Question

This is the circuit of Prob. 14.2 (page 826) of Cannon, reported below for your convenience. Ri LA www Kz mi GI C2+ Rg3 9 v1 The voltage-current relationship for an ideal inductor is given on page 67 of the text. Answer the following:

Answer 1

As per the question, the circuit diagram is shown below Ria 0 www K3 + WO CON We need to obtain the equation for each subsystem and compute the transfer function vals/vi(s) and plot the impulse response for the duration of t=-0.05 to t=0.15 sec. To solve the above circuit, we assume that voltages across the terminal a, b and c is Va, Vb and vc respectively. Applying KCL across the terminal a, the corresponding equation for the subsystem a is Applying Laplace transform on the above equation, we get Cs\@ter kan ko

Or, Va(9) = RocystiĽ(9) Therefore, the output of the amplifier K3, the output voltage will be VK3(s) = K2 * Va(s) For the next subsystem, if we apply KCL, we will obtain Esſ (vka – Vo)dt = Applying Laplace transforms on the above equation and then by solving for Vb, we get R5 V>(s) = Rs+s + LVk3() Therefore, the output of the amplifier Ko, the output voltage will be Vk6(s) = Ko * Vy(s) For the final subsystem, if we apply KCL, then we will obtain

Applying Laplace transforms on the above equation and then by solving for Vs we get Vc(S SRgC7 1 + SRO C7 And the final output voltage is Va(s) = Kg * V(s) Now, if we model the TF of the above system, it will be RS SROC, Va(s) = K, * * 1+sRgC* K * R$ +s+L4* K3 * RC25 +1*V1 (5) Therefore, the TF of the system is V O = Kg • Kg * Ks het om ho ho ha ricost1 As no parametric values are provided, hence we assume the following values for the parameters R2 = 1 ohm, Rs = 1 ohm, Rs = 1 ohm, Cz = C, = 1F, La = 1H, K3 = Ko = Kg = 1. Inserting the values, we obtain ho 1 to a to Coto Cotone The following matlab command can be used in order to obtain the impulse response of the above system

clear all
clc

s = tf('s');
%% model the system
G = s/(s+1)^3;

%% time duration
t = -0.05:0.01:0.15; % in sec

%% compute the impulse resposne
impulse(G,t);

the corresponding plot is shown below

Impulse Response 0.12 0.1 0.08 Amplitude 0.06 0.04 0.02 -0. 050 1 0. 0 .15 0.05 Time (seconds)