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Quarter-Wave Transformer

#matching#quarter wave#transformer#impedance transformation

Quarter-Wave Transformer

A quarter-wave transformer is a simple and elegant matching technique that uses a transmission line exactly λ/4 long to transform one impedance to another. It provides a perfect match at the design frequency.

ZT=Z0⋅ZLZ_T = \sqrt{Z_0 \cdot Z_L}

Alternative Forms

Length Formula
L=λ4=c4fL = \frac{\lambda}{4} = \frac{c}{4f}
Physical length of the transformer section
Bandwidth Approximation
Δff0=2−4πcos⁡−1(Γm1−Γm2⋅2Z0ZL∣ZL−Z0∣)\frac{\Delta f}{f_0} = 2 - \frac{4}{\pi}\cos^{-1}\left(\frac{\Gamma_m}{\sqrt{1-\Gamma_m^2}}\cdot\frac{2\sqrt{Z_0 Z_L}}{|Z_L - Z_0|}\right)
Fractional bandwidth for a maximum acceptable reflection Γm (single section, Pozar)

Input Variables

Ω

Impedance to match from (typically 50Ω)(Range: 1 – 1000 Ω)

Ω

Impedance to match to(Range: 1 – 1000 Ω)

MHz

Design frequency(Range: 1 – 100000 MHz)

Results

Transformer Impedance (Z_T)
—
Transformer Length (L)
—

📖 Example: 50Ω to 100Ω Match

Design a quarter-wave transformer to match 50Ω to 100Ω at 1 GHz

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