Question

If Z1, Z2 are same type of reactance, and if α = 0, then the value of β is?

(a) β=2 sin^-1⁡(√(Z1/4 Z2))

(b) β=2 sin^-1⁡(√(4 Z1/Z2))

(c) β=2 sin^-1⁡(√(4 Z1/Z2))

(d) β=2 sin^-1⁡(√(Z1/Z2))

The question was posed to me during an internship interview.

Enquiry is from Classification of Pass Band and Stop Band in division Filters and Attenuators of Network Theory

Answer 1

Right option is (a) β=2 sin^-1⁡(√(Z1/4 Z2))

The best explanation: If α = 0, sin β/2 = x(√(Z1/4 Z2). But sine can have a maximum value of 1. Therefore the above solution is valid only for Z1/4 Z2, and having a maximum value of unity. It indicates the condition of pass band with zero attenuation and follows the condition as -1 < Z1/4 Z2 <= 0. So β=2 sin^-1⁡(√(Z1/4 Z2)).