Free Coaxial Stub Filter Calculator
Calculate precise physical cut lengths, notch attenuation depth, and harmonic suppression for open and short-circuited quarter-wave coaxial stubs.
📻 Frequency & Cable Parameters
Quarter-wave open stub presents a dead short (deep notch > 25 dB) at f_0, while passing even harmonics (2*f_0) transparently.
Quarter-Wave Electrical Length (Free Space λ0 = 80.53 in)
Trimming & Tuning Rule: Never cut coaxial stubs to exact theoretical length in one slice! Connector adapters (T-connectors) add 0.5" to 1.0" of equivalent electrical length. Cut 1/2" long, connect to a NanoVNA or antenna analyzer, and snip 1/16" (1.5mm) off the open end until the SWR notch hits your exact frequency.
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Transmission Line Stub Filtering Principles
A length of transmission line exhibits impedance transformation properties governed by telegrapher's equations. When teed across a transmission line feeding an antenna or receiver, a resonant stub acts as an ultra-high-Q notch trap or bandpass filter without requiring inductors or capacitors:
Coaxial Wavelength: λ_coax = λ0 × VF (Velocity Factor)
λ/4 Physical Length: L_q = (λ0 × VF) / 4
λ/2 Physical Length: L_h = (λ0 × VF) / 2
Quarter-Wave Open vs. Shorted Stubs
- Quarter-Wave (λ/4) Open Stub: An open circuit at the far end transforms into an effective dead short circuit ($Z_{in} approx 0 Omega$) at the tee connector at frequency $f_0$. This dumps unwanted RF power to ground, creating a deep 25 dB to 35 dB rejection notch. At $2 f_0$, it becomes a half-wave open stub ($Z_{in} approx infty$), passing signals transparently.
- Quarter-Wave (λ/4) Shorted Stub: A short circuit at the far end transforms into an open circuit ($Z_{in} approx infty$) at $f_0$, leaving your desired signal unaffected. However, at even harmonics ($2 f_0, 4 f_0$), it acts as a dead short to ground, making it an ideal 2nd harmonic transmitter suppression trap.
Why Cable Loss Governs Notch Depth
In an ideal lossless coaxial line, the impedance at resonance would be zero or infinity (yielding infinite attenuation). In real-world cables, the line's attenuation per foot determines the finite $Q$-factor of the stub. Low-loss cables like LMR-400 or RG-213 produce significantly deeper notches (30 dB to 40 dB) and narrower attenuation skirts than high-loss miniature lines like RG-174 or RG-58.
Frequently Asked Questions
How does a coaxial T-connector affect the stub length?
The metal body of a standard UHF (SO-239/PL-259) or BNC T-connector introduces approximately 15 mm to 25 mm (0.6" to 1.0") of dielectric and conductor path. This electrical length is part of your stub! Always start with your cable cut slightly long, then trim the far end while watching the transmission response (S21) on a NanoVNA.
What is Velocity Factor (VF) and why does it shorten the cable?
Radio waves travel slower through plastic dielectric insulation than through vacuum or air. In solid polyethylene (RG-58, RG-8), waves travel at only 66% the speed of light (VF = 0.66). In gas-injected foam (LMR-400, RG-8X), waves travel at 82% to 85% of light speed. A 0.66 VF cable will be physically 34% shorter than a free-space quarter-wavelength.
Can an open stub handle high transmitter power without arcing?
At the resonant frequency of a quarter-wave shorted stub, extremely high RF voltages develop at the open points. If you run 500W to 1,500W of transmitter power, use Teflon (PTFE) dielectric cable (such as RG-393 or RG-142) and insulate the open stub tip with heat shrink and silicone to prevent high-voltage RF corona arcing.