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_net

Series Reactance

x_series = q_net * r_lo

Shunt Reactance

x_shunt = r_hi / q_net

Variables

VariableDescriptionDefault
r_sourceSource Impedance(Ω)50
r_loadLoad Impedance(Ω)200
frequency_mhzFrequency(MHz)100
r_hiDerived value= r_source > r_load ? r_source : r_loadcalculated
r_loDerived value= r_source > r_load ? r_load : r_sourcecalculated
q_netDerived value= sqrt(r_hi / r_lo - 1)calculated
freq_hzDerived value= frequency_mhz * 1000000calculated

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
  1. 01Q = sqrt(200/50 - 1) = sqrt(3) = 1.732
  2. 02X_series = 1.732 x 50 = 86.6 ohms
  3. 03X_shunt = 200 / 1.732 = 115.5 ohms

Ready to run the numbers?

Open Impedance Matching Calculator