Guided Wavelength in Dielectric
λg = c / (f · √εr)
Quick answer
This calculator solves λg = c / (f × √εr) for Guided Wavelength. With Frequency 2.4 GHz, Dielectric Constant 0.5, the result is 17.67 cm. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A wave travels slower inside a dielectric, so its wavelength on a PCB is shorter than in free space by the square root of the effective permittivity. The guided wavelength sets the physical length of quarter-wave stubs, patch antennas, couplers, and matching sections. Designing any distributed RF structure starts from this shortened wavelength.
Variables
- λg — Guided wavelength in the medium (m)
- f — Frequency (Hz)
- εr — Effective dielectric constant
- c — Speed of light
Practical Notes
On FR-4 (εr ≈ 4.3) a structure is about half its free-space size. Use the effective permittivity of the actual line type (microstrip εeff is between 1 and εr) for accurate lengths.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| lambda | Guided Wavelength | mm | mm, cm, m, km |
| f | Frequency | GHz | Hz, kHz, MHz, GHz |
| er | Dielectric Constant | — | — |
Step by step
- 1. What you know: Frequency 2.4 GHz, Dielectric Constant 0.5
- 2. The relation: λg = c / (f × √εr)
- 3. Substitute: f = 2.4 GHz, er = 0.5
- 4. Result: Guided Wavelength = 17.67 cm
Worked examples
Minimum range
Given: Frequency 100 MHz, Dielectric Constant 0.025
Result: Guided Wavelength = 18.96 m
Low range
Given: Frequency 1 GHz, Dielectric Constant 0.25
Result: Guided Wavelength = 0.5996 m
Typical
Given: Frequency 2.4 GHz, Dielectric Constant 0.5
Result: Guided Wavelength = 17.67 cm
High range
Given: Frequency 10 GHz, Dielectric Constant 0.8
Result: Guided Wavelength = 3.352 cm
Maximum range
Given: Frequency 100 GHz, Dielectric Constant 8
Result: Guided Wavelength = 1.06 mm
Solving for each variable
Solve for Guided Wavelength
Frequency 100 MHz, Dielectric Constant 0.025 → 18.96 m
Solve for Frequency
Guided Wavelength 0.1 mm, Dielectric Constant 0.025 → 18960 GHz
Solve for Dielectric Constant
Guided Wavelength 0.1 mm, Frequency 100 MHz → 8.99 × 10⁸
How Guided Wavelength changes with Frequency
| Frequency (input) | Guided Wavelength (result) |
|---|---|
| 0.24 GHz | 1.767 m |
| 0.6 GHz | 0.7066 m |
| 1.2 GHz | 35.33 cm |
| 1.8 GHz | 23.55 cm |
| 2.4 GHz | 17.67 cm |
| 3.6 GHz | 11.78 cm |
| 4.8 GHz | 8.833 cm |
| 9.6 GHz | 4.416 cm |
| 16.8 GHz | 2.524 cm |
| 24 GHz | 1.767 cm |
The same result in other units
| Unit | Value |
|---|---|
| mm | 176.7 |
| cm | 17.67 |
| m | 0.1767 |
| km | 0.0001767 |
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<p><a href="https://vbatpower.com/formulas/guided-wavelength/">Guided Wavelength in Dielectric</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Guided Wavelength in Dielectric?
Use λg = c / (f × √εr). With Frequency 2.4 GHz, Dielectric Constant 0.5, Guided Wavelength works out to 17.67 cm.
How do you calculate guided wavelength?
Rearrange for Guided Wavelength: with Frequency 1 GHz, Dielectric Constant 0.25, Guided Wavelength is 0.5996 m.
What is the formula for Guided Wavelength in Dielectric?
The formula is λg = c / (f × √εr). A wave travels slower inside a dielectric, so its wavelength on a PCB is shorter than in free space by the square root of the effective permittivity.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Guided Wavelength 0.1 mm, Dielectric Constant 0.025, Frequency is 18960 GHz.
How do you find Dielectric Constant when you know the other values?
Rearrange for Dielectric Constant: with Guided Wavelength 0.1 mm, Frequency 100 MHz, Dielectric Constant is 8.99 × 10⁸.
What units does Guided Wavelength in Dielectric use?
Guided Wavelength is shown in mm, cm, m, km. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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