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. That is, the stub is made capacitive or inductive according to whether the main line is presenting an inductive or capacitive impedance respectively. The length of the stub is chosen so that it exactly cancels the reactive part of the presented impedance. 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 stub is positioned a distance from the load. Stubs can be used to match a load impedance to the transmission line characteristic impedance. 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. The length of an open circuit stub to act as a capacitor C at the same frequency is: The length of an open circuit stub to act as an Inductor L at an angular frequency of ω is: It follows that whether cot(βl) is positive or negative, the stub will be capacitive or inductive, respectively.

The input impedance of a lossless open circuit stub is given by

The length of a stub to act as an inductor L at the same frequency is given by: The Length of a stub to act as a capacitor C at an angular frequency of ω is then given by: Thus, depending on whether tan(βl) is positive or negative, the stub will be inductive or capacitive, respectively. Where j is the imaginary unit, Z0 is the characteristic impedance of the line, β is the phase constant of the line, and l is the physical length of the line. The input impedance of a lossless short circuited line is,

Smith charts can also be used to determine what length line to use to obtain a desired reactance. Stubs are commonly used in antenna impedance matching circuits and frequency selective filters. Stubs may thus be considered to be frequency-dependent capacitors and frequency-dependent inductors.īecause 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. 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. The free end of the stub is either left open-circuit or (especially in the case of waveguides) short-circuited. In microwave and radio-frequency engineering, a stub is a length of transmission line or waveguide that is connected at one end only. IMPEDANCE MATCHING BY STUBS, SINGLE STUB AND DOUBLE STUB MATCHING.

How to use smith chart