Question

Solve h(s) =v0/vs for the following circuits. And plot the magnitude and phase in matlab(I need the codes) thanks in advance.

ST.66. 1 F ΙΩ 1 H 1S2 ΙΩ e 14.88 ob. 14.57

Answer 1

a)

In S domain capacitive reactance can be represented as 1/Sc where C: capacitance. Using Mesh analysis: Mesh 1: V_S = 1 x i_1 + 1/S (i_1 - i_2) V_s = i_1 (1 + 1/s) - 1/s i_2 - (1) Mesh 2 i_2 times 1/s + I_2 times 1 + 1/s (i_2 - i_1) = 0 - 1/s i_1 + (1/s + 1 + 1/s) i_2 = 0 - (2) i_2 (1 + 2/5) = 1/6 i_1 i_1 = S i_2 (s + 2/S) = (2 + S) i_2 --- (3) put (3) in (1), we get V_S = (s + 2) i_2 (1 + 1/s) - 1/s i_2 = i_2 (s + 1 + 2 + 2/3) - 1_2/s v_S = i_2 (s + 3 + 1/s) - (4) \r\n i_2 = v_s/s + 3 + 1/s - (5) v_0 = i_2 times 1 ohm = i_2 = v_s/s + 3 + 1/s h(s) = v_0/v_s = 1/s + 3 + 1/s = s/s^2 + 3 s

b)

h(s) is same for both the circuits.

Code For Magnitude and Phase plot is:

n=[1 0]; -----------------> Indicates Coefficients of numerator: 1 (coefficient of S), 0 (Constant)
d=[1 3 1]; --------------> Indicates coefficients of denominator
sys=tf(n,d); -------------> Indicates transfer function
bode(sys) ------------> For plotting bode plot