---
title: "Reciprocal two-port and condition in Y parameters"
subject: "Electrical Circuit Theory"
chapter: 7
key: "semester_3/electrical_circuit_theory:reciprocal-two-port-condition-y-parameters"
source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/reciprocal-two-port-condition-y-parameters
site: BCT Engineering
---

# Reciprocal two-port and condition in Y parameters

Electrical Circuit Theory · Chapter 7: Two-port Parameter of Networks

- Asked in: 2068 Chaitra, 4 marks
- Video: [Y- Parameters Explained | Condition of Reciprocity and Symmetry for Y- parameters](https://www.youtube.com/watch?v=Ph0UlER9S08) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/reciprocal-two-port-condition-y-parameters
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-7

## Question

What do you understand by a reciprocal two port network? Derive the condition for reciprocity in terms of 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.

## Answer

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):

```text
I2a = y21 Va
```

**Case 2.** The same source, now Vb = Va, applied at port 2, port 1 short-circuited (V1 = 0):

```text
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):

```text
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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In case 1, a source Va at port 1 produces what at port 2?
   A. Open circuit voltage
   B. Short-circuit current I2a = y21 Va
   C. I2a = y12 Va
   D. Current I2a = y22 Va
   Answer: B. With V2 = 0, I2 = y21 V1 so I2a = y21 Va. (Key point: Case 1 setup)

2. What condition for reciprocity in y-parameters is derived?
   A. y11 = y22
   B. y12 = y21
   C. y11 y22 = y12 y21
   D. y12 = -y21
   Answer: B. Equal currents for the interchanged source gives I2a/Va = I1b/Vb, so y21 = y12. (Key point: Reciprocity condition)

3. When is a reciprocal network also symmetrical?
   A. When y12 = 0
   B. When y11 = y22
   C. When AD - BC = 1
   D. When y21 = 0
   Answer: B. The ports can then be interchanged without changing terminal behaviour. (Key point: Symmetry)

## Close variants set in other exams

- [Reciprocal two-port and condition in T parameters](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Areciprocal-two-port-condition-t-parameters) — Electrical Circuit Theory, chapter 7, asked 2×

## Related in Electrical Circuit Theory

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