RF Toolbox

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 ▸
\(Q = \sqrt{\dfrac{R_{high}}{R_{low}}-1}\)
fMatching frequency.
RₛSource resistance (Ω). The port with higher impedance gets the shunt element.
R_LLoad resistance (Ω).
QNetwork Q = √(R_high/R_low − 1). Also sets bandwidth: BW = f/Q.
Solution 1Low-pass: shunt C at high-Z port, series L toward low-Z port. Passes DC.
Solution 2High-pass: series C, shunt L. Blocks DC, better harmonic rejection.
Physical constants used
cSpeed of light = 2.998×10⁸ m/s
µ₀Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m
ε₀Permittivity of free space = 8.854×10⁻¹² F/m
Inputs
Ω
Ω
Must differ from Rₛ
Results

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