---
title: "Fresnel zone and knife edge diffraction"
subject: "Propagation and Antenna"
chapter: 5
key: "semester_6/propagation_and_antenna:fresnel-zone-knife-edge"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/fresnel-zone-knife-edge
site: BCT Engineering
---

# Fresnel zone and knife edge diffraction

Propagation and Antenna · Chapter 5: Propagation between Antennas

- Asked in: 2071 Magh, 4 marks
- Video: [LoRa/LoRaWAN tutorial 7: Fresnel Zone](https://www.youtube.com/watch?v=HWOivbJjw7s) — Mobilefish.com
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/fresnel-zone-knife-edge
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-5

## Question

Explain Fresnel zone and knife edge diffraction.

## Short answer

Fresnel zones are ellipsoids with path difference nλ/2; blocking the first zone increases diffraction loss. Knife-edge diffraction occurs when a sharp obstacle obstructs the path; loss depends on parameter v = h√[2(d1+d2)/(λ d1 d2)] (h is edge height above LOS), and equals ~6 dB when v=0.

## Answer

#### Fresnel zones

**Fresnel zones** are concentric ellipsoids around the direct Tx–Rx line. A path through any point on the boundary of the *n*th zone is longer than the direct path by nλ/2.

```text
          _..--~~~~~~~~--.._     1st zone
   Tx o<------- d1 ------>|<----- d2 ---->o Rx
          ~~--..______..--~~
```

Radius of the nth zone at distances d1 and d2 from the ends:

```text
rn = √( n·λ·d1·d2 / (d1 + d2) )
```

- Waves from successive zones differ in phase by 180°, so most useful energy travels inside the first zone.
- Blocking part of the first zone causes diffraction loss even if the optical path is clear. Links are designed to keep at least 0.6r1 clear.

#### Knife-edge diffraction

When a single sharp obstacle (ridge, building edge) blocks the path, the wave bends over the edge into the shadow region (Huygens' principle: each point on the wavefront above the edge acts as a new source). The obstruction is measured by the **Fresnel–Kirchhoff parameter**

```text
v = h·√( 2(d1 + d2) / (λ·d1·d2) )
```

where *h* is the height of the edge above the LOS line (negative if below).

| Condition | v | Diffraction loss |
|---|---|---|
| Path well clear | v ≤ −1 | ≈ 0 dB |
| Edge touches LOS | v = 0 | 6 dB |
| Edge blocks LOS | v = 1 | ≈ 14 dB |
| Deep shadow | v > 2.4 | ≈ 20 log(v/0.225) dB |

The two ideas are linked: v = √2·h/r1, so the loss depends on how much of the first Fresnel zone the edge covers.

## Check yourself

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

1. Blocking part of the first Fresnel zone causes:
   A. Diffraction loss even if the optical LOS is clear
   B. Gain increase
   C. Polarisation rotation
   D. No effect if the optical LOS is clear
   Answer: A. The first zone carries most of the energy. (Key point: Fresnel zone)

2. When the knife edge just touches the LOS (v = 0), the diffraction loss is about:
   A. 0 dB
   B. 6 dB
   C. 14 dB
   D. 20 dB
   Answer: B. Grazing gives 6 dB. (Key point: Knife edge loss)

3. The Fresnel–Kirchhoff parameter v depends on:
   A. Earth radius
   B. Edge height h, wavelength and distances d1, d2
   C. Only the frequency
   D. Only the antenna gain
   Answer: B. v = h sqrt(2(d1+d2)/(λd1d2)). (Key point: Parameter v)

4. The relation v = √2·h/r1 shows that:
   A. Loss is independent of h
   B. v is always negative
   C. Loss depends on how much of the first zone the edge covers
   D. v is independent of r1
   Answer: C. v scales with h relative to r1. (Key point: Link to Fresnel zone)

## Related in Propagation and Antenna

- [Knife edge diffraction](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aknife-edge-diffraction) — Propagation and Antenna, chapter 5, asked 13×

## Related in other subjects

- [Diffraction and Fresnel zone phase difference](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adiffraction-fresnel-zone) — Wireless Communication, chapter 3