode plot is done using MATLAB. The MATLAB script and the plots are shown below: MATLAB Script: > > num = [5000]: > > den = [1 20000]: > > sys = tf(num, den) sys = 5000 --------- s + 20000 Continuous-time transfer function. > > bode(sys)

B. The bodeplot is done using MATLAB. The MATLAB script and the plots are shown below:

MATLAB Script:

>> num=[5000];
>> den=[ 1 20000];
>> sys=tf(num,den)

sys =

5000
---------
s + 20000

Continuous-time transfer function.

>> bode(sys)