Question

If the value of β is π, and Z1, Z2 are same type of reactance, then the value of β is?

(a) α=2 cosh^-1⁡√(Z1/2 Z2)

(b) α=2 cosh^-1⁡√(Z1/Z2)

(c) α=2 cosh^-1⁡√(4 Z1/Z2)

(d) α=2 cosh^-1⁡√(Z1/4 Z2)

This question was addressed to me during an online exam.

My question is based upon Classification of Pass Band and Stop Band in chapter Filters and Attenuators of Network Theory

Answer 1

Right option is (d) α=2 cosh^-1⁡√(Z1/4 Z2)

To explain: If the value of β is π, cos β/2 = 0. So sin β/2 = ±1; cosh α/2 = x = √(Z1/4 Z2). This solution is valid for negative Z1/4 Z2 and having magnitude greater than or equal to unity. -α &lt= Z1/2 Z2 <= -1. α=2 cosh^-1⁡√(Z1/4 Z2).