Quarter Wave Impedance Transformer Calculator

Calculator Inputs

Source impedance (Ω)

Load impedance (Ω)

Design frequency (MHz)

Velocity factor

Operating frequency (MHz)

Custom transformer impedance (Ω)

This model assumes resistive source and load impedances, plus a lossless matching section.

Example Data Table

Source Ω	Load Ω	Frequency MHz	Velocity Factor	Ideal Transformer Ω	Quarter Length cm
50	100	1000	0.66	70.71	4.95
75	300	433	0.82	150.00	14.20
50	25	915	0.70	35.36	5.73
50	200	2450	0.80	100.00	2.45

Formula Used

Ideal transformer impedance: Z_T = √(Z_S × Z_L)

Quarter-wave length in free space: l_free = c / (4f)

Quarter-wave length in medium: l = (c × VF) / (4f)

Wavelength in medium: λ = (c × VF) / f

Electrical length at another frequency: θ = (π / 2) × (f_op / f_design)

Input impedance of the section: Z_in = Z_T × (Z_L + jZ_Ttanθ) / (Z_T + jZ_Ltanθ)

Reflection coefficient: Γ = (Z_in − Z_S) / (Z_in + Z_S)

VSWR: (1 + |Γ|) / (1 − |Γ|)

Return loss: −20 log₁₀(|Γ|)

How to Use This Calculator

Enter the source impedance, usually your feed line impedance.
Enter the load impedance you want to match.
Set the design frequency in MHz.
Enter the transmission medium velocity factor.
Use the operating frequency to test off-design behavior.
Leave custom transformer impedance blank for the ideal value.
Click Calculate Transformer to show results above the form.
Review the chart, summary metrics, and export files if needed.

Frequently Asked Questions

1) What does a quarter-wave transformer do?

It matches one resistive impedance to another at a chosen frequency. The matching section is one quarter wavelength long in the selected transmission medium.

2) Why is the square root used?

For a lossless quarter-wave section, the ideal characteristic impedance equals the geometric mean of source and load impedances. That condition gives the best match at the design frequency.

3) Why does frequency matter so much?

The section works best when its electrical length is exactly 90 degrees. When frequency changes, the electrical length changes too, so matching quality also changes.

4) What is velocity factor?

Velocity factor shows how fast waves travel in the line compared with free space. A lower velocity factor means a shorter physical quarter-wave section.

5) Can I use this for complex impedances?

This page assumes positive resistive source and load values. For reactive or complex loads, you usually need additional network steps or a more detailed transmission-line design.

6) What does return loss tell me?

Return loss measures how much power reflects because of mismatch. Higher return loss generally means a better match and less reflected power.

7) Why can I enter a custom transformer impedance?

Real transmission lines come in fixed impedance values. A custom entry lets you test practical cable choices and see the mismatch created by non-ideal values.

8) What should I export?

Use the summary CSV for quick documentation, the sweep CSV for deeper analysis, and the PDF when you want a neat printable report.