Question

R WU CSR (a) Obtain the transfer function between input v and output i. Use complex impedances to solve this. (b) Plot the output given v(t) = sint. Let R=112, C = 1 farad, L = 1 henry. Use 1sim to simulate 30 seconds of the system output.

use any programming language (Matlab is prefered)

Answer 1

su Solution: Giren se da igane Management circuit diagram - UCHO Transforming the above circuit into frequency domain - SWL R Let Zijos) = R+jWL pielem vejws & seju) - wc Zalju) = Rll we S RX ! zaljud - Talveg - Rot the Rt Two

" Redrawing the circuit - Using Kul in the mein - vigas) = Digung [ z, jus)+ 2,4jaz] vegjia) = Pejos ( R + jaxu + fore]

JUL) ( It w RC) +R 1 Howre 2c + jual + (jw)? RLC TR I! HWRC) (A4 j =-1) ** vepwa) = Dejw) (200* RLC + jw (+c) +287 (+jWRC) & Transfer function in frequency. domain - usia - 1+jwRc (-*RLC + jw (4+R+C) 4 QR) Answers For R=122 C=1F and L=1H As s=jw , Using Transfer function model we can obtain the response using MATLAB

MATLAB CODE FOR SOLUTION clc close all clear all syms 3 R-1; C=1; L-1; Define transfer function of the circuit sys=tf([O (R*C) 1], [(R*L*C) ((R*R*C)+L) (2*R)]); t =0:0.001:30; Time Vector upto 30 seconds Vi - 1*sin (1*t); i = lsim (sys, Vi, t); Forcing Function Calculate System Response figure (1) plot(t, Vi, 'b') Plot of Input voltage vi(t) hold on plot(t,i,'r') Plot of Output current Ii(t) xlabel('\bf time'); ylabel('\bf Amplitude') legend ('Input Voltage (Vi)', 'Output Current (i)'); grid on

Input Voltage (Vi) -Output Current (i) Amplitude ---- time Plot of output current repsonse (in red) is obtained using MATLAB