Question

000 vs() 14 FOR 1002 T-circuit

Assume the load resistor RL= 100 Ohms. Assume vS(t) = 1cos(wt). Rs=3ohms, L1=7H, L2=9H, and C=8uF

write a MATLAB code which takes in vS(t) with various frequencies for the range of frequencies from 0Hz to 20kHz, and finds vL(t) for each of those frequencies, and the computes the gain ratio of the amplitudes |vL(t)|/|vS(t)| which is also equal to g = |VL |/|VS|. Use at least 1000 data points for w, within the frequency range. Plot g versus w: a) using normal scale and also b) in the log g vs log w scale, using the logspace command or loglog command. Type “help logspace” or “help loglog” in MATLAB. Provide the codes and the plots here. Which plot do you like better, why? Adjust the horizontal and vertical axis limits if necessary, for better viewing. Inspect the curves, at what frequency does the non-zero frequency “peak” occur? Why at this particular frequency? Can you find a relationship of this frequency to the circuit variables?

Answer 1

SLI V, 12 TÁC VI I r II (SL₂+R) Ru +AL, & [ 1 (AL 2 TR] → V, (s) = (shatRu) V (1) 3 CLIL 2 + ² (CL p R + CRL) 1 (CR, RAAL, +22) +R+RL (3)= SL RL R & SL 2 (1) > Ve (8) = sta R₂ V (A) $3CL,L2+(CL2R,+ CRC-) +ACCRERA + Ly the)+RAtri SLaRL 83C Loke+s4(CL2Rn+ CR44) +BCCRRA+4+2)+R+R Vica) 3 V (10) VCjW) jw LzR, (jw) C1812+ (jw)?(CL2R+CR41)+ją (CRL Rythey +-2) +Ryth jo L₂ RL - jw² CLIC2-W² (CL₂ Rs +CR2L) +jW (CR,R, +2, +2₂) + R, the Valio) Scanned with CamScanner

Matlab Code:

wlog=logspace(-2,5,1000) %creating 1000 points from 10^(-2) to 10^(5)
Rl=100 %values given
Rs=3
L1=7
L2=9
C=0.000008
for i=1:1000
denom(i) = (-j*(w(i).^3)*C*L1*L2)-((w(i).^2)*(C*L2*Rs+C*Rl*L1))+(j*w(i)*(C*Rl*Rs+L1+L2))+Rs+Rl

%defiining denominator of transfer function
H(i) =(L2*Rl*j*w(i))/ denom(i);
end
HdB=20*log10(abs(H)) %this is gain in dB
figure
plot(w,abs(H)) %ploting gain vs w=frequency in (rad/s)
xlabel('frequency (rad/s)')
ylabel ('|H(jw)|')
figure
semilogx(wlog,HdB) %ploting gain in dB vs log(w)
xlabel('frequency (rad/s)')
ylabel ('|H(jw)| in dB')

a) Plot og gain vs frequency (rad/s) :

b) Plot of gain in dB vs frequency in log scale:

| H(jw) 10 12 14 C 8 frequency (rad/s) X 104

From the two curves it is clear that the 2nd plot is better for viewing.

| H(jw) in dB -80 10-2 10° 104 106 102 - frequency (rad/s)

At frequency in rad/s=125.8 rad/s gain is maximum which is equal to 112.1

Thus at frequency =20Hz gain is maximum.

This is the resonant frequency at which gain is maximum.