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RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while typing up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

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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

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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