L-Network Impedance Matcher
An L-network uses one series and one shunt reactive element to match two different real impedances at a single frequency. The shunt element always connects at the high-impedance port. Two complementary solutions exist: low-pass (shunt C, series L) and high-pass (series C, shunt L).
Equations & Parameters ▸
\(Q = \sqrt{\dfrac{R_{high}}{R_{low}}-1}\)
| f | Matching frequency. |
| Rₛ | Source resistance (Ω). The port with higher impedance gets the shunt element. |
| R_L | Load resistance (Ω). |
| Q | Network Q = √(R_high/R_low − 1). Also sets bandwidth: BW = f/Q. |
| Solution 1 | Low-pass: shunt C at high-Z port, series L toward low-Z port. Passes DC. |
| Solution 2 | High-pass: series C, shunt L. Blocks DC, better harmonic rejection. |
Physical constants used
| c | Speed of light = 2.998×10⁸ m/s |
| µ₀ | Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m |
| ε₀ | Permittivity of free space = 8.854×10⁻¹² F/m |
Inputs
Ω
Ω
Must differ from RₛResults
Network Q
Q factor—
Solution 1 — Low-pass
Shunt capacitor, C—
Series inductor, L—
Solution 2 — High-pass
Series capacitor, C—
Shunt inductor, L—
Diagram