Question

The driving point impedance of an LC network is given by Z(s)=(s^4+4s^2+3)/(s^3+2s). By taking the continued fraction expansion using second Cauer form, find the value of C1.

(a) 2/3

(b) 2/2

(c) 1/2

(d) 4/2

I got this question during an online exam.

The question is from Synthesis of Reactive One-Ports by Cauer Method in portion Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

Correct option is (a) 2/3

Easiest explanation: To obtain the second Cauer form, we have to arrange the numerator and the denominator of given Z(s) in ascending powers of s before starting the continued fraction expansion.

By taking the continued fraction expansion we get the first quotient as 3/2s.

So 1/sC1 = 3/2s

C1 = 2/3F.