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

# Knife edge diffraction

Propagation and Antenna · Chapter 5: Propagation between Antennas

- Asked in: 2081 Chaitra, 3 marks; 2080 Chaitra, 3 marks; 2079 Chaitra, 3 marks; 2077 Chaitra, 4 marks; 2076 Bhadra, 3 marks; 2075 Bhadra, 4 marks; 2075 Baisakh, 4 marks; 2074 Bhadra, 4 marks; 2073 Magh, 4 marks; 2072 Magh, 3 marks; 2072 Asoj, 3 marks; 2070 Magh, 2 marks; 2070 Bhadra, 5 marks (asked 13 times)
- Video: [Knife Edge Diffraction](https://www.youtube.com/watch?v=sE2XPQx00bs) — Shaveta puri
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/knife-edge-diffraction
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-5

## Question

Describe (write a short note on) Fresnel knife edge diffraction phenomenon.

## Short answer

Knife-edge diffraction describes wave bending around a sharp obstacle, allowing energy into the shadow region. The diffraction parameter v = h*sqrt(2(d1+d2)/(lambda*d1*d2)) quantifies obstruction; v=0 (grazing) gives 6 dB loss. Diffraction loss Gd is obtained from Fresnel integral approximations; for clear path, first Fresnel zone should be 60% clear.

## Answer

**Knife-edge diffraction** is the bending of a radio wave around a single sharp obstacle (a hill ridge, building edge) that blocks part of the line-of-sight path. It lets some energy reach a receiver in the "shadow" region, and the amount depends on how much of the first Fresnel zone is blocked.

#### Geometry

```text
                     /\  obstacle edge
                    /  \
   Tx o------------h----\-------------o Rx
        <--- d1 ---->|<----- d2 ----->
   h = height of edge above the LOS line
```

#### Huygens' principle

Every point on the wavefront above the edge acts as a secondary source. These secondary wavelets add up (with different phases) behind the obstacle, so the field in the shadow is weak but not zero.

#### Fresnel–Kirchhoff diffraction parameter

The obstruction is described by the dimensionless parameter

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

- v < 0: edge is below the LOS line (path clear)
- v = 0: edge just touches the LOS line
- v > 0: edge blocks the LOS line (receiver in shadow)

#### Diffraction loss

The received field is E = F(v)·E0, where E0 is the free-space field and F(v) is the complex Fresnel integral. The diffraction gain Gd = 20 log|F(v)| is read from a chart or approximated (Lee):

| Range of v | Gd (dB) |
|---|---|
| v ≤ −1 | 0 |
| −1 ≤ v ≤ 0 | 20 log(0.5 − 0.62v) |
| 0 ≤ v ≤ 1 | 20 log(0.5·e^(−0.95v)) |
| 1 ≤ v ≤ 2.4 | 20 log(0.4 − √(0.1184 − (0.38 − 0.1v)²)) |
| v > 2.4 | 20 log(0.225/v) |

#### Key points

- When the edge just grazes the LOS (v = 0), the field is halved: a loss of **6 dB**.
- For a clear path (v strongly negative) the field oscillates around E0 (±1 dB).
- Loss rises quickly in the shadow, roughly 20 log(0.225/v) for large v.
- For a negligible loss the first Fresnel zone should be at least about 60% clear of obstacles; this is used to fix tower heights in microwave link design.

## Check yourself

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

1. What does knife-edge diffraction describe?
   A. Reflection from the ionosphere
   B. Bending of radio waves around a sharp obstacle into the shadow region
   C. Absorption by rain
   D. Scattering in the troposphere
   Answer: B. Waves bend around a single sharp edge; wavelets from the wavefront above the edge fill the shadow weakly. (Key point: Concept)

2. What does v > 0 mean?
   A. The edge is below the LOS line
   B. The edge blocks the LOS line
   C. The path is clear
   D. No diffraction occurs
   Answer: B. v > 0 means the obstacle protrudes above the LOS line; v < 0 means clear path. (Key point: Parameter v)

3. What is the loss when the edge just touches the LOS (v = 0)?
   A. 0 dB
   B. 3 dB
   C. 6 dB
   D. 20 dB
   Answer: C. The field is halved, giving a 6 dB loss. (Key point: Grazing loss)

4. For negligible loss, how much of the first Fresnel zone should be clear?
   A. At least 60%
   B. 10%
   C. Exactly 0%
   D. 200%
   Answer: A. About 0.6 of the first Fresnel zone is used to fix tower heights. (Key point: Fresnel clearance)

## Related in Propagation and Antenna

- [Fresnel zone and knife edge diffraction](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afresnel-zone-knife-edge) — Propagation and Antenna, chapter 5

## 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