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

# Reciprocal two-port and condition in T parameters

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

- Asked in: 2072 Chaitra, 4 marks
- Video: [Condition for Reciprocity in Two−Port Networks (Part 1)](https://www.youtube.com/watch?v=zk8Fzg6ahAA) — Neso Academy
- 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-t-parameters
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-7

## Question

What do you understand by reciprocal two-port network? Also derive the condition for the same in terms of T parameters.

## Short answer

A reciprocal two-port yields identical transfer ratios when excitation and response are swapped. From T equations, apply voltage at port1 with port2 shorted: I2 = −V/B. Apply same voltage at port2 with port1 shorted: I1 = V(BC−AD)/B. Reciprocity requires I2/V = I1/V, so AD − BC = 1.

## Answer

A two-port network is **reciprocal** if the ratio of the response at one port to the excitation at the other port is the same when the positions of excitation and response are interchanged (the reciprocity theorem). Networks made only of R, L, C and mutual inductance (no dependent sources, no gyrators) are reciprocal.

#### Derivation for T (ABCD) parameters

The equations are V1 = A V2 − B I2 and I1 = C V2 − D I2.

**Case 1.** Voltage Va applied at port 1, port 2 short-circuited (V2 = 0):

```text
Va = −B I2a    →   I2a = −Va/B
```

**Case 2.** Voltage Vb applied at port 2, port 1 short-circuited (V1 = 0):

```text
0 = A Vb − B I2b   →   I2b = A Vb/B
I1b = C Vb − D I2b = C Vb − D A Vb/B = Vb (BC − AD)/B
```

For a reciprocal network the transfer admittances are equal: (current at port 2 due to voltage at port 1) = (current at port 1 due to the same voltage at port 2). That is I2a/Va = I1b/Vb:

```text
−1/B = (BC − AD)/B   →   AD − BC = 1
```

**Condition for reciprocity: AD − BC = 1 (i.e. determinant of the T matrix = 1).**

(Reciprocity in other parameters: z12 = z21, y12 = y21. A reciprocal network is also *symmetrical* if A = D.)

## Check yourself

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

1. A two-port is reciprocal when:
   A. Its response to excitation at one port is the same ratio when excitation and response ports are interchanged
   B. It has equal impedance at both ports
   C. It contains dependent sources
   D. Its determinant of Z is zero
   Answer: A. This is the reciprocity theorem; networks of R, L, C and mutual inductance satisfy it. (Key point: Definition of reciprocity)

2. In case 2 of the derivation, what is set at port 1?
   A. Open circuit I1 = 0
   B. Short circuit V1 = 0
   C. A source Va
   D. A load
   Answer: B. Voltage Vb is applied at port 2 with port 1 shorted (V1 = 0), giving I2b = A Vb/B. (Key point: Case 2 setup)

3. What condition for reciprocity results in terms of T parameters?
   A. A = D
   B. AD - BC = 1
   C. B = C
   D. AD + BC = 1
   Answer: B. Equating -1/B with (BC - AD)/B gives AD - BC = 1. (Key point: Final condition)

## Close variants set in other exams

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

## Related in Electrical Circuit Theory

- [Z and g parameters, neither reciprocal nor symmetrical](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Az-and-g-parameters-neither-reciprocal) — Electrical Circuit Theory, chapter 7
- [Transmission and y parameters, prove not reciprocal or symmetrical](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Atransmission-and-y-parameters-neither-reciprocal) — Electrical Circuit Theory, chapter 7, asked 2×

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