Parallel Resonator Approximations

Transmission lines with shorted loads may be used to approximate parallel LC resonators. To approximate LC resonators, the null frequency of the transmission line must be set to match the LC resonant frequency. Aliasing occurs at twice the null frequency. Therefore, it is not practical to approximate a wide band LC resonator with a single transmission line.

Shorted lossless line input impedance may be described mathematically below.

Shorted Load Lossless Input Impedance

 

It may be seen with this equation that the infinite impedance length of the stub is calculated by setting the length of the line such that

Parallel Resonator Stub Length Equation

 

The impedance of the line that approximates a parallel LC resonator is stated below without derivation

Parallel Resonator Impedance Equation