Question

For performing second Foster form, after splitting the Z (S) in The driving point impedance of a one-port reactive network is given by Z(s)=5(s^2+4)(s^2+25)/s(s^2+16), what is the coefficient of s/((s^2+4)) is?

(a) 4/35

(b) 3/35

(c) 2/35

(d) 1/35

I had been asked this question in an online interview.

This interesting question is from Synthesis of Reactive One-Ports by Foster’s Method topic in chapter Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

The correct choice is (c) 2/35

To elaborate: The coefficient of s/((s^2+4)) is B=(1/5)((s(s^2+16)))/(s-j5)(s^2+4) at s=-j5. On solving we get B = 2/35.