--- title: "Z and T parameters with dependent source 2I1" subject: "Electrical Circuit Theory" chapter: 7 key: "semester_3/electrical_circuit_theory:z-and-t-parameters-2i1-two" source: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/z-and-t-parameters-2i1-two site: BCT Engineering --- # Z and T parameters with dependent source 2I1 Electrical Circuit Theory · Chapter 7: Two-port Parameter of Networks - Asked in: 2070 Asar (old course), 8 marks - Video: [Find Z parameters -Two port network - Dependent Source example - Hindi](https://www.youtube.com/watch?v=cssFA4Lo-Qo) — Electronics Subjectified - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electrical_circuit_theory/z-and-t-parameters-2i1-two - Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_circuit_theory/chapter-7 ## Question Find the Z-parameter and T-parameter for the two-port network given in the following figure. [Figure: port 1 (V1, I1) with a 2 Ω series resistor; a 1 Ω shunt resistor; a dependent voltage source 2I1 (+ on left, − on right) in the series arm; a 3 Ω shunt resistor; a 1 Ω series resistor to port 2 (V2, I2)] ## Short answer Formulating mesh equations with the dependent source yields Z11 = 13/4 Ω, Z12 = 3/4 Ω, Z21 = −3/4 Ω, Z22 = 7/4 Ω. The corresponding T-parameters are A = −13/3, B = −25/3 Ω, C = −4/3 S, D = −7/3. ## Answer Z-parameters: V1 = z11 I1 + z12 I2, V2 = z21 I1 + z22 I2. T-parameters: V1 = A V2 − B I2, I1 = C V2 − D I2. **Reading the figure (assumption).** 2 Ω series at port 1, then a 1 Ω shunt at node a, then the dependent voltage source 2I1 in the series arm (+ on the port 1 side, Va − Vb = 2I1) reaching node b, a 3 Ω shunt at node b, and a 1 Ω series resistor to port 2. #### Equations Let Is be the current through the 2I1 source (from a to b). ```text V1 = Va + 2 I1 Vb = Va − 2 I1 Node a: I1 = Va + Is (1 Ω shunt) Node b: Is = Vb/3 + (Vb − V2) (3 Ω shunt and the 1 Ω series) Port 2: I2 = V2 − Vb ``` From port 2: V2 = Vb + I2. Node b: Is = Vb/3 − I2, so Vb = 3 Is + 3 I2. Node a: Is = I1 − Va, and Va = V1 − 2 I1, so Is = 3 I1 − V1. Hence Vb = 9 I1 − 3 V1 + 3 I2. Also Vb = Va − 2 I1 = V1 − 4 I1. Equate: ```text V1 − 4 I1 = 9 I1 − 3 V1 + 3 I2 → 4 V1 = 13 I1 + 3 I2 V1 = (13/4) I1 + (3/4) I2 V2 = I2 + Vb = I2 + V1 − 4 I1 = −(3/4) I1 + (7/4) I2 ``` #### Z-parameters ```text z11 = 13/4 Ω z12 = 3/4 Ω z21 = −3/4 Ω z22 = 7/4 Ω Δz = (13/4)(7/4) + (3/4)(3/4) = 100/16 = 25/4 ``` #### T-parameters (from Z) ```text A = z11/z21 = −13/3 B = Δz/z21 = −25/3 Ω C = 1/z21 = −4/3 S D = z22/z21 = −7/3 ``` Check: AD − BC = 91/9 − 100/9 = −1 (not 1, so not reciprocal), and A ≠ D, so not symmetrical. **Answer: Z = [13/4 3/4; −3/4 7/4] Ω; T: A = −13/3, B = −25/3 Ω, C = −4/3 S, D = −7/3.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What relation does the source 2I1 impose? A. Vb = Va - 2I1 B. Vb = Va + 2I1 C. Vb = 2I1 D. Vb = V1 - 2I1 only Answer: A. The source has its + on the port 1 side, so Va - Vb = 2I1. (Key point: Controlled source) 2. What is the Z matrix? A. [13/4 3/4; -3/4 7/4] ohm B. [13/4 -3/4; 3/4 7/4] ohm C. [7/4 3/4; -3/4 13/4] ohm D. [2 1; 1 3] ohm Answer: A. V1 = (13/4)I1 + (3/4)I2 and V2 = -(3/4)I1 + (7/4)I2. (Key point: Z result) 3. With delta z = 25/4 and z21 = -3/4, what is B? A. -25/3 ohm B. 25/3 ohm C. -13/3 ohm D. -4/3 ohm Answer: A. B = delta z/z21 = (25/4)/(-3/4) = -25/3. (Key point: Z to T) 4. AD - BC = -1. What does it imply? A. Reciprocal B. Not reciprocal, and A differs from D so not symmetrical C. Symmetrical D. Lossless Answer: B. Reciprocity needs AD - BC = 1. (Key point: Reciprocity check) ## Close variants set in other exams - [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 Electrical Circuit Theory - [Transmission and Y parameters with dependent current source](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Atransmission-and-y-parameters-0-5i3) — Electrical Circuit Theory, chapter 7 - [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 - [Laplace: i1, i2 in unenergised two-mesh network](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Alaplace-two-mesh-unenergised-100v-10ohm) — Electrical Circuit Theory, chapter 4, asked 3× - [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 - [Voltage ratio transfer function of two-section LC network](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Avoltage-ratio-tf-two-1h-shunt) — Electrical Circuit Theory, chapter 5 ## Related in other subjects - [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 - [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× - [Importance of S-parameters and two-port derivation](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3As-parameters-two-port-derivation) — RF and Microwave Engineering, chapter 3, asked 3× - [S-parameters and three-port network S-matrix](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3As-matrix-three-port-network) — RF and Microwave Engineering, chapter 3, asked 4×