FREE ENGINEERING TOOLS · FORMULAS & REFERENCES
L-Match Impedance Matching Calculator: L, C & Q
Calculate inductor, capacitor and Q for a two-element L matching network from source resistance, load resistance and frequency. Choose low-pass or high-pass, with shunt placement and an input-impedance check.
Enter parameters
Load an example:
Calculated results
Parameters changed. Recalculate before viewing or exporting results.
| Network matching Q | 1.732050808 |
|---|---|
| Inductance L | 1378.322239 nH |
| Capacitance C | 137.8322239 pF |
| Series reactance magnitude | 86.60254038 Ω |
| Shunt reactance magnitude | 115.4700538 Ω |
Shunt branch: Load side
Place L in series with the signal and C to ground on the higher-resistance side.
| f (MHz) | Re(Zin) Ω | Im(Zin) Ω |
|---|---|---|
| 5 | 114.2857143 | -55.67306167 |
| 10 | 50 | 0 |
| 20 | 15.38461538 | 119.9112098 |
Matches two positive real resistances using ideal lossless components. Complex antenna impedances need their reactance handled separately. PCB parasitics and component losses are excluded.
Calculation formulas
RH = max(Rs, RL), Rlow = min(Rs, RL) · Q = √(RH/Rlow − 1) · |Xs| = Q·Rlow · |Xp| = RH/Q
Which side gets the shunt component?
The shunt element belongs on the higher-resistance side. If RL exceeds Rs, place it at the load; if Rs exceeds RL, place it at the source. The series reactance cancels the remaining imaginary part. Low-pass uses a series inductor and shunt capacitor; high-pass reverses their types.
Example: 50 Ω to 200 Ω at 10 MHz
Q = √3, series reactance is about 86.6025 Ω and shunt reactance about 115.470 Ω. The low-pass form uses about 1378.32 nH in series and 137.832 pF shunted at the load. A complex-impedance check gives approximately 50 + j0 Ω at the source at the design frequency.
What if source and load are equal?
Two equal real resistances do not need this impedance transformation. The calculator reports no matching network required instead of generating infinite component values. If filtering is still needed, design a filter to its own specifications.
Is network Q the same as component Q?
No. This Q follows from the impedance transformation ratio and is not the inductor datasheet quality factor. Real designs also need self-resonance, ESR, package and layout parasitics checked through simulation or network-analyzer measurements.