---
title: "Thevenin theorem for antennas"
subject: "Propagation and Antenna"
chapter: 1
key: "semester_6/propagation_and_antenna:thevenin-theorem"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/thevenin-theorem
site: BCT Engineering
---

# Thevenin theorem for antennas

Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals

- Asked in: 2079 Chaitra, 3 marks
- Video: [Thevenin's equivalent of antenna in transmitting mode](https://www.youtube.com/watch?v=ObDdLZ5-nGA) — Rekha Labade
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/thevenin-theorem
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1

## Question

State the Thevenin theorem for an antenna.

## Short answer

Thevenin theorem: any linear two-terminal network equals open-circuit voltage V_th in series with impedance Z_th (sources replaced by internal impedances). For receiving antenna, induced voltage V_oc in series with antenna impedance Z_A = R_r + R_L + jX_A. Load current I = V_oc/(Z_A+Z_L); maximum power transfer with conjugate matching Z_L = Z_A*.

## Answer

**Thevenin theorem:** Any linear two-terminal network containing sources and impedances can be replaced by a single voltage source V_th (the open-circuit voltage at the terminals) in series with an impedance Z_th (the impedance seen into the terminals with all sources replaced by their internal impedances).

#### Applied to a receiving antenna
An incident wave induces an emf on the antenna. Seen from its terminals, the antenna is a voltage source **V_oc** (open-circuit induced voltage) in series with the **antenna impedance**

```text
Z_A = (R_r + R_L) + j X_A
```

where R_r = radiation resistance, R_L = loss resistance, X_A = antenna reactance.

```text
      Z_A = R_r + R_L + jX_A
   +-----/\/\/\-----+
   |                |
  (~) V_oc         [Z_L]  receiver
   |                |
   +----------------+
```

Current in the receiver load:

```text
I = V_oc / (Z_A + Z_L)
```

With conjugate matching (Z_L = Z_A*), maximum power is delivered: P = |V_oc|²/(8 R_A) (peak V_oc).

Use: finding received power, effective aperture and mismatch loss of a receiving antenna system.

## Check yourself

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

1. What does Thevenin's theorem replace a linear two-terminal network with?
   A. A current source in series with a resistor
   B. A voltage source V_th (open-circuit voltage) in series with Z_th
   C. Two parallel resistors
   D. A capacitor
   Answer: B. V_th is the open-circuit voltage and Z_th the impedance seen with sources replaced by their internal impedances. (Key point: Statement)

2. How is a receiving antenna represented using Thevenin's theorem?
   A. A voltage source V_oc in series with Z_A = (R_r + R_L) + jX_A
   B. A current source with no impedance
   C. A radiation resistance only
   D. A capacitor in series with V_oc
   Answer: A. The incident wave induces V_oc; the antenna impedance includes radiation resistance, loss resistance and reactance. (Key point: Receiving antenna model)

3. What is the receiver load current?
   A. I = V_oc·(Z_A + Z_L)
   B. I = V_oc/Z_L
   C. I = V_oc/(Z_A - Z_L)
   D. I = V_oc/(Z_A + Z_L)
   Answer: D. The series loop gives I = V_oc/(Z_A + Z_L). (Key point: Load current)

4. With conjugate matching Z_L = Z_A*, the power delivered is:
   A. |V_oc|^2/(8 R_A)
   B. |V_oc|^2/(2 R_A)
   C. |V_oc|^2/R_A
   D. 0
   Answer: A. Maximum power is P = |V_oc|^2/(8R_A) for peak V_oc. (Key point: Matched power)

## Related in Propagation and Antenna

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## Related in other subjects

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- [Current in 5Ω using Thevenin theorem](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Athevenin-5-ohm-cd-1a-8v) — Basic Electrical Engineering, chapter 3
- [Thevenin theorem, current in 10Ω](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Athevenin-current-10-ohm-20v-12v) — Basic Electrical Engineering, chapter 3