What is the formula for Guided Wavelength in Dielectric?

The Guided Wavelength in Dielectric formula is λg = c / (f × √εr), where λg—Guided wavelength in the medium (m); f—Frequency (Hz); εr—Effective dielectric constant; c—Speed of light.

What does λg mean in the Guided Wavelength in Dielectric formula?

λg is Guided wavelength in the medium (m).

Guided Wavelength in Dielectric

Q: How do you calculate Guided Wavelength in Dielectric?

Use the formula 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. Enter the values you know in the calculator above and it solves for the remaining variable.

λg = c / (f · √εr)

Calculator

Guided Wavelength

Frequency

Dielectric Constant

Result

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Formula

λg = c / (f × √εr)

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.

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