L-Network Impedance Matching Calculator
Design an L-network to match a source resistance to a load resistance at any frequency: loaded Q, series and shunt reactance and the inductor and capacitor values for low-pass or high-pass versions.
How it works
Q = √(R_high ÷ R_low − 1) · X_series = Q × R_low · X_shunt = R_high ÷ Q · L = X ÷ (2πf) · C = 1 ÷ (2πf × X) · the shunt element sits across the higher resistance
An L-network uses one series and one shunt reactance to transform one resistance into another at a single frequency. The shunt element goes across the larger resistance, and the ratio of the two resistances fixes the loaded Q, so an L-network cannot choose its bandwidth — use a Pi or T network for that. The low-pass version (series inductor, shunt capacitor) also attenuates harmonics, which is why it is common at transmitter outputs; the high-pass version passes DC blocking for free. Values assume purely resistive source and load; absorb any load reactance into the adjacent element.
Worked example
Matching a 50 Ω source to a 200 Ω load at 14 MHz: Q = √(200 ÷ 50 − 1) = 1.732, X_series = 86.6 Ω and X_shunt = 115.5 Ω. The low-pass version uses a 984.5 nH series inductor and a 98.45 pF shunt capacitor across the 200 Ω load, with roughly 8.083 MHz of bandwidth.
Frequently asked questions
Which side does the shunt element go on?
Always across the higher resistance. Matching 50 Ω to 200 Ω puts the shunt capacitor (or inductor) across the 200 Ω load and the series element toward the 50 Ω source.
Should I use the low-pass or high-pass L-network?
Low-pass (series L, shunt C) suppresses harmonics and is the usual choice after an amplifier. High-pass (series C, shunt L) blocks DC and passes a DC path to ground through the inductor, useful for biasing.
What does the Q of the network mean?
It is fixed by the resistance ratio: Q = √(R_high/R_low − 1). Higher ratios mean higher Q, a narrower bandwidth and more loss in real components.
How do I match a complex load?
Cancel the load reactance first (or absorb it into the adjacent element), then match the remaining resistance. A Smith chart handles the general case.
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This calculator is for educational purposes. Double-check important results before acting on them.