A stub is a length of transmission line terminated with a fixed impedance, typically a short-circuit or open-circuit. To take advantage of this fact, stub lengths are usually related to a specific wavelength.
Open-circuits and short-circuits in 1/4-wavelength long transmission lines reflect 100% of the energy.
The incoming wave passing to the end of the stub shifts 90°. At the open end of the stub, all of the energy is reflected with the voltages in phase. The reflected wave shifts an additional 90°, for a total shift of 180°. At the junction with the main transmission line, the incoming voltage wave is cancelled by the shifted reflected wave from the stub. This creates the appearance of a short-circuit. The incoming current and reflected current, however, are out of phase and cancel each other. This results in zero current at the point of the stub open-circuit.
The exact opposite occurs for transmission lines terminated in a short-circuit. The incoming wave passing to the end of the stub shifts 90°. At the shorted end of the stub, all of the energy is reflected with the voltage shifted 180°. The reflected wave shifts an additional 90°, for a total shift of 360°. At the junction with the main transmission line, the incoming voltage wave and reflected wave are in phase. This creates the appearance that the stub is not even connected. The incoming and reflected currents remain in phase and add.
The most common application for stubs is to filter out harmonics of transmitted signals. Impedance in a transmission line repeats every (electrical) 1/2-wavelength along the line.
The free end of a 1/4-wave shorted stub presents an open circuit at its fundamental frequency. At the second harmonic, the stub is 1/2-wave long and presents a short-circuit. Since the stub is a multiple of 1/2-wavelengths for each even (4th, 6th, ...) harmonic, the stub presents a short-circuit for each of those harmonics.
Shorted stubs that are a 1/2-wavelength long filter filter harmonics at one-half of its fundamental frequency. This occurs because the 1/2-wave stub is 1/4-wave long at the that lower frequency. The stub acts like a short circuit at the fundamental and all harmonics.
Putting it all together
The table below lists the filtering effect of various stubs for various bands. The HF bands are used because they are harmonically related to each other.
|10 ||15 ||20
||40 ||80 ||160 |
|160-m, shorted ||Null ||Null ||Null ||Null ||Null ||Pass|
|80-m, shorted ||Null ||Null ||Null ||Null ||Pass ||---|
|80-m, open ||--- ||--- ||Pass ||Pass ||Null ||---|
|40-m, shorted ||Null ||Pass ||Null ||Pass ||--- ||---|
|40-m, open ||Pass ||Null ||Pass ||Null ||--- ||---|
|20-m, shorted ||Null ||--- ||Pass ||--- ||--- ||---|
|20-m, open ||Pass ||--- ||Null ||--- ||--- ||---|
Based on Hands-On Radio from Nov-2004 QST