Resonant stub

Resonant stub

Stubs are often used as resonant circuits in oscillators and distributed element filters. An open circuit stub of length ${\displaystyle \ \ell }$ will have a capacitive impedance at low frequency when ${\displaystyle \ \beta \ell <\pi /2}$. Above this frequency the impedance is inductive. At precisely ${\displaystyle \beta \ell =\pi /2}$ the stub presents a short circuit. This is qualitatively the same behaviour as a series resonant circuit. For a lossless line the phase change constant is proportional to frequency,