Lumped Circuit Approximations

Lumped Element Replacements

Transmission line filters are transmission line circuit filters that approximate lumped circuit filters. Lumped elements are replaced with transmission line stubs, which are opened or shorted at their terminations. Transmission line elements such as this always produce aliasing. If each individual element is replaced with a corresponding transmission line stub, extending the stub lengths and recalculating the stub impedances accordingly can control this aliasing.

 

LC Resonator Replacements

It is possible to replace lumped LC resonators with single transmission line stubs by setting the stub length such that the zero or infinite impedance matches the resonant frequency of the lumped LC resonator. Transmission line filters with this feature require fewer stubs than when simulating each element individually, however significant aliasing is always produced.

 

Example 1

The following 1G Hz lumped element filter contains undesirable element values

 

The following transmission line filters are approximately equivalent:

 

The two shorted stubs may be replaced with transmission line segments as shown below. This implementation may be realized as a micro strip or strip line.

 

The resonator section may be combined into one stub as shown below. Although this topology is more efficient, it produces significant aliasing.

 

The segment distance between the stubs should ideally be zero, but may be manually set to any finite value to simulate real world parameters.