Impedance Matching Calculator Formula
Understand the math behind the impedance matching calculator. Each variable explained with a worked example.
Formulas Used
Network Q
network_q = q_netSeries Reactance
x_series = q_net * r_loShunt Reactance
x_shunt = r_hi / q_netVariables
| Variable | Description | Default |
|---|---|---|
r_source | Source Impedance(Ω) | 50 |
r_load | Load Impedance(Ω) | 200 |
frequency_mhz | Frequency(MHz) | 100 |
r_hi | Derived value= r_source > r_load ? r_source : r_load | calculated |
r_lo | Derived value= r_source > r_load ? r_load : r_source | calculated |
q_net | Derived value= sqrt(r_hi / r_lo - 1) | calculated |
freq_hz | Derived value= frequency_mhz * 1000000 | calculated |
How It Works
L-Network Impedance Matching
Q = sqrt(R_high/R_low - 1)
X_series = Q x R_low
X_shunt = R_high / Q
Choose series inductor + shunt capacitor, or vice versa, to realize the reactance values at the operating frequency.
Worked Example
Match 50 ohms to 200 ohms at 100 MHz.
r_source = 50r_load = 200frequency_mhz = 100
- 01Q = sqrt(200/50 - 1) = sqrt(3) = 1.732
- 02X_series = 1.732 x 50 = 86.6 ohms
- 03X_shunt = 200 / 1.732 = 115.5 ohms
Ready to run the numbers?
Open Impedance Matching Calculator