L-Network Impedance Matching Calculator (Antenna Tuner, RF Match)
Coil and capacitor values of an L-network that matches one resistance to another at a chosen frequency, in both the low-pass and the high-pass version.
Results
The dashed line marks the value you entered.
What this tool does
The L-network is the simplest way to match two different resistances: a series element on the side with the lower resistance and a shunt element across the higher one. The match is set entirely by the ratio of the resistances, Q = √(R_high ÷ R_low − 1), and the reactances follow: X_series = Q × R_low and X_shunt = R_high ÷ Q. The low-pass version (series coil, capacitor to ground) also attenuates harmonics, which is why it is the usual choice in transmitters, while the high-pass version blocks low frequencies. Real coils have losses, which grow with Q.
Formula
Q = √(R_high ÷ R_low − 1) · X_series = Q × R_low · X_shunt = R_high ÷ Q · L = X ÷ 2πf · C = 1 ÷ (2πf X)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
rs | Source resistance | Ω |
rl | Load resistance to be matched | Ω |
f | Frequency | MHz |
Q | Q of the matching network | — |
LS | Low-pass version: series inductor (low-resistance side) | µH |
CP | Low-pass version: capacitor to ground (high-resistance side) | pF |
CS | High-pass version: series capacitor (low-resistance side) | pF |
LP | High-pass version: inductor to ground (high-resistance side) | µH |
Worked example
- Source resistance50 Ω
- Load resistance to be matched200 Ω
- Frequency14.2 MHz
- Q of the matching network1.732
- Low-pass version: series inductor (low-resistance side)0.971 µH
- Low-pass version: capacitor to ground (high-resistance side)97.1 pF
- High-pass version: series capacitor (low-resistance side)129.4 pF
- High-pass version: inductor to ground (high-resistance side)1.294 µH
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.