---
title: "Antenna input impedance"
subject: "Propagation and Antenna"
chapter: 2
key: "semester_6/propagation_and_antenna:input-impedance"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/input-impedance
site: BCT Engineering
---

# Antenna input impedance

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2079 Chaitra, 3 marks
- Video: [Introduction, Input Impedance - Antenna Basics](https://www.youtube.com/watch?v=vYERon53ysk) — Uniinfo Telecom Services Ltd.
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/input-impedance
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Explain the input impedance of an antenna.

## Short answer

Input impedance Z_in = R_in + jX_in, where R_in includes radiation resistance Rr and loss resistance R_L. Antenna is resonant when X_in=0. For a λ/2 dipole Z_in ≈73+j42.5 Ω (shortened to ~73 Ω resonant). Matching ensures maximum power transfer.

## Answer

**Input impedance** is the impedance seen at the antenna's feed terminals, i.e. the ratio of voltage to current there (or of E to H at a reference point).

```text
Z_in = R_in + j X_in
R_in = Rr + RL
```

- **Rr** (radiation resistance) represents power radiated; **RL** represents ohmic and dielectric loss.
- **X_in** represents energy stored in the near field.
- The antenna is **resonant** when X_in = 0.

Z_in depends on frequency, antenna length, feed point, and nearby objects/ground. Examples: λ/2 dipole ≈ 73 + j42.5 Ω (slightly shortened → 73 Ω), λ/4 monopole ≈ 36.5 Ω, folded dipole ≈ 292 Ω.

For maximum power transfer, Z_in must match the line Z0 (Γ = (Z_in − Z0)/(Z_in + Z0) → 0). Mismatch gives VSWR > 1 and reflected power; matching networks or baluns are used.

## Check yourself

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

1. What does the resistive part of Z_in contain?
   A. Only the reactance of the near field
   B. Radiation resistance plus loss resistance (R_in = Rr + RL)
   C. Only the radiation resistance, losses are ignored
   D. The characteristic impedance of the line
   Answer: B. Rr represents radiated power and RL ohmic and dielectric loss; X_in is the stored near-field energy. (Key point: Components of Z_in)

2. When is an antenna resonant?
   A. When R_in = 0
   B. When Rr = RL
   C. When the reactance X_in = 0
   D. When VSWR is infinite
   Answer: C. At resonance the input impedance is purely resistive. (Key point: Resonance)

3. What happens if Z_in is not matched to the line impedance Z0?
   A. Γ is non-zero, VSWR > 1 and power is reflected
   B. Γ = 0 and all power is radiated
   C. The antenna stops being reciprocal
   D. The radiation resistance becomes zero
   Answer: A. Maximum power transfer needs Z_in = Z0; mismatch causes reflected power. (Key point: Matching)

## Related in Propagation and Antenna

- [Comparing λ/2, λ and 3λ/2 dipoles](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Adipole-lengths-comparison) — Propagation and Antenna, chapter 1

## Related in other subjects

- [Input intrinsic impedance via reflection](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Ainput-intrinsic-impedance-reflection) — Electromagnetism, chapter 4
- [Derive input impedance of transmission line](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aderive-input-impedance-line) — Electromagnetism, chapter 5
- [CE small-signal model, gain and input impedance](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-small-signal-gain-input-impedance) — Electronics Devices and Circuit, chapter 2
- [Input impedance of inverting op-amp](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ainverting-input-impedance) — Advanced Electronics, chapter 2