Hong Life CalculatorsUnderstanding the impedance matching calculator — concept and principle
This calculator designs an L-network, one series and one shunt reactance, that matches a source resistance to a different load resistance at a given frequency. It returns the network Q, the reactances and the inductor and capacitor values, and tells you which side the shunt element goes on. It is used for antenna matching, RF amplifier stages and transmitter output networks.
How it is calculated
Q = √(R_high ÷ R_low − 1)
Series reactance X_s = Q × R_low (placed next to the smaller resistance)
Shunt reactance X_p = R_high ÷ Q (placed across the larger resistance)
L = X ÷ (2π f); C = 1 ÷ (2π f X)
- Low-pass version: series inductor, shunt capacitor. High-pass version: series capacitor, shunt inductor.
- Frequency in MHz; L in nH, C in pF.
The principle
A reactance placed in parallel with the larger resistance transforms it into a smaller resistance in series with a reactance. Choosing the shunt reactance so that this smaller resistance equals R_low, then cancelling the leftover reactance with a series element of the opposite type, leaves a purely resistive match. The ratio of the two resistances fixes Q, so a basic L-network has no free choice of bandwidth.
Worked example
Default inputs: R_s = 50 Ω, R_L = 200 Ω, 100 MHz, low-pass.
- Q = √(200 ÷ 50 − 1) = √3 = 1.732.
- X_s = 1.732 × 50 = 86.6 Ω; X_p = 200 ÷ 1.732 = 115.47 Ω.
- Series inductor = 86.6 ÷ (2π × 10⁸) = 137.8 nH.
- Shunt capacitor = 1 ÷ (2π × 10⁸ × 115.47) = 13.78 pF.
- The load is the larger resistance, so the shunt element goes across the load side.
| Source resistance Rs (Ω) | Network Q |
|---|---|
| 12.5 | 3.873 |
| 25 | 2.646 |
| 37.5 | 2.082 |
| 50 | 1.732 |
| 62.5 | 1.483 |
| 75 | 1.291 |
| 100 | 1 |
How to read the result
A higher resistance ratio means a higher Q and a narrower bandwidth. If the ratio is large, a two-section network or a different topology (pi or T) gives more control over bandwidth. The low-pass form also helps suppress harmonics, which is useful after a transmitter.
Common mistakes
- Putting the shunt element on the wrong side.
- Applying the formulas to a complex load without first absorbing its reactance.
- Ignoring component self-resonance and parasitics at high frequencies.
Frequently asked questions
Why is the Q fixed in an L-network?
It is set entirely by the ratio of the two resistances.
Which version should I choose?
Low-pass when you want harmonic suppression; high-pass when the series path must block DC.
Can it match equal resistances?
Equal resistances are already matched and need no network.
Sources: M. B. Steer, Microwave and RF Design III – Networks, section 6.4 "The L Matching Network"