In microwave and radio-frequency engineering, a stub is a length of transmission line or waveguide that is connected at one end only. The free end of the stub is either left open-circuit or (especially in the case of waveguides) short-circuited. Neglecting transmission line losses, the input impedance of the stub is purely reactive; either capacitive or inductive, depending on the electrical length of the stub, and on whether it is open or short circuit. Stubs may thus be considered to be frequency-dependent capacitors and frequency-dependent inductors. Because stubs take on reactive properties as a function of their electrical length, stubs are most common in UHF or microwave circuits where the line lengths are more manageable. Stubs are commonly used in antenna impedance matching circuits and frequency selective filters. Smith charts can also be used to determine what length line to use to obtain a desired reactance. In their simplest form, stubs that are some multiple of a quarter wavelengths are used to kill harmonics or sub-harmonics of the operating frequency. One property of a transmission line is that it inverts the impedance every quarter wavelength, so a quarter-wave stub with a short at one end looks like an open circuit at the other end. At the second harmonic, that same stub is two quarter-waves long, so the short is inverted twice, and looks like a short circuit to the harmonic. At the third harmonic, it's three quarter-waves, so it's an open circuit again, then at a full wavelength it's a short circuit again. Likewise, a quarter wave stub that is open at the far end looks like a short circuit, but an open circuit at the second harmonic. A stub works by placing a short circuit across the line at the frequency of interference. Placing a stub on a line forms a voltage divider between the line impedance and the stub impedance. The higher the line impedance at the point of connection, the greater the attenuation. If the line is well matched at both ends, the position doesn't matter, because the impedance at every point along the line is the same. But if there's a mismatch, the impedance will vary along the length of the line, and if the impedance at the location of the stub is low, it won't be very effective.
In a strip line circuit, a stub may be placed just before an output connector to compensate for small mismatches due to the device's output load or the connector itself. Stubs can be used to match load impedance to the transmission line characteristic impedance. The stub is positioned a distance from the load. This distance is chosen so that at that point the resistive part of the load impedance is made equal to the resistive part of the characteristic impedance by impedance transformer action of the length of the main line. The length of the stub is chosen so that it exactly cancels the reactive part of the presented impedance. That is, the stub is made capacitive or inductive according to whether the main line is presenting inductive or capacitive impedance respectively. This is not the same as the actual impedance of the load since the reactive part of the load impedance will be subject to impedance transformer action as well as the resistive part. Matching stubs can be made adjustable so that matching can be corrected on test. A single stub will only achieve a perfect match at one specific frequency. For wideband matching several stubs may be used spaced along the main transmission line. The resulting structure is filter-like and filter design techniques are applied. For instance, the matching network may be designed as a Chebyshev filter but is optimised for impedance matching instead of passband transmission. The resulting transmission function of the network has a passband ripple like the Chebyshev filter, but the ripples never reach 0dB insertion loss at any point in the passband, as they would do for the standard filter. Stub matching is of two types:
(i) Single stub...