During a recent balloon launch, I communicated with the other chase teams with my mobile rig, transmitting around 441 MHz with a transmit power of 10 watts = +40 dBm.

For the next balloon launch, I also wanted to put a 144 MHz APRS receiver on my car, but was worried about damaging the RTL-SDR dongle I would be using for receiving. RTL-SDR dongles have a maximum input of around +10 dBm with absolutely no filtering on the input, so I could potentially permanently damage the RTL-SDR dongle when I transmitted.

Moving and separating the antennas around on the car roof and trunk might give 20 dB of isolation, but we're still at risk of permanently damaging the receiver.

I needed a band-stop or band-pass filter for my APRS receiver. I already had a band-pass cavity filter for 144-148 MHz, but the 3rd harmonic of 145 MHz is 432 MHz, so this filter won't really keep 441 MHz transmissions out of my 144 MHz receiver. Bummer.

Open and Shorted Stubs

Fundamentally, stub filters are based around the concept of constructive and destructive interference. Split an incoming signal into two paths with a regular Tee, do some phase shifting for one of the signals, then reflect the phase-shifted signal back and combine it with the original signal. The two signals will either add or subtract, giving you a band-stop or band-pass filter.

For an open stub, the total phase shift is 180-degrees, so the frequency of interest will destructively combine. This is is a band-stop filter.

Shorted stubs have a total phase shift of 360-degrees, so the fundamental frequency is passed through the filter. Other frequencies are attenuated.

The open or shorted cable end reflects all RF energy, so you don't need to worry about signal leakage out the end of a stub filter.

Note that if you're going to put this on the output of a transmitter, there could be high voltages on the open end of the stub. Cut the shield back away from the end of the dielectric, and add plenty of insulation to prevent arcing.

Math

The math to build a quarter-wavelength stub is incredibly easy. Convert the frequency you want into a wavelength, then multiply that wavelength by the coaxial cable velocity factor.

For example, let's say I want to make a open stub filter for 441 MHz. The wavelength in air is 67.9 cm:

I'm using Belden 1671A (RG-405) 0.085" semi-rigid coax cable with a teflon (PTFE) dielectric, which has a velocity factor of 70%. One wavelength in this coax is 47.5 cm:

And a quarter wavelength in coax is 11.9 cm:

So we need our stub to be 11.9 cm long, from the center of the through transmission line to the open end. As is standard whenever building antennas, always add 10% length and trim it down to get an exact match with a network analyzer.

Thinking about harmonics: A 180-degree phase shift is the same as a 180-degree plus 360-degrees phase shift, so this filter will also attenuate the 3rd harmonic at 3 times the fundamental frequency. So we can expect a null at around 1323 MHz.

Initial Construction

For the initial construction, I used a standard SMA tee with a length of 0.085" semi-rigid coax. I had a bunch of extra semi-rigid coax, and it's easy to cleanly cut the end. Always cut the stub coax length a little long (lower design frequency) and do the fine trimming with a network analyzer.

Measuring the S21 of the filter showed the null move higher in frequency as I trimmed more semi-rigid coax from the stub. Don't trim too much or you'll need to get another piece of coax! I ended up with 34.8 dB of insertion loss at 441 MHz, and only 0.4 dB at 144 MHz. This is pretty good.

Looking at a wider frequency span on the network analyzer, we can see the attenuation of the 3rd harmonic up around 1337 MHz. As noted above, the third harmonic is calculated at 1323 MHz, so we're pretty close.

Building for Portability

While the diagrams show the stub length physically perpendicular to of the main line, there's nothing that actually requires any specific orientation or position of the stub. Having a coax stub sticking perpendicular is not an ideal form factor, and since geometry doesn't impact the performance of the stub filter, I decided to bend the stub length towards the main line with a right-angle SMA adapter.

This prevents the stub from getting caught on any other cables, or bending back and forth during normal usage and breaking.

For an open stub, it's important to ensure the open end doesn't accidentally get shorted, so I wrapped the end with electrical tape. You can also use adhesive-lined heat-shrink tubing for wet locations. Water getting into the open caox end will cause lots of intermittent problems.

Always remember to do a final S21 check with a network analyzer, and write down the type and frequency of the stub filter.

References

Interestingly, there aren't a lot of references about stub filters on the internet.

• Simple Filters from Transmission Line Stubs by Ward Silver N0AX. (local pdf)
• K1TTT Technical Reference for HF stubs. By David Robbins K1TTT. (local pdf)