---
title: "Equivalent Y-parameter of parallel two-ports"
subject: "Electrical Circuit Theory"
chapter: 7
key: "semester_3/electrical_circuit_theory:equivalent-y-parameter-parallel-two-ports"
source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/equivalent-y-parameter-parallel-two-ports
site: BCT Engineering
---

# Equivalent Y-parameter of parallel two-ports

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

- Asked in: 2069 Chaitra, 4 marks; 2068 Shrawan, 4 marks (asked 2 times)
- Video: [Parallel−Parallel Interconnection of Two−Port Networks](https://www.youtube.com/watch?v=fj2GH5oCc0E) — 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/equivalent-y-parameter-parallel-two-ports
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-7

## Question

With necessary circuit diagram, obtain the equivalent Y-parameter if two-port networks are connected in parallel.

## Short answer

When two two-port networks are connected in parallel, they share the same port voltages, and the port currents add. The overall Y-parameter matrix is the sum of the individual Y-matrices: [Y] = [Ya] + [Yb], provided the port condition is satisfied.

## Answer

When two-port networks N_a and N_b are connected in parallel, their input ports are connected together and their output ports are connected together, so they share the same port voltages. The Y-parameters add.

```text
        +------------------+
 I1a -->|       Na         |--> ... I2a
        +------------------+
 I1 o---+                  +---o I2
        +------------------+
 I1b -->|       Nb         |--> ... I2b
        +------------------+
 V1 (common)                  V2 (common)
```

#### Derivation

For each network (Y-parameter equations):

```text
I1a = y11a V1 + y12a V2          I1b = y11b V1 + y12b V2
I2a = y21a V1 + y22a V2          I2b = y21b V1 + y22b V2
```

The connection gives V1a = V1b = V1 and V2a = V2b = V2, while the currents add:

```text
I1 = I1a + I1b = (y11a + y11b) V1 + (y12a + y12b) V2
I2 = I2a + I2b = (y21a + y21b) V1 + (y22a + y22b) V2
```

Comparing with I1 = y11V1 + y12V2, I2 = y21V1 + y22V2:

```text
[Y] = [Ya] + [Yb]
```

So y11 = y11a + y11b, y12 = y12a + y12b, y21 = y21a + y21b, y22 = y22a + y22b. For three networks in parallel: [Y] = [Ya] + [Yb] + [Yc] (and likewise for any number).

**Condition.** The result is valid only if the connection does not alter the individual Y-parameters (the port condition: the current entering one terminal of a port must equal the current leaving the other). When this fails (Brune test), isolating ideal 1:1 transformers are used.

## Check yourself

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

1. In a parallel connection of two two-port networks, which quantities are common to both networks?
   A. Port currents I1 and I2
   B. Port voltages V1 and V2
   C. Only V1
   D. Only I2
   Answer: B. Input ports are tied together and output ports are tied together, so both networks share the same V1 and V2 while the currents add. (Key point: Parallel connection variables)

2. What is the equivalent Y matrix of networks a and b in parallel?
   A. [Y] = [Ya][Yb]
   B. [Y] = [Ya] + [Yb]
   C. [Y] = [Ya]^-1 + [Yb]^-1
   D. [Y] = [Ya][Yb]^-1
   Answer: B. Since I1 = I1a + I1b and I2 = I2a + I2b with common voltages, each y-parameter is the sum of the individual ones. (Key point: Equivalent Y matrix)

3. When the Brune/port condition fails for a parallel connection, what is done?
   A. Z-parameters are used instead and multiplied
   B. Ideal 1:1 isolating transformers are used
   C. The networks are connected in cascade instead
   D. The result y = ya + yb is still valid
   Answer: B. If the connection alters the individual Y-parameters, isolating ideal 1:1 transformers restore the port condition. (Key point: Validity condition)

## Close variants set in other exams

- [Equivalent Z-parameter of three series two-ports](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aequivalent-z-parameter-three-series-two) — Electrical Circuit Theory, chapter 7, asked 3×

## Related in Electrical Circuit Theory

- [Equivalent T from Y parameters of series two-ports](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aequivalent-t-parameter-two-y-networks) — Electrical Circuit Theory, chapter 7
- [Cascaded two-ports: ABCD matrices multiply](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Acascade-transmission-matrix-product) — Electrical Circuit Theory, chapter 7
- [G21 and α21 of two-port terminated in 2 Ω](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Aterminated-two-port-g21-alpha21) — Electrical Circuit Theory, chapter 5
- [G21(S) and Z21(S) of two-port with 0.5 F, 1 H](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Ag21-z21-two-port-half-f) — Electrical Circuit Theory, chapter 5

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