Coax Stubs and Quarter-Wave Transformers: Filtering and Matching

Some of the cheapest and most effective parts in a ham station are not components at all. They are short lengths of coaxial cable cut to a precise electrical length. Used the right way, coax stubs remove an interfering signal from a receiver, protect an antenna from static and suppress a harmonic, while a quarter-wave section of cable can match two impedances that do not otherwise agree. The ideas are old, the materials are in your junk box and the results are measurable with an antenna analyzer. This guide explains how a stub behaves, the difference between open and shorted types, how to calculate and trim the length, the transformer formula and where each trick is useful in a real station.

How a Length of Cable Changes Impedance

A transmission line does more than carry power. When it is terminated in something other than its own characteristic impedance, the impedance seen at the input depends on the length of the line. After a quarter of a wavelength, the impedance transforms into its inverse: a short circuit at the far end appears as an open circuit at the near end, and an open circuit appears as a short. After half a wavelength the line repeats the load impedance exactly. The article on stubs shows the general theory, and the same principle underlies the quarter-wave transformer described by the impedance transformer page.

This behaviour depends on frequency. A line that is a quarter wavelength long at 14.2 MHz is a half wavelength long at 28.4 MHz and three quarters of a wavelength at 42.6 MHz. Each of these lengths gives a different impedance, and that is why a stub acts as a filter. At one frequency it passes the signal and at another it blocks it. A stub is simply a short length of line connected to the main line at one end, with the other end left open or shorted.

Open and Shorted Stubs

A stub can be open at its far end or shorted, and it can be connected in parallel across the line, through a T connector, or in series. The common amateur use is the parallel stub. What it does depends on the length and on the end.

The Open Quarter-Wave Stub as a Notch

An open stub that is a quarter wavelength long at the frequency you want to remove acts as a short circuit at that frequency, so it removes the signal from the line. At other frequencies it has a much higher impedance and barely affects the signal. This makes it useful against a single strong interferer: a nearby broadcast carrier, a pager, or a transmitter on another band at the same site. Because the open stub is also an odd quarter-wave multiple at three times the frequency, it creates notches there as well, which is often an advantage.

The Shorted Quarter-Wave Stub as Protection

A shorted stub of the same length has the opposite character. At the design frequency its impedance is very high, so it has almost no effect on the signal. At all lower frequencies, and at DC, it is a short, which is why a shorted quarter-wave stub on an antenna feed point drains static and gives some lightning protection. At twice the design frequency the stub is a half wavelength long and shorted, so it presents a short and removes the second harmonic. That is a useful side effect for a transmitter feeding a simple antenna. The J-pole antenna uses the same idea: its matching section is a shorted quarter-wave stub, as described in our article on 2 metre J-pole and collinear antennas.

Calculating the Length

Electrical length is not the same as physical length. A signal moves more slowly in cable than in free space, by a fraction called the velocity factor. Solid polyethylene coax has a velocity factor of about 0.66 and foam types are commonly 0.78 to 0.85, though the exact value comes from the data sheet or from measurement. Our guide on the velocity factor of coax and wire explains the effect in detail.

The length of a quarter-wave stub in feet is 246 times the velocity factor divided by the frequency in MHz. In metres, it is 75 times the velocity factor divided by the frequency. For example, a stub for 14.2 MHz using cable with a velocity factor of 0.66 is 246 times 0.66 divided by 14.2, which comes to about 11.4 feet, or 3.5 metres. Treat that number as a starting point. Connectors, the T fitting and variations in the cable mean that you will trim the length by measurement.

The Quarter-Wave Transformer

A quarter-wave section of line can also match two resistances. The characteristic impedance of the section must be the geometric mean of the two impedances: the square root of the product of source and load. To match 50 ohms to 100 ohms you need a line of about 70.7 ohms, because the square root of 50 times 100 is 70.7. Cables of exactly that value are not standard, but 75 ohm cable is close and gives a good result.

A well-known use is in phasing two antennas. Two 50 ohm antennas connected in parallel present 25 ohms, which is a poor match for a 50 ohm transmitter. If each antenna is fed through a quarter-wave section of 75 ohm cable, the 75 ohm section transforms each 50 ohm load to about 112.5 ohms, because 75 squared divided by 50 is 112.5. Two of these in parallel give about 56 ohms at the junction, which is a match to 50 ohm coax with a very low SWR. The same trick appears in stacked antennas and in some vertical arrays, where cables of the right length also set the phase.

Limits of the Transformer

A transformer made from a quarter-wave line works best near its design frequency and gets worse as the frequency moves away. On a single band this is fine, but on a wide range it is not. The section must also be made of a cable with a known velocity factor, and the length must be measured, not guessed. Because the transformation is exact only for a resistive load, any reactance at the load changes the result, so check the final match with an analyzer.

Making and Testing a Stub

You need a piece of cable a little longer than the calculated length, a T connector, a connector for the stub end and an antenna analyzer or a vector network analyzer. Our guide to the NanoVNA and calibration covers the instrument setup. The steps are simple.

1. Cut the cable to the calculated length plus 5 to 10 percent.
2. Fit a connector at one end for the T. Leave the other end open for a notch stub, or short it with a connector and a shorting cap for a protection stub.
3. Connect the stub to the analyzer through a T connector, with the other arm of the T terminated or connected to the line you are testing.
4. Sweep around the target frequency and look for the notch in a through measurement, or for the frequency at which the stub alone shows a very low or very high impedance.
5. Trim the open end a little at a time. A shorter stub raises the notch frequency and a longer stub lowers it.
6. When the notch sits at the correct frequency, weatherproof the connection and note the result in your station records.

Cut in small steps, because you cannot add cable back. A few millimetres shifts the notch by tens or hundreds of kilohertz at HF, depending on the band. If you have cut too much, make a new stub rather than splicing.

Where Stubs Help in a Real Station

• Multi-station operation. A notch at the frequency of the transmitter on the next band reduces the strong signal that blocks a second receiver, but it does not replace a proper band-pass filter. See the article on band-pass filters for multi-station operation for the full solution.
• Harmonic reduction. A shorted stub reduces even harmonics. It is not a substitute for the filter described in the guide to low-pass filters, but it can help a simple transmitter.
• Static drain. A shorted quarter-wave stub at the feed point gives static a path to ground.
• Broadcast and local interference. A notch on the receive line can remove a strong local carrier that overloads a receiver.
• Phasing and matching. Quarter-wave and half-wave sections make arrays work without any electronic components.

A Worked Example

Suppose a strong station on 7.100 MHz overloads a receiver that you want to use on the 20 metre band at the same site. You decide to try an open quarter-wave stub as a notch. With cable that has a velocity factor of 0.66, the length is 246 times 0.66 divided by 7.1, which is about 22.9 feet or 6.97 metres. You cut 7.5 metres to leave a margin, connect the stub to the receive line through a T connector and sweep from 6 to 8 MHz with the analyzer. The first sweep shows a notch near 6.6 MHz, which is below the target because the stub is long. Trim 20 centimetres, sweep again and note that the notch has moved up. Repeat until it sits at 7.1 MHz. The whole job takes half an hour, costs a small piece of cable and gives an attenuation of the unwanted signal that can be 20 decibels or more, with only a small loss at the frequencies you want to receive.

Common Mistakes

• Cutting to the free-space length. Without the velocity factor, the stub will be far too long.
• Trusting the data sheet blindly. The velocity factor varies from one batch to another, so measure.
• Cutting too much at once. Trim in small steps, test and repeat.
• Using a notch with a transmitter on the same frequency. A short circuit in the line can damage a transmitter. Use stubs only where you know the effect on the transmitted band.
• Forgetting the connector length. The T and the connectors add electrical length.
• Weak weatherproofing. Water in the stub end detunes it and degrades the cable.

The Bottom Line

A stub is a very simple device with a very specific action. An open quarter-wave stub shorts the line at its design frequency and works as a notch. A shorted quarter-wave stub is invisible at its frequency, drains static and shorts the even harmonics. A quarter-wave section of the right impedance matches two resistances. Calculate the length with the velocity factor, add a margin, trim in small steps with an analyzer and check the result. Combine stubs with proper filters where more suppression is needed, and keep them away from your transmit frequency unless you know exactly what they do. A few feet of cable can remove an annoying signal at almost no cost.

Frequently Asked Questions

What is a coax stub?

A coax stub is a short length of cable, open or shorted at the far end, connected to a transmission line to filter or protect it. Its behaviour depends on its length relative to the wavelength.

How long is a quarter-wave stub?

In feet, 246 times the cable’s velocity factor divided by the frequency in MHz. For solid polyethylene coax with a velocity factor of 0.66 at 14.2 MHz, about 11.4 feet. Trim it using an analyzer.

What is the difference between an open and a shorted stub?

An open quarter-wave stub looks like a short at its frequency and notches the signal. A shorted quarter-wave stub looks like an open circuit at its frequency and shorts lower frequencies and even harmonics.

How do I match 50 ohms to 100 ohms with coax?

Use a quarter-wave section with an impedance of about 70.7 ohms, the square root of 50 times 100. A 75 ohm cable is a common practical choice and gives a good match.

Will a stub damage my transmitter?

It can if the stub is resonant at your transmit frequency, because it presents a short circuit there. Use a stub only for frequencies you want to remove and check with an analyzer first.

Can I use any coax for a stub?

Yes, but you must know its velocity factor and keep the stub in one piece. Use good quality cable and sealed connectors so that the stub stays stable over time.