RF quarter-wave transformer calculator

Calculate ideal transformer impedance and quarter-wave physical length with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use ideal transformer impedance and quarter-wave physical length to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Source resistance (ohms)
50
Load resistance (ohms)
100
Frequency (MHz)
100
Velocity factor
0.66
Ideal transformer impedance (ohms)
70.710678
Quarter-wave physical length (m)
0.494658

Try another scenario

Source resistance (ohms)
55.00000000000001
Load resistance (ohms)
100
Frequency (MHz)
100
Velocity factor
0.66
Ideal transformer impedance (ohms)
74.161985
Quarter-wave physical length (m)
0.494658
Calculation method

Calculation method

Ideal transformer impedance (ohms)

sqrt(source resistance × load resistance).

Quarter-wave physical length (m)

c velocity factor/(4 frequency).

Symbols and units
a
Source resistance (ohms)
b
Load resistance (ohms)
c
Frequency (MHz)
d
Velocity factor

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Source-load resistances, frequency, velocity factor. Returns Ideal transformer impedance and length. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Source resistance (ohms): minimum 1e-12, maximum 1000000000000.0. Load resistance (ohms): minimum 1e-12, maximum 1000000000000.0. Frequency (MHz): minimum 1e-12, maximum 1000000000000.0. Velocity factor: minimum 1e-12, maximum 1.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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