Octave Bandwidth Calculator | Qucs-S S-parameter Viewer Documentation

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# Octave Bandwidth Calculator

## Overview

Given a low and high corner frequency, computes the bandwidth, number of octaves and decades, center frequencies, and quality factor of the band.

## Formulas

### Center Frequencies

    f_c (arithmetic) = (f_high - f_low) / 2
    f_c (geometric)  = √(f_low × f_high)

### Bandwidth

    BW = f_high - f_low

### Octaves and Decades

    Octaves = log₂(f_high / f_low)
    Decades = log₁₀(f_high / f_low)

### Quality Factor

    Q = f_c (arithmetic) / BW

## Input Parameters

Parameter | Range | Default | Description
--- | --- | --- | ---
f_low | 1 – 10¹² | 1000 | Lower corner frequency
f_high | 1 – 10¹² | 2000 | Upper corner frequency

Both frequencies must share the same unit (Hz, kHz, MHz, etc.). The calculator does not perform unit conversion — the outputs inherit whatever unit the inputs use.

## Output

Parameter | Description
--- | ---
Central freq (Arithmetic mean) | Midpoint of the band
Central freq (Geometric mean) | Log-scale midpoint; preferred for RF
BW | Linear bandwidth
# Octaves | Number of frequency doublings in the band
# Decades | Number of frequency ×10 steps in the band
Q | Quality factor of the band

An error is displayed if f_high ≤ f_low. Q is shown as ∞ when BW is effectively zero.

## Example

Input:

- f_low: 1000 MHz

- f_high: 4000 MHz

Calculation:

    f_c (arithmetic) = (4000 - 1000) / 2        = 1500 MHz
    f_c (geometric)  = √(1000 × 4000)           = 2000 MHz
    BW               = 4000 - 1000              = 3000 MHz
    Octaves          = log₂(4000 / 1000)        = log₂(4) = 2.0
    Decades          = log₁₀(4000 / 1000)       = log₁₀(4) ≈ 0.6
    Q                = 1500 / 3000              = 0.5

Output:

Parameter | Value
--- | ---
Central freq (Arithmetic mean) | 1500.0
Central freq (Geometric mean) | 2000.0
BW | 3000.0
# Octaves | 2.0
# Decades | 0.6
Q | 0.5

## Notes

- Exactly 1 octave corresponds to a 2:1 frequency ratio; 1 decade to a 10:1 ratio