---
title: "Single wire radiation and travelling wave long wire"
subject: "Propagation and Antenna"
chapter: 1
key: "semester_6/propagation_and_antenna:single-wire-travelling-long-wire"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/single-wire-travelling-long-wire
site: BCT Engineering
---

# Single wire radiation and travelling wave long wire

Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals

- Asked in: 2078 Chaitra, 2+3+3 marks
- Video: [Travelling Wave antenna (Basics, Structure, Operation, Designing, Radiation, Pros & Cons) Explained](https://www.youtube.com/watch?v=xRbf4tNFDnw) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/single-wire-travelling-long-wire
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1

## Question

Define antenna. Explain the radiation mechanism in single wire antenna. Explain travelling wave long wire antenna with required diagrams.

## Short answer

A long wire fed at one end and terminated in its characteristic impedance carries only a forward travelling wave I=I0 e^(−jkz). Its pattern is E(θ)∝ sinθ sin[(kL/2)(1−cosθ)]/(1−cosθ); for L=5λ the main lobe angle is about 22.2° from the wire. It is unidirectional and broadband but loses power in the termination.

## Answer

An **antenna** is a device that converts guided EM energy from a transmission line into radiated free-space waves, and vice versa.

#### Radiation mechanism in a single wire
Radiation comes from **accelerated charges**, i.e. time-varying current:

```text
l · dI/dt = l · q · dv/dt
```

- No charge motion, or uniform motion along a straight infinite wire → no radiation.
- Uniform motion along a bent, curved, discontinuous or terminated wire → radiation at those points.
- Oscillating (AC) current → radiation along the whole wire.

So an antenna is fed with RF alternating current; the oscillating charges radiate. The field lines formed between the charges detach every half cycle and travel outward as free-space waves.

#### Travelling wave long wire antenna
A long wire (L of several wavelengths) a height h above ground, fed at one end and **terminated at the far end in a resistor equal to its characteristic impedance** (about 400–600 Ω). Because the end is matched, there is no reflection and only a **forward travelling wave** exists: I(z) = I0 e^(−jkz).

```text
 feed                         R = Z0 (matched)
  |  ------> travelling wave     |
 (~)===========================[R]
  |                               |
 ////////////// ground //////////////
         |<-------- L -------->|
```

Pattern (θ from the wire axis):

```text
E(θ) ∝ sinθ · sin[(kL/2)(1 − cosθ)] / (1 − cosθ)
Main lobe angle θm ≈ cos⁻¹(1 − 0.371 λ/L)
```

Example: L = 5λ → θm ≈ cos⁻¹(1 − 0.0742) ≈ 22.2° from the wire.

```text
         main lobes (cone about wire)
           \       /
            \     /   ---> towards load end
 feed o------\---/-------[R]
            /     \
           /       \
```

Characteristics:
- **Unidirectional:** radiation is in a cone towards the terminated end; no backward lobe.
- **Non-resonant and broadband**, since no standing wave; input impedance ≈ Z0 (resistive).
- Gain increases and the main lobe moves closer to the wire as L increases.
- Efficiency is reduced because part of the power is lost in the terminating resistor (about 30–50 %).
- Example: **Beverage antenna** for LF/MF reception; two such wires form V and rhombic antennas.

Compared with a resonant (standing-wave) long wire, which has lobes in both directions, the travelling-wave antenna has a single-direction pattern and wider bandwidth.

## Check yourself

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

1. What is the basic cause of radiation in a single wire?
   A. Resistance of the wire
   B. Static charge
   C. Accelerated charges, i.e. time-varying current
   D. Uniform charge motion on a straight infinite wire
   Answer: C. Radiation follows l·dI/dt = l·q·dv/dt, so time-varying current or accelerated charge radiates. (Key point: Radiation cause)

2. How is a travelling-wave long wire antenna terminated, and why?
   A. Open-circuited, to build a standing wave
   B. Short-circuited to ground
   C. In a resistor equal to its characteristic impedance, so there is no reflection
   D. In a capacitor to store energy
   Answer: C. A matched termination removes the reflected wave so only a forward travelling wave exists. (Key point: Termination)

3. What is the pattern of a travelling-wave long wire?
   A. Bidirectional with equal lobes both ways
   B. Omnidirectional
   C. Unidirectional, in a cone towards the terminated end with no backward lobe
   D. Radiates only broadside
   Answer: C. With only a forward wave, radiation is in a cone towards the load end. (Key point: Directional pattern)

4. What happens to the main lobe as the wire length L increases?
   A. It moves away from the wire
   B. It moves closer to the wire and gain increases
   C. It splits into two backward lobes
   D. It becomes omnidirectional
   Answer: B. θm ≈ cos^-1(1 - 0.371λ/L): the lobe tilts toward the wire as L grows and gain rises. (Key point: Effect of length)

5. Compared with a resonant long wire, the travelling-wave antenna is:
   A. Narrowband and 100% efficient
   B. Narrowband with a backward lobe
   C. Resonant with high reactance
   D. Broadband and non-resonant, but less efficient due to loss in the terminating resistor
   Answer: D. No standing wave gives wide bandwidth and input impedance near Z0, but part of the power is dissipated in the load resistor. (Key point: Bandwidth and efficiency)

## Related in Propagation and Antenna

- [Antenna definition and single wire radiation conditions](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Asingle-wire-radiation-conditions) — Propagation and Antenna, chapter 1, asked 4×
- [Single wire radiation and omnidirectional antenna characteristics](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Asingle-wire-radiation-omnidirectional) — Propagation and Antenna, chapter 1
- [Travelling wave antenna and V antenna](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Atravelling-wave-v-antenna) — Propagation and Antenna, chapter 3, asked 2×
- [Standing vs travelling wave; V antenna](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Astanding-travelling-v-antenna) — Propagation and Antenna, chapter 3, asked 2×
- [Standing vs travelling wave; Rhombic antenna](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Astanding-travelling-rhombic) — Propagation and Antenna, chapter 3, asked 2×
- [Single wire antenna and field line detachment](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Asingle-wire-field-line-detachment) — Propagation and Antenna, chapter 1, asked 3×

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