What is a gamma match?
A gamma match is an impedance-matching technique commonly used on Yagi antennas, verticals, and other balanced driven elements that need to be fed with unbalanced coaxial cable. It combines two effects:
- An autotransformer-like resistance transformation set by the gamma rod geometry.
- A series capacitive reactance used to cancel inductive reactance from the gamma section.
The goal is to bring the feedpoint close to your transmission line impedance (often 50 ohms) with low SWR and predictable bandwidth.
How this gamma match calculator works
This tool uses a practical, first-pass engineering model that is widely used for initial gamma match design. It computes current division factor, transformed resistance, characteristic impedance of the gamma section, and the capacitor needed to tune out reactance at your selected frequency.
Core equations used
- u = a / a′
- v = s / a′
- α = ln(v) / [ln(v) − ln(u)]
- Step-up ratio = (1 + α)2
- Rg = (Ra / 2) × (1 + α)2
- Z0 ≈ 276 × log10(s / √(a·a′))
- XL = Z0 × tan(2πl), where l is electrical length in wavelengths
- C = 1 / (2πf|XL|)
After canceling reactance with the capacitor, the remaining mismatch is mostly resistive, and the estimated SWR is computed against your target line impedance.
Input guidance
Frequency and resistance
Set your operating frequency and the measured or modeled feedpoint resistance of the driven element before gamma tuning. If you do not have measurements yet, start with simulation values and refine later with an antenna analyzer.
Geometry values
Use actual physical radii and spacing in millimeters. Spacing is center-to-center between the driven element and gamma rod. Reasonable geometry is critical, because small changes in spacing can move transformed resistance significantly.
Electrical length
The gamma rod electrical length is entered as percent of wavelength. Typical useful values are below 25%. Very near 25%, reactance rises rapidly and real-world losses, coupling, and end effects become more sensitive.
Practical tuning workflow
- Start with a mechanically safe gamma spacing and rod length.
- Use this calculator to estimate initial capacitor value.
- Install a variable capacitor or adjustable capacitor arrangement.
- Measure SWR at low power and adjust capacitor first for minimum reactance.
- Adjust rod position/spacing/length to improve resistive match to 50 ohms.
- Repeat until SWR and bandwidth are acceptable at your target band.
Important limitations
This is a design estimator, not a substitute for measurement. Real antennas include boom effects, element coupling, nearby structures, conductor losses, weatherproofing parts, and component parasitics. Always validate final settings with an analyzer and observe RF safety procedures when testing.
Bottom line
A gamma match can be a robust way to feed antennas with coax while preserving practical mechanical construction. Use this calculator to get close quickly, then fine-tune on the antenna for best on-air performance.