Question

Preliminary Work a) Derive the exact equation for V/V, for the circuit of Fig. 5.1 and find an expression for the cutoff frequency (c. Using semilog paper, plot the frequency response (magnitude vs. frequency) of the filter up to 10fc using the specified component values. Plot the horizontal axis for frequency on a logarithmic scale and the vertical axis for magnitude V/Vs (dB), on a linear scale. b) Repeat part (a) for the circuit of Fig. 5.2.

Answer 1

Execute the following MATLAB code for the magnitude plots:

a brow the dirat a) Draw the circuit in s-doonain. is G sé t to Apply the voltage division. cut off : vo = us ( helse) Viten: RC)? (We RC 5 = 1 We are sadis fc = I 25RC Hz 6) Draw the circuit in s-domain. + + sLg. Vo > Cut-off- Apply the voltage division. Y = rs ( s ) van he ħ with I y = SL R+SL 45 R² + wall 2 a we har We = R/ radis fc o p Hz

%Assumptions
R=10*10^3;
L=10^(-3);
C=10^(-6);
%Cut-off frequencies
fc1=(1/2*pi*R*C);
fc2=R/(2*pi*L);
wc1=2*pi*fc1;
wc2=2*pi*fc2;
%Transfer function system 1
H1=tf([1],[1 R*C]);
%Transfer function system 2
H2=tf([0 L],[R L]);
figure(1)
bode(H1,{0.01,10*wc1})
grid on
figure(2)
bode(H2,{0.01,10*wc2})
grid on

Obtain the magnitude plots.

Figure 1 - O X File Edit View Insert Tools Desktop Window Help Figure 2 File Edit View Insert Tools Desktop Window Help DOK SA O E O Bode Diagram Bode Diagram 40 -100 Magnitude (dB) Magnitude (dB) -89.5382 -89.9996 Phase (deg) -89.9998 -90 -902 102 100 Frequency (rad/s) Frequency (rad/s) 10°