Uncategorised

# Short-circuited quarter wavelength wave resonator

This post tells about short-circuited quarter wavelength line resonator. Quarter wavelength line resonator is depicted below, it is short circuited at one end.

Input impedance for this resonator with length $l$ is ${Z}_{in}={Z}_{0}\mathrm{tan}h\left(\alpha +j\beta \right)l={Z}_{0}\frac{1–j\mathrm{tan}h\alpha lcot\beta l}{\mathrm{tan}h\alpha l–jcot\beta l}$.

If .

Here we can conclude that $\beta l=\frac{\pi }{2}+\frac{\pi ∆\omega }{2{\omega }_{0}}$, then $cot\beta l\approx –\frac{\pi ∆\omega }{2{\omega }_{0}}$. And $\mathrm{tan}h\alpha l\approx \alpha l$, then ${Z}_{in}\approx \frac{{Z}_{0}}{\alpha l+\frac{\mathrm{j\pi }∆\mathrm{\omega }}{2{\omega }_{0}}}$