Question

For a T-network if the Short circuit admittance parameters are given as y11, y21, y12, y22, then y21 in terms of Inverse Hybrid parameters can be expressed as ________

(a) y21 = \(\left(g_{11} – \frac{g_{12} g_{21}}{g_{22}}\right)\)

(b) y21 = \(\frac{g_{12}}{g_{22}} \)

(c) y21 = –\(\frac{g_{21}}{g_{22}} \)

(d) y21 = \(\frac{1}{g_{22}}\)

I have been asked this question in an interview.

My doubt stems from Inverse Hybrid (g) Parameter in portion Two-Port Networks of Network Theory

Answer 1

The correct choice is (c) y21 = –\(\frac{g_{21}}{g_{22}} \)

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

I2 = y21 V1 + y22 V2 ………. (2)

And, I1 = g11 V1 + g12 I2 ………. (3)

V2 = g21 V1 + g22 I2 ……….. (4)

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

I1 = \(\left(g_{11} – \frac{g_{12} g_{21}}{g_{22}}\right)V_1 + \frac{g_{12}}{g_{22}}   V_2\)………. (5)

And I2 = –\(\frac{g_{21} V_1}{g_{22}} + \frac{V_2}{g_{22}}\)………. (6)

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

y11 = \(\left(g_{11} – \frac{g_{12} g_{21}}{g_{22}}\right)\)

y12 = \(\frac{g_{12}}{g_{22}} \)

y21 = –\(\frac{g_{21}}{g_{22}} \)

y22 = \(\frac{1}{g_{22}}\).