Strong out-of-band radio frequency (RF) signals—such as nearby broadcast FM stations or pager transmitters—frequently desensitize amateur radio repeaters and VHF/UHF receivers. A coaxial quarter-wave stub provides a simple, highly effective passive notch filter. Connected in parallel across a feedline using a coaxial T-connector, an open-circuit transmission line measuring exactly one-quarter electrical wavelength transforms an open into a virtual RF short circuit at its resonant frequency, severely attenuating the offending interference while passing adjacent channels with minimal loss.

### Quarter-Wave Stub Mechanics and Velocity Factor Radio waves travel slower through coaxial cable dielectrics than through free space vacuum. The physical cutting length of a transmission line stub must be shortened by the cable dielectric velocity factor (VF): Physical Quarter-Wave Length (meters) = (c * Velocity Factor) / (4 * f_Hz) where c = 299,792,458 m/s and f_Hz = f_MHz * 10^6. - Solid Polyethylene Dielectrics (VF = 0.66): Found in standard RG-58, RG-8, and RG-213 cables. - Foam Polyethylene Dielectrics (VF = 0.82–0.85): Found in low-loss RG-8X, RG-6, and Times Microwave LMR-400 cables.

### Worked Numeric Scenario Suppose you construct an open-circuit quarter-wave notch filter to reject interference at 146.52 MHz using standard RG-58 coaxial cable: - Target Notch Frequency: 146.52 MHz - Cable Dielectric: Solid Polyethylene (Velocity Factor VF = 0.66) - Calculation: L = (299,792,458 * 0.66) / (4 * 146,520,000) = 197,863,022 / 586,080,000 = 0.3376 meters - Physical Cutting Length: 337.6 mm (13.29 inches)

When constructing the stub, cut the cable approximately 1/2-inch longer than calculated to allow room for trimming and tuning with an antenna analyzer or nanoVNA to account for connector pin inductance.

### Client-Side RF Privacy All wavelength formulas and dielectric calculations execute entirely inside your local web browser session. No operating frequencies, antenna parameters, or station configurations are uploaded to external servers.

How to Use

1
Enter your target notch frequency in MHz (e.g. 146.52 MHz).
2
Select your coaxial cable velocity factor (0.66 for solid PE, 0.82 for foam PE).
3
Choose stub termination (Quarter-Wave Open for notch filtering).
4
Note the calculated cutting length displayed in millimeters and inches.

Frequently Asked Questions

Why does an open-circuit quarter-wave stub act as a notch filter?

Transmission line impedance transformation causes an open circuit at the end of a quarter-wavelength line to reflect a 180-degree phase shift back to the input, creating a virtual dead short to ground at the resonant frequency.

Should I cut the cable to the exact calculated length immediately?

No. It is recommended to cut the coax slightly longer (about 10–15 mm) and trim it back while monitoring the notch frequency on an RF analyzer to achieve exact resonance.

Are my frequency parameters uploaded to a remote database?

No. All transmission line equations evaluate locally in client-side memory.

Coaxial Quarter-Wave Stub Notch Filter Calculator