- Asked 2/12
- 2068 Chaitra · 4 marks
Reciprocal two-port and condition in Y parameters
Short answer
A reciprocal network gives equal transfer admittances. From I1 = y11V1 + y12V2 and I2 = y21V1 + y22V2, apply V at port1 with port2 shorted: I2 = y21V. Apply V at port2 with port1 shorted: I1 = y12V. Reciprocity requires y12 = y21.
What do you understand by a reciprocal two port network? Derive the condition for reciprocity in terms of y-parameters.
A two-port network is reciprocal if the ratio of the response at one port to the excitation at the other is unchanged when the excitation and the response are interchanged. Networks of R, L, C and mutual inductance only (no dependent sources, no gyrators) are reciprocal.
Derivation for y-parameters
The equations are I1 = y11 V1 + y12 V2 and I2 = y21 V1 + y22 V2.
Case 1. A voltage source Va at port 1, port 2 short-circuited (V2 = 0):
I2a = y21 Va
Case 2. The same source, now Vb = Va, applied at port 2, port 1 short-circuited (V1 = 0):
I1b = y12 Vb
The reciprocity theorem states that the current produced at the shorted port by a voltage source at the other port is the same in both cases (when the source is moved from port 1 to port 2):
I2a/Va = I1b/Vb → y21 = y12
Condition for reciprocity: y12 = y21. Similarly z12 = z21 for Z-parameters, and AD − BC = 1 for transmission parameters.
If, in addition, y11 = y22, the network is also symmetrical (the ports can be interchanged without changing the terminal behaviour).
✓ Answer checked by Claude Opus 5.5 (high effort)
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