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L-network calculator

Why there is nothing to choose here

A two-element L-network has exactly one solution: you do not set the Q, it follows unambiguously from the ratio of the impedances. The only freedom is which version to take — with a series coil (low-pass) or a series capacitor (high-pass). They match identically and filter differently.

Rsrc 50 ΩLCRload 200 Ω
The series element always goes on the low-impedance side, the shunt one on the high side
Frequency (MHz)
Source impedance (Ω)
Resistive part of the load (Ω)
Reactive part of the load (Ω)
Low-pass version — series coil, shunt capacitor
Series coil
Shunt capacitor
High-pass version — series capacitor, shunt coil
Series capacitor
Shunt coil
Shared
Network Q
Network bandwidth
Series element — on the side of

📐 The formulas​

Let R_high be the larger of the two impedances and R_low the smaller:

Q  = √( R_high / R_low − 1 )
Xs = Q × R_low        ← the series element, on the low-impedance side
Xp = R_high / Q       ← the shunt element, on the high-impedance side

The low-pass version — series coil, shunt capacitor:

L = Xs / (2πf)         C = 1 / (2πf × Xp)

The high-pass version is the mirror image: series capacitor, shunt coil.

Bandwidth:

BW ≈ f / Q

Symbols:​

  • load reactance is compensated by the series element: −X_load is added to Xs
Where this calculator stops:
  • An L-network exists only for different impedances; for equal ones it is not needed, and the calculator says so
  • The Q is fixed — wanting a different bandwidth means a Pi- or T-network with three elements
  • Losses in a real coil and capacitor are not accounted for, and at high Q they show
  • Compensating the load reactance is a first approximation; for a strongly reactive load, work through the parallel equivalent

🎯 In practice​

  • Matching an antenna to 50 Ω when the feedpoint impedance has been measured.
  • Interstage matching in a transistor amplifier.
  • A quick check on whether this pair of impedances can be matched by a simple network at all.
Practical advice:
  1. At a transmitter output take the low-pass version — it suppresses harmonics as well.
  2. A network Q > 10 means large currents and voltages inside: check the component ratings.
  3. Load reactance is easily measured with a NanoVNA right at the point of connection.
  4. The network's bandwidth is narrower than the band — moving to the other edge will need retuning.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «L-network calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/l_network (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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