Frequency ↔ Wavelength Converter | Qucs-S S-parameter Viewer Documentation

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# Frequency ↔ Wavelength Converter

## Overview

The Frequency-Wavelength converter provides bidirectional conversion between frequency and wavelength, accounting for the medium’s relative permittivity.

## Formulas

### Frequency to Wavelength

    λ = c / (f × √εᵣ)

### Wavelength to Frequency

    f = c / (λ × √εᵣ)

Where:

- `λ` = wavelength in meters

- `f` = frequency in Hz

- `c` = speed of light (299,792,458 m/s)

- `εᵣ` = relative permittivity of the medium

## Conversion Modes

The calculator supports two modes:

1. Frequency → Wavelength: Input frequency, calculate wavelength

2. Wavelength → Frequency: Input wavelength, calculate frequency

## Output

The calculator displays:

- Frequency (f): Operating frequency

- λ: Wavelength

- λ/2: Half wavelength

- λ/4: Quarter wavelength

## Example 1: Frequency to Wavelength

Input:

- Mode: Frequency → Wavelength

- Frequency: 1000 MHz

- εᵣ: 4.7 (FR4)

Calculation:

    f = 1×10⁹ Hz
    √εᵣ = √4.7 ≈ 2.168
    λ = 299,792,458 / (10⁹ × 2.168)
      = 13.8 cm

## Example 2: Wavelength to Frequency

Input:

- Mode: Wavelength → Frequency

- Wavelength: 30 cm

- εᵣ: 1.0 (vacuum/air)

Calculation:

    λ = 0.30 m
    √εᵣ = √1.0 = 1.0
    f = 299,792,458 / (0.30 × 1.0)
      = 999.3 MHz

## Common Material Permittivities

Material | εᵣ (Typical)
--- | ---
Vacuum/Air | 1.0
RO4003C | 3.55
FR4 | 4.3 - 4.7
Alumina | 9.8

## Notes

- The wavelength is shorter in materials with higher permittivity

- Permittivity must be ≥ 1