Question

Consider the impedance function, Z(s)=(2s^2+8s+6)/(s^2+8s+12). Find the value of R1 after converting into second Cauer form.

(a) 1

(b) 3/4

(c) 1/2

(d) 1/4

I got this question in an international level competition.

Origin of the question is Synthesis of R-L Network by Cauer Method in division Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

The correct answer is (c) 1/2

The best explanation: To find out the second Cauer form, we have to write the impedance function in ascending powers and by taking the continued fraction expansion of Z (s).

On solving, the first quotient obtained is 1/2. So the value of R1 as 1/2 Ω.