In admittance parameters : (A) y11 is short circuit input impedance Choose the most appropriate answer from the options given below :
(B) y22 is open circuit o/p admittance
(C) y21 is short circuit transfer admittance
(D) y12 is open circuit transfer admittance
(E) y12 and y21 are both short circuit transfer admittances
(A), (C), (E) Only
Every y parameter is measured with a short circuit on the other port — that single fact decides all five statements.
The defining equations are
\(I_{1}=y_{11}V_{1}+y_{12}V_{2},\qquad I_{2}=y_{21}V_{1}+y_{22}V_{2}\)
To isolate any one parameter, the voltage at the other port must be set to zero — and a zero voltage is a short circuit:
| Parameter | Definition | Condition |
|---|---|---|
| y11 | \(I_{1}/V_{1}\) | V2 = 0, output shorted |
| y12 | \(I_{1}/V_{2}\) | V1 = 0, input shorted |
| y21 | \(I_{2}/V_{1}\) | V2 = 0, output shorted |
| y22 | \(I_{2}/V_{2}\) | V1 = 0, input shorted |
So (B) and (D) fail on the word "open". An open-circuit condition sets a current to zero, which is how Z parameters are measured, not Y parameters. Statement (B) calls y22 an open-circuit admittance and (D) calls y12 an open-circuit transfer admittance; both have borrowed the Z-parameter condition. That eliminates options 2, 3 and 4 at once, leaving option 1.
(C) and (E) are both correct, and (E) simply states the general rule that (C) illustrates: the two transfer parameters are measured with the opposite port shorted, so both are short-circuit transfer admittances. For a reciprocal network they are moreover equal, \(y_{12}=y_{21}\).
A note on statement (A). It is included in the official answer, and its condition — short circuit — is right, but its wording is loose: y11 is the short-circuit input admittance, measured in siemens, not an impedance. Since the whole parameter set is defined by \([I]=[Y][V]\), every entry must carry the dimensions of admittance. The paper evidently intends the short-circuit condition to be the point being tested, and no option offers (C) and (E) without (A).
Why the short-circuit condition suits Y parameters practically. At high frequencies a good short is easier to realise than a good open, since stray capacitance ruins an open circuit while only lead inductance troubles a short. Y parameters also add directly when two-ports are connected in parallel, exactly as Z parameters add for series connection.
Hence, the correct statements are (A), (C) and (E).