Question

1. The difference equation for a single stage RC circuit, when the input is 1v., is
   shown below (see Lab 4):

            y(n) = (y(n-1) + a * Ts) / (1 + a * Ts)         (0 < t < 1)

            where   a = 1 / (RC)

    Ignore the difference equation for the case t > 1, when the input is 0v.

(a) Find the Z-transform of y(n) analytically, assuming a time constant of a = 5 and sampling interval of Ts = 0.1. Then apply MATLAB’s iztrans function to generate y as a vector, and display the values of y(n) using
            y = abs(double(subs(y, n))); y = [0, y]

(b) Verify the result with MATLAB using the for loop below. Note that k = a*Ts.

        y(1) = 0;
        for n = 1:11
           y(n+1) = (y(n) + k) / (1 + k);
        end
        y

(c) Repeat parts (a) and (b), changing the time constant from 5 to 1. Your results should be consistent with those from Lab 4. The sampling time has been changed from 0.01 to 0.1, resulting in the value at t = 1 corresponding to n = 10, instead of
n = 100.

2. (a) Verify the output sequence for the two stage RC circuit (see Lab 6) using MATLAB’s iztrans function.

    (b) Find the output sequence y(n) analytically using the Z-transform, residues and the inverse Z-transform.

Answer 1

on em we will get AMume that Rc The 2- tamfm O.o Rcャ0.01

xC2) ol n-l c+ 2-1 2TTJ Re yl?) С RC+ 0.0) o.ol

RC七001 n- y(n-i) -'. y(2)长 PC c+o.ol