Series Capacitors Calculator | Qucs-S S-parameter Viewer Documentation

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# Series Capacitors Calculator

## Overview

Calculates the equivalent capacitance of any number of capacitors connected in series.

## Formula

    C_eq = 1 / (1/C₁ + 1/C₂ + ... + 1/Cₙ)

Series capacitance follows the same reciprocal-sum structure as parallel resistances and parallel inductances. The equivalent capacitance is always less than the smallest individual capacitor.

## Input Parameters

Parameter | Default | Description
--- | --- | ---
C₁…Cₙ | 1pF | Capacitance values

## Capacitance Parsing

Values are entered as strings using standard shorthand notation, where the prefix letter replaces the decimal point. A trailing `F` is optional and ignored.

Input | Parsed Value
--- | ---
`100` | 100 F
`1pF` | 1 pF
`4n7` | 4.7 nF
`0p5F` | 0.5 pF
`22uF` | 22 μF
`10n` | 10 nF

Supported prefixes: `p` (10⁻¹²), `n` (10⁻⁹), `u` (10⁻⁶), `m` (10⁻³). Output formatting also covers `fF` (10⁻¹⁵).

## Output

- C_{eq}: Equivalent capacitance of the series network

## Example

Input:

- C₁ = 1pF, C₂ = 2p2, C₃ = 4n7

Calculation:

    C_eq = 1 / (1/1e-12 + 1/2.2e-12 + 1/4.7e-9)
         = 1 / (1e12 + 4.545e11 + 2.128e8)
         ≈ 1 / (1.4549e12)
         ≈ 0.6873 pF

Output:

Parameter | Value
--- | ---
C_{eq} | 0.6873 pF

In this case C₁ and C₂ dominate because they are orders of magnitude smaller than C₃ — the series result is pulled toward the smallest capacitor.

## See Also

- Parallel Resistors Calculator
- Parallel Inductors Calculator
- RF Engineering Calculators