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Quarter-Wave Transformer Calculator (lambda/4 Impedance Match)

Single-section quarter-wave transformer between Z1 and Z2. Returns the geometric-mean Zt, the lambda_g/4 length, and the three microstrip section widths (W1, Wt, W2) on your stackup.

Quarter-Wave Transformer Calculator

A lambda_g/4 line of impedance sqrt(Z1 Z2) matches Z2 to Z1 at a single frequency. Lay out all three sections (Z1, Zt, Z2) on your microstrip stackup in one go.

Units
Length
Frequency

Inputs

Impedances and frequency
Ω
Ω
GHz
Microstrip stackup
mm
Z₁ = 50.0 ΩZt = 100.0 ΩZ₂ = 200.0 Ωλg/4 = 18.915 mm
Quarter-wave transformer
Transformer Zt
100.00Ω
Section length
18.915mm
744.67 mil

Microstrip widths

W1 (source side)1.112 mm
Wt (transformer)0.276 mm
W2 (load side)0.021 mm

More

Pre-match Γ0.600
Pre-match return loss4.4 dB
Effective eeff (Zt section)2.616
Guided lambda_g75.66 mm

Analytical calculation

Every step the calculator runs, with the formula, your numbers plugged in, and the result.

Transformer impedance
A lambda/4 line matches via the geometric mean of source and load.
Pre-match reflection
What you would see if you skipped the transformer.
Microstrip widths
Solve Hammerstad-Jensen W(Z) on this stackup so each section is laid out, not just sized.
Effective permittivity (Zt section)
Use the Zt section's eeff so the lambda_g/4 length matches what you will fabricate.
Section length
Guided quarter-wave at f0.

Frequently asked

Why sqrt(Z1 Z2)?

It is the geometric mean. A lambda/4 line transforms Z_load to Z0^2/Z_load; set Z0 to sqrt(Z1 Z2) and the load looks like Z1 exactly at f0.

Why are the section widths different?

Lower characteristic impedance needs a wider trace on the same stackup. Z1 (50 ohm) is wider than Zt (about 100 ohm), which is wider than Z2 (200 ohm). All three sections need to be on the same stackup so the eeff (and therefore the lambda_g/4 length) is consistent.

References

  • PrimaryPozar, D. M. Microwave Engineering, 4th ed., Wiley 2011, Sec. 5.4 (single-section quarter-wave transformer). Section length is lambda_g/4 with eeff drawn from the Zt section's microstrip geometry.
  • Microstrip layoutHammerstad, E. & Jensen, O. 1980 (per-section width and the section eeff that drives the lambda_g/4 length).
  • ConceptQuarter-wave impedance transformer (overview)

Closed-form is just the start.

These calculators hand you the analytical starting point. RayRF takes you the rest of the way: antennas, filters, feedlines, and more, simulated on your real stackup with copper losses, dielectric loss, and finite ground. Roughly a second per iteration.

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