Question

If a two port network is passive, then we have, with the usual notation, the relationship as _________

(a) h21 = h12

(b) h12 = -h21

(c) h11 = h22

(d) h11 h22 – h12 h22 = 1

I have been asked this question in an international level competition.

This intriguing question originated from Inverse Hybrid (g) Parameter topic in section Two-Port Networks of Network Theory

Answer 1

Correct answer is (d) h11 h22 – h12 h22 = 1

For explanation: We know that, I1 = y11 V1 + y12 V2 ……… (1)

I2 = y21 V1 + y22 V2 ………. (2)

And, V1 = h11 I1 + h12 V2 ………. (3)

I2 = h21 I1 + h22 V2 ……….. (4)

Now, (3) and (4) can be rewritten as,

I1 = \(\frac{V_1}{h_{11}}  – \frac{h_{12} V_2}{h_{11}}\)  ………. (5)

And I2 = \(\frac{h_{21} V_1}{h_{11}}  + \left(- \frac{h_{21} h_{12}}{h_{11}} + h_{22}\right) V_2\) ………. (6)

Therefore using the above 6 equations in representing the hybrid parameters in terms of the Y parameters and applying ∆Y=0, we get,

h11 h22 – h12 h22 = 1 [hence proved].