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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
RF Cafe - Lumped inductor shunt inductor RF Cafe - Distributed inductor shunt to ground equivalent
Capacitor Shunted to Ground
RF Cafe - Lumped element capacitor to ground RF Cafe - Distributed element open stub equivalent
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.
RF Cafe - Lumped element parallel LC tank to ground RF Cafe - Distributed element parallel LC tank to ground equivalent
Series LC In Series
RF Cafe - Lumped element series LC RF Cafe - Distributed element series LC
Series Inductor
RF Cafe - Lumped element series inductor RF Cafe - Distributed element series inductor equivalent
Shunt Capacitor
RF Cafe - Lumped element shunt capacitor RF Cafe - Distributed element series component equivalent
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.
RF Cafe - Lumped element series LC tank to ground RF Cafe - Lumped element series LC tank to ground equivalent

Information originated from "HF Filter Design and Computer Simulation

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