How do you design an L-network matching circuit?

An L-network matches two resistances with one series and one shunt reactance. The shunt element goes across the larger resistance. With Q = √(Rhigh/Rlow − 1), the series reactance is Xs = Q·Rlow and the shunt reactance is Xp = Rhigh/Q, of opposite sign.^[1][2]

What is a worked example?

Match R_low = 10 Ω to R_high = 50 Ω at 900 MHz. Q = √(50/10 − 1) = 2. X_s = 20 Ω, X_p = 25 Ω. Low-pass form (series L, shunt C across 50 Ω): L = 20/(2π·900 MHz) ≈ 3.54 nH, C = 1/(2π·900 MHz·25) ≈ 7.07 pF. The loaded Q of about 2 implies a fractional bandwidth on the order of 1/Q ≈ 50%.

Should you use low-pass or high-pass form?

• Low-pass (series L, shunt C) attenuates harmonics, useful at PA outputs.
• High-pass (series C, shunt L) blocks DC and can provide a bias path through the shunt inductor.

How do you handle complex impedances?

Absorb existing reactance into the network: subtract the load’s series reactance from X_s, or its parallel susceptance from the shunt element. If absorption is impossible, use resonance to cancel it first. The Smith chart makes these choices visual; see Smith chart.^[1]

What about component parasitics and loss?

Real chip inductors have finite Q and self-resonance; capacitors have ESL and ESR. Loss in the network is approximately Qnetwork/Qcomponent as a fraction of power, so high transformation ratios with low-Q parts are lossy. See RF passive components.

Frequently asked questions

See also

• Pi and T networks
• Smith chart
• Impedance matching
• Q factor

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

1. “RF Circuit Design, 2nd ed.”. C. Bowick, Newnes. 2008.
2. “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.