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Quarter-wave impedance transformer
Line impedance and length between two resistive impedances.
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Formula & context
Zt = √(R₁R₂); L = c · VF/(4f)
A lossless quarter-wave line transforms a resistive load according to Zin = Zt²/Rload. The geometric mean of the resistances gives the required line impedance.
A worked example
An ideal match between 50 and 100 Ω requires 70.71 Ω. Length then depends on frequency and VF.
Assumptions & limits
Narrowband match for resistive impedances. Complex antenna impedances need additional treatment; an arbitrary cable does not replace the calculated impedance.
Impedance and matchingUnderstand the reasoning →From reading to experimenting
Quarter-wave impedance transformer
An ideal match between 50 and 100 Ω requires 70.71 Ω. Length then depends on frequency and VF.
Open example with starting values →Side A impedance: 50 Ω · Side B impedance: 100 Ω · Frequency: 14.2 MHz · Velocity / shortening factor: 0.66 Back to the learning article →Then change exactly one value. Compare the result and use the formula to explain why it changes. The model limits below the calculator also apply here.