Stub (circuit)

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In electronics, a stub is a calculated length section of transmission line used for impedance matching or to obtain an exact value of capacitance or inductance.

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 often used for antenna matching.

Smith charts can also be used to determine what length line to use to obtain a desired reactance.

[edit] Short circuited stubs

The general equation for the input impedance of a short circuited line is

$Z_{in}^{SC} = j \cdot Z_{0} \cdot tan(\beta\ \cdot l_{line})$

where j is the imaginary unit, $Z 0$ is the characteristic impedance of the line, β is the phase constant of the line, and l is the physical length of the line.

Thus, depending on whether $\tan(\beta\ \cdot l_{line})$ is positive or negative, the stub will be inductive or capacitive, respectively.

d = 1/B *(pi - tan^-1(1/(wCZo)) + n*pi)........ length of stub to act as a capacitor

d = 1/B *(tan^-1(wL/Zo) + n*pi)................length of stub to act as an Inductor

[edit] Open circuited stubs

For an open circuit, the general equation for input impedance is

$Z_{in}^{OC} = -j \cdot Z_{0} \cdot cot (\beta\ \cdot l_{line})$

where j is the imaginary unit, $Z 0$ is the characteristic impedance of the line, β is the phase constant of the line, and l is the physical length of the line.

It follows that whether $\cot(\beta\ \cdot l_{line})$ is positive or negative, the stub will be capacitive or inductive, respectively.