Question

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). After taking the partial fractions, find the coefficient of 1/s.

(a) 25/4

(b) 50/4

(c) 100/4

(d) 125/4

The question was asked in an online interview.

This is a very interesting question 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

Right choice is (d) 125/4

To explain: Since there is an extra term in the numerator compared to the denominator and also an s term in the denominator, the two poles exists at 0 and infinity. Therefore the network consists of first element and last element.

By taking the partial fraction expansion of Z(s), we obtain A=5(s^2+4)(s^2+25)/((s^2+16))|s=0

=(5×4×25)/16=125/4.