Impedance Matching Calculator Formula
Understand the math behind the impedance matching calculator. Each variable explained with a worked example.
Formulas Used
Q Factor
q_val = q_factorShunt Reactance
shunt_reactance = x_shuntSeries Reactance
series_reactance = x_seriesShunt Inductor (if inductive)
shunt_inductor = x_shunt / (2 * pi * frequency_mhz * 1e6) * 1e9Series Capacitor (if capacitive)
series_capacitor = 1 / (2 * pi * frequency_mhz * 1e6 * x_series) * 1e12Variables
| Variable | Description | Default |
|---|---|---|
z_source | Source Impedance(Ω) | 50 |
z_load | Load Impedance(Ω) | 200 |
frequency_mhz | Frequency(MHz) | 100 |
r_high | Derived value= max(z_source, z_load) | calculated |
r_low | Derived value= min(z_source, z_load) | calculated |
q_factor | Derived value= sqrt(r_high / r_low - 1) | calculated |
x_shunt | Derived value= r_high / q_factor | calculated |
x_series | Derived value= q_factor * r_low | calculated |
How It Works
L-Network Impedance Matching
An L-network uses two reactive components (one series, one shunt) to transform impedances for maximum power transfer.
Formula
Q = sqrt(R_high / R_low - 1)
X_shunt = R_high / Q
X_series = Q x R_low
The shunt element goes across the higher impedance side. You choose inductor or capacitor based on the desired network topology (lowpass or highpass).
Worked Example
Match 50 ohms to 200 ohms at 100 MHz.
- 01Q = sqrt(200/50 - 1) = sqrt(3) = 1.73
- 02Shunt reactance: 200 / 1.73 = 115.5 ohms
- 03Series reactance: 1.73 x 50 = 86.6 ohms
- 04Shunt inductor: 115.5 / (2pi x 100e6) = 183.8 nH
- 05Series capacitor: 1 / (2pi x 100e6 x 86.6) = 18.38 pF
Frequently Asked Questions
Why is impedance matching important?
Mismatched impedances cause power reflection, reduced efficiency, and potential damage to transmitters.
What is the bandwidth of an L-network?
Bandwidth is inversely proportional to Q. Higher impedance ratios yield higher Q and narrower bandwidth.
When should I use a pi or T network instead?
When you need to control bandwidth independently of the impedance ratio, or when matching complex impedances.
Ready to run the numbers?
Open Impedance Matching Calculator