Open circuited stub - input impedance

Description

In microwave and radio-frequency engineering, a stub or resonant 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 (always 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 function as capacitors, inductors and resonant circuits at radio frequencies.

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

Related formulas

Variables

ZocThe input impedance of a lossless opne circuited line (ohm)
jImaginary unit
Z0characteristic impedance of the line (ohm)
βphase constant of the line (radian/m)
lphysical length of the line (m)