Question

For a T-network if the Open circuit impedance parameters are given as z11, z21, z12, z22, then z21 in terms of Hybrid parameters can be expressed as ________

(a) z21 = \(\left(h_{11} – \frac{h_{21} h_{12}}{h_{22}}\right) \)

(b) z21 = – \(\frac{h_{21}}{h_{22}} \)

(c) z21 = \(\frac{h_{12}}{h_{22}} \)

(d) z21 = \(\frac{1}{h_{22}} \)

This question was posed to me in examination.

My doubt is from Relation between Hybrid Parameters with Short Circuit Admittance and Open Circuit Impedance Parameters topic in portion Two-Port Networks of Network Theory

Answer 1

Correct answer is (b) z21 = – \(\frac{h_{21}}{h_{22}} \)

Explanation: We know that, V1 = z11 I1 + z12 I2 ……… (1)

V2 = z21 I1 + z22 I2 ………. (2)

And, V1 = h11 I1 + h12 V2 ………. (3)

I2 = h21 I1 + h22 V2 ……….. (4)

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

V1 = \(\left(h_{11} – \frac{h_{21} h_{12}}{h_{22}}\right) \frac{I_1 + h_{12}}{h_{22}}I_2\) ………… (5)

And V2 = \(\frac{I_2}{h_{22}}  – \frac{h_{21} I_1}{h_{22}}\)  ……….. (6)

∴ Comparing (1), (2) and (5), (6), we get,

z11 = \(\left(h_{11} – \frac{h_{21} h_{12}}{h_{22}}\right) \)

z12 = \(\frac{h_{12}}{h_{22}} \)

z21 = – \(\frac{h_{21}}{h_{22}} \)

z22 = \(\frac{1}{h_{22}} \).