Question

For the active first order filter circuit shown in Figure 1, a) Find the transfer function $H(s)$ of the filter circuit; (5 marks) b) Find the frequency response function $H(j\omega)$ of the filter circuit and obtain the magnitude and phase expressions of $H(j\omega)$; (10 marks) c) Find the DC ($\omega = 0$) gain of the filter circuit; (5 marks) d) Find the gain when the frequency approaches infinity, i.e., $\lim_{\omega \to \infty} H(j\omega)$; (5 marks) e) Calculate the -3dB cut off frequency in rad/sec of the filter with $R_1 = 1 k\Omega$, $R_2 = (a+10) k\Omega$, where a is the last digit of your VU student ID number, $C = 20nF$ with an ideal LM741 operational amplifier; (10 marks) f) Plot the straight-line approximation of the magnitude Bode diagram of $H(j\omega)$ using semi-log paper with $R_1 = 10 k\Omega$, $R_2 = 50k\Omega$, and $C = 20nF$; (10 marks) g) State the type of the filter according to the Bode plot obtained. (5 marks) Figure 1: Circuit for Question 1

          For the active first order filter circuit shown in Figure 1,
a) Find the transfer function $H(s)$ of the filter circuit;
(5 marks)
b) Find the frequency response function $H(j\omega)$ of the filter circuit and obtain the
magnitude and phase expressions of $H(j\omega)$;
(10 marks)
c) Find the DC ($\omega = 0$) gain of the filter circuit;
(5 marks)
d) Find the gain when the frequency approaches infinity, i.e.,
$\lim_{\omega \to \infty} H(j\omega)$;
(5 marks)
e) Calculate the -3dB cut off frequency in rad/sec of the filter with $R_1 = 1 k\Omega$,
$R_2 = (a+10) k\Omega$, where a is the last digit of your VU student ID number, $C = 20nF$
with an ideal LM741 operational amplifier;
(10 marks)
f) Plot the straight-line approximation of the magnitude Bode diagram of $H(j\omega)$
using semi-log paper with $R_1 = 10 k\Omega$, $R_2 = 50k\Omega$, and $C = 20nF$;
(10 marks)
g) State the type of the filter according to the Bode plot obtained.
(5 marks)
Figure 1: Circuit for Question 1

For the active first order filter circuit shown in Figure 1,
a) Find the transfer function H(s) of the filter circuit;
(5 marks)
b) Find the frequency response function H(jω) of the filter circuit and obtain the
magnitude and phase expressions of H(jω);
(10 marks)
c) Find the DC (ω = 0) gain of the filter circuit;
(5 marks)
d) Find the gain when the frequency approaches infinity, i.e.,
limω→∞ H(jω);
(5 marks)
e) Calculate the -3dB cut off frequency in rad/sec of the filter with R1 = 1 kΩ,
R2 = (a+10) kΩ, where a is the last digit of your VU student ID number, C = 20nF
with an ideal LM741 operational amplifier;
(10 marks)
f) Plot the straight-line approximation of the magnitude Bode diagram of H(jω)
using semi-log paper with R1 = 10 kΩ, R2 = 50kΩ, and C = 20nF;
(10 marks)
g) State the type of the filter according to the Bode plot obtained.
(5 marks)
Figure 1: Circuit for Question 1

Added by Mark S.

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