Lumped / Distributed Transmission Line Element Conversions

When designing with transmission line elements, whether with microstrip, stripline, waveguide, or coaxial cable, it is sometimes necessary to create lumped element equivalents for shunt and series capacitors and inductors.

These formulas provide the conversion. Keep in mind that the conversions only hold exactly at one frequency, ω. Angles, θ, are portions of a full wavelength at the desired frequency.

Inductor Shunted to Ground

Capacitor Shunted to Ground

Parallel LC Shunted to Ground
A 90° transmission line shorted at the far end acts like a parallel LC tank circuit. To behave similarly, the reactance of the tank inductor will be equal to 4/π times the line impedance.

Series LC In Series

Series Inductor

Shunt Capacitor

Series LC Shunted to Ground
A 90° transmission line left open at the far end acts like a series LC circuit. To behave similarly, the reactance of the tank inductor will be equal to π/4 times the line impedance.

Information originated from "HF Filter Design and Computer Simulation

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