Impedance Matching Calculator — L-Network Design

Background.

Connect a 50 Ω source straight to a 200 Ω load and 36% of the power arriving at the load is reflected back toward the source. The reflection coefficient is (200 − 50) ÷ (200 + 50) = 0.6, the standing-wave ratio on the line is 4, and the power actually delivered falls by 1.9382 dB. Two well-chosen components between them can make the load look like 50 Ω to the source at the frequency you care about.

Those two components form an L-network: one element in series on the low-impedance side, one in shunt across the high-impedance side. Reactive parts dissipate no power in principle, so the network transforms impedance rather than burning off the excess. You choose only which kind of part goes where. A series inductor with a shunt capacitor makes a low-pass network that also attenuates harmonics, the usual choice after an amplifier. A series capacitor with a shunt inductor makes a high-pass network that blocks DC. Either matches the same pair of impedances with the same Q and the same reactance magnitudes.

The Q is set by the impedance ratio alone: a 4:1 step gives 1.7321 and a 17:1 step exactly 4. The higher it is, the faster the match degrades away from the design frequency and the more it suffers from component tolerance, and two components give you no way to lower it.

Two assumptions sit under every answer. Both impedances are treated as pure resistances, so a real antenna or transistor input with a reactive part needs that reactance dealt with first. And the components are calculated for one frequency only.

What is impedance matching calculator?

Impedance matching means arranging for a load to present, at the source's terminals, the impedance that delivers the most power. For a resistive source that is a load equal to the source resistance, by the maximum power transfer theorem; any difference reflects a share |Γ|² of the incident power, where Γ = (Z_L − Z_S) ÷ (Z_L + Z_S). An L-network is the smallest lossless circuit that does the job: two reactances whose values follow from the two resistances, converted into an inductor and a capacitor once a frequency is named.

How to use this calculator.

1. 01Enter the source and load impedances in ohms as resistances. They must differ; equal values are already matched and an L-network between them has no meaning.
2. 02Choose low-pass for a series inductor and shunt capacitor, or high-pass for a series capacitor and shunt inductor. Low-pass helps suppress harmonics; high-pass blocks DC and gives the shunt side a DC path to ground.
3. 03Enter the design frequency and pick Hz, kHz, MHz or GHz. Only the component values depend on it; Q and both reactances do not.
4. 04Build the network with the series element on the lower-impedance side and the shunt element across the higher-impedance side. Reversed, it transforms in the wrong direction.
5. 05Check the mismatch loss before building anything. If it is a fraction of a decibel, the network's own losses and tolerances may cost nearly as much as it saves.

The formula.

Following Steer's derivation in Microwave and RF Design III, §6.4, the series leg and the shunt leg must have Q values of equal magnitude. That condition leaves no free parameter: Q = √(R_high ÷ R_low − 1), the series reactance is |X_S| = Q × R_low and the shunt reactance is |X_P| = R_high ÷ Q. Multiplying the two shows |X_S| × |X_P| = R_high × R_low, a quick check on any design. Component values follow from ω = 2πf: for low-pass, L = X_S ÷ ω and C = 1 ÷ (ω X_P); for high-pass, C = 1 ÷ (ω X_S) and L = X_P ÷ ω. Inductors are reported in microhenries and capacitors in picofarads. The unmatched figures come from Γ = (Z_L − Z_S) ÷ (Z_L + Z_S): VSWR = (1 + |Γ|) ÷ (1 − |Γ|), return loss = −20 log₁₀|Γ| and mismatch loss = −10 log₁₀(1 − |Γ|²), the last being the share of power lost to reflection. The transformer alternative uses the reflected-resistance relation from OpenStax University Physics, R_primary = (N_P ÷ N_S)² × R_secondary, which inverts to a turns ratio n = √(Z_S ÷ Z_L). Not modelled: losses in real inductors and capacitors, parasitic inductance and capacitance, complex impedances and the full frequency response.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Michael Steer, Microwave and RF Design III — Networks, §6.4 'The L Matching Network' (Engineering LibreTexts). Source of the design equations: Eq. (4)/(5) Q_S = |X_S/R_S| and Q_P = |R_L/X_P|; Eq. (6) |Q_S| = |Q_P| = √(R_L/R_S − 1) for R_S < R_L; Eq. (11) √(R_S/R_L − 1) for R_S > R_L; Eq. (12) Q_S = X_S/R_L and Q_P = R_S/X_P; and the topology showing the shunt element on the load side when R_S < R_L. Open access; retrieved 2026-07-29.
2. [2]Michael Steer, Microwave and RF Design II — Transmission Lines, §2.6 'Reflections at Interfaces' (Engineering LibreTexts). Source of the reflection coefficient Γ = (Z_L − Z_0)/(Z_L + Z_0) (Eq. 2.3.7) and of the reflected-power relation P_R = |Γ|²P_I (Eq. 2.6.13), from which the return-loss and mismatch-loss expressions on this page follow. Open access; retrieved 2026-07-29.
3. [3]Steven W. Ellingson (Virginia Tech), Electromagnetics I, §3.14 'Standing Wave Ratio' (Engineering LibreTexts). Source of SWR = (1 + |Γ|)/(1 − |Γ|), with SWR defined as 'the ratio of the maximum magnitude of the standing wave to minimum magnitude of the standing wave'. Open access; retrieved 2026-07-29.
4. [4]OpenStax (Rice University), University Physics Volume 2, §15.6 'Transformers'. Source of the transformer relations V_S/V_P = N_S/N_P (Eq. 15.21) and i_S(t) = (N_P/N_S)i_P(t) (Eq. 15.22), and of the reflected-resistance result R_P = (N_P/N_S)²R_S, which inverts to the impedance-matching turns ratio n = √(Z_s/Z_l) reported here. Open access; retrieved 2026-07-29.