---
title: "Transmission and Y parameters with dependent current source"
subject: "Electrical Circuit Theory"
chapter: 7
key: "semester_3/electrical_circuit_theory:transmission-and-y-parameters-0-5i3"
source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/transmission-and-y-parameters-0-5i3
site: BCT Engineering
---

# Transmission and Y parameters with dependent current source

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

- Asked in: 2073 Shrawan
- Video: [PROBLEMS ON TWO PORT NETWORK WITH DEPENDANT SOURCES](https://www.youtube.com/watch?v=IOxzF6UYhKA) — Chaitanya Deshpande
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/transmission-and-y-parameters-0-5i3
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-7

## Question

For the Two Port network shown in figure find Transmission parameter and Y-parameter.
[Figure: port 1 (V1, I1); a dependent current source 0.5I3 (arrow pointing down) as a shunt branch at port 1 side, where I3 is the current flowing into the 10 Ω series resistor; a 10 Ω series resistor; a 6 Ω shunt resistor at port 2 side (V2, I2)]

## Short answer

Y = [0.15 −0.15; −0.1 0.2667] S. Transmission parameters: A = 8/3, B = 10 Ω, C = 0.25 S, D = 1.5.

## Answer

Transmission parameters: V1 = A V2 − B I2, I1 = C V2 − D I2. Admittance parameters: I1 = y11V1 + y12V2, I2 = y21V1 + y22V2.

**Reading the figure.** At port 1 side a dependent current source 0.5 I3 (arrow downward, to the bottom wire) is in shunt; then a 10 Ω series resistor carrying I3 (I3 flows from the port 1 node into the 10 Ω); and a 6 Ω shunt resistor across port 2. Since nothing lies between port 1 and the source, the port 1 node voltage is V1.

#### Equations

```text
I3 = (V1 − V2)/10
KCL at port 1 node:   I1 = I3 + 0.5 I3 = 1.5 I3
KCL at port 2 node:   I2 + I3 = V2/6
```

#### Y-parameters

```text
I1 = 1.5 (V1 − V2)/10 = 0.15 V1 − 0.15 V2
I2 = V2/6 − (V1 − V2)/10 = −0.1 V1 + (1/6 + 1/10) V2 = −0.1 V1 + 0.2667 V2
```

```text
y11 = 0.15 S = 3/20     y12 = −0.15 S = −3/20
y21 = −0.1 S = −1/10    y22 = 4/15 S = 0.2667 S
```

#### Transmission parameters

From the I2 equation: V1 = (0.2667 V2 − I2)/0.1 = 2.667 V2 − 10 I2, so A = 8/3, B = 10 Ω.
Then I1 = 0.15 V1 − 0.15 V2 = 0.15(2.667 V2 − 10 I2) − 0.15 V2 = 0.25 V2 − 1.5 I2, so C = 0.25 S, D = 1.5.

```text
A = 8/3 = 2.667     B = 10 Ω
C = 0.25 S          D = 1.5
Check: AD − BC = 4 − 2.5 = 1.5 ≠ 1  → network is not reciprocal (y12 ≠ y21).
```

**Answer: Y = [0.15 −0.15; −0.1 0.2667] S; T = [2.667 10 Ω; 0.25 S 1.5].**

## Check yourself

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

1. What does KCL at the port 1 node give?
   A. I1 = I3
   B. I1 = 1.5 I3
   C. I1 = 0.5 I3
   D. I1 = 2 I3
   Answer: B. I1 supplies both the current I3 into the 10 ohm resistor and the source current 0.5 I3. (Key point: KCL at port 1)

2. What are y11 and y21?
   A. y11 = 0.15 S, y21 = -0.1 S
   B. y11 = 0.1 S, y21 = -0.15 S
   C. y11 = 0.15 S, y21 = 0.1 S
   D. y11 = 0.2667 S, y21 = -0.1 S
   Answer: A. I1 = 0.15V1 - 0.15V2 and I2 = -0.1V1 + 0.2667V2. (Key point: Y-parameter results)

3. The answer finds AD - BC = 1.5. What does this mean?
   A. The network is reciprocal
   B. The network is not reciprocal (and y12 differs from y21)
   C. The network is symmetrical
   D. The determinant must be 0
   Answer: B. A reciprocal network has AD - BC = 1; here it is 1.5 because of the dependent source. (Key point: Reciprocity check)

## Related in Electrical Circuit Theory

- [Y and g parameters with dependent source 4V1](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Ay-and-g-parameters-1h-2f) — Electrical Circuit Theory, chapter 7
- [Z and T parameters with dependent source 2I1](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Az-and-t-parameters-2i1-two) — Electrical Circuit Theory, chapter 7, asked 2×
- [Z and T' parameters with dependent sources](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Az-and-t-parameters-dependent-sources) — Electrical Circuit Theory, chapter 7
- [Transmission and Y parameters, reciprocity and symmetry](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Atransmission-admittance-parameters-reciprocity-symmetry-2v2) — Electrical Circuit Theory, chapter 7
- [Z and T parameters with CCCS 4V1](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Az-and-t-parameters-4v1-2ohm) — 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×

## Related in other subjects

- [Series-parallel circuit with I1, I2, I3 phasors](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aseries-parallel-ac-v100-z1-z2-z3) — Basic Electrical Engineering, chapter 6, asked 2×
- [Two-port network model and parameters](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Atwo-port-network-model) — RF and Microwave Engineering, chapter 3
- [Source current from parallel branch currents](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aparallel-branch-currents-time-expression) — Basic Electrical Engineering, chapter 5
- [10 kVA 200/400 V LV-side parameters](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atransformer-10kva-oc-sc-lv-circuit) — Electrical Machine, chapter 2