Impedance Matching Calculator — L-Network Design

Background.

Impedance matching is what you do when a source and a load have different impedances and you want the power to go into the load instead of bouncing back. This calculator designs the simplest network that does it — the two-element L-network — and tells you exactly what the mismatch was costing before you added it.

The L-network is two components: one in series with the lower-impedance side, one shunting the higher-impedance side. That is the whole topology, and the arrangement is not optional — the series element always goes on the low side. What you do choose is which kind of component goes where. The low-pass arrangement uses a series inductor and a shunt capacitor, which also attenuates harmonics and is the usual choice after an amplifier stage. The high-pass arrangement uses a series capacitor and a shunt inductor, which blocks DC and passes the higher frequencies. Both give exactly the same Q and the same reactance magnitudes for the same pair of impedances; only the component types and the out-of-band behaviour differ.

The network Q is the headline number, and it is worth understanding why it is not a design choice. For an L-network, Q is fixed entirely by the impedance ratio: the square root of the high impedance divided by the low one, minus one. A 4:1 transformation always gives a Q of about 1.73; a 17:1 transformation always gives a Q of 4. You cannot trade Q for anything with two components. That matters because Q sets bandwidth — a high-Q match is a narrow match, sensitive to component tolerance and to frequency drift. If a two-element network gives you more Q than you can live with, the answer is a three-element network or a cascade, not a different pair of values.

The four mismatch outputs describe the situation before the network exists: the reflection coefficient, the VSWR it implies, the return loss, and the mismatch loss. The last of those is the practical one, because it is the actual power you are losing. A VSWR of 4 sounds alarming but costs about 1.94 dB, roughly a third of the power. A VSWR of 2 costs about 0.51 dB, which is often not worth a network at all. Note that this page reports these figures to quantify the problem, not to be a VSWR meter — if you are working from measured forward and reflected power rather than from two impedances, that is a different calculation.

Two scope limits belong right next to the answer rather than in a footnote, because both of them change how the result should be read. First, both impedances here are purely resistive. Real antennas, real transistor inputs and real transducers are complex, and a reactive load has to be resolved into its resistive part with the reactance either absorbed into the network or cancelled first. This page does not do that step, and applying its answer to a complex load without doing it will not produce a match. Second, an L-network matches at exactly one frequency. The component values scale with the design frequency, and the fractional bandwidth narrows as Q rises. Away from the design frequency the match degrades, and how fast it degrades is precisely what the Q figure is telling you.

If the required Q is uncomfortably high, or the bandwidth is uncomfortably narrow, the transformer turns ratio shown alongside is the alternative worth considering: a broadband transformer matches over decades rather than at a point, at the price of size, insertion loss and a low-frequency limit set by its magnetising inductance.

What is impedance matching calculator?

Impedance matching is the design of a network that makes a load look, to a source, like the impedance the source wants to see. The reason it matters is the maximum power transfer theorem: a source delivers the most power into a load equal to its own impedance, and any departure from that reflects some of the incident power back. The fraction reflected is |Γ|², where Γ is the reflection coefficient (Z_L − Z_S)/(Z_L + Z_S), so a load twice the source impedance reflects about 11 % of the power and one four times the source reflects 36 %. An L-network fixes this with two reactive components, which dissipate nothing and simply transform the impedance. The series element on the low-impedance side raises the apparent impedance; the shunt element on the high-impedance side brings the reactive part back to zero. Solving for the two values gives Q = √(R_high/R_low − 1), |X_S| = Q·R_low and |X_P| = R_high/Q — a result with no free parameters, which is why an L-network's Q is dictated by the impedance ratio alone. Converting the reactances into component values requires a frequency, because a reactance of 86.6 Ω is 138 nH at 100 MHz and 13.8 µH at 1 MHz. The alternative to a reactive network is a transformer, whose turns ratio for impedance matching is the square root of the impedance ratio, and which works over a wide band rather than at a single frequency.

How to use this calculator.

1. 01Enter the source and load impedances as resistances in ohms. They must be different — equal impedances are already matched, and the calculator says so rather than returning a meaningless network.
2. 02If your load is complex, resolve it first. Take the resistive part, and either absorb its reactance into the series or shunt element or cancel it with an extra component. This page assumes purely resistive impedances and will not warn you otherwise.
3. 03Choose the arrangement. Low-pass (series inductor, shunt capacitor) also suppresses harmonics; high-pass (series capacitor, shunt inductor) blocks DC. Q and both reactances are identical either way.
4. 04Set the design frequency. It has no effect on Q or on the reactances, only on the component values — which is why the reactance outputs are the ones to quote when you are comparing designs across bands.
5. 05Build it with the series element on the lower-impedance side and the shunt element across the higher one. Getting that the wrong way round gives a network that transforms in the wrong direction.
6. 06Read the network Q to judge bandwidth. A Q under about 3 is a comfortably broad match; above 10, component tolerance and frequency drift start to dominate and a multi-section network is usually the better answer.
7. 07Read the mismatch loss to decide whether the network is worth building at all. Below about half a decibel — roughly a 2:1 VSWR — the network often costs more in component loss and board area than the mismatch was costing in power.

The formula.

The design. Steer's Microwave and RF Design III §6.4 derives the L-network by requiring that the series leg's Q and the shunt leg's Q be equal in magnitude, with Q_S = |X_S/R_S| and Q_P = |R_L/X_P| (Eq. 4 and 5). Solving gives Eq. (6), |Q_S| = |Q_P| = √(R_L/R_S − 1) when R_S is the smaller of the two, and Eq. (11), √(R_S/R_L − 1), when it is the larger. Those are the same expression with the roles swapped, which is exactly the max/min form this calculator implements: Q = √(R_high/R_low − 1), then |X_S| = Q·R_low and |X_P| = R_high/Q. The series element goes on the low-impedance side, which is what Steer's figures show and what the derivation requires.

The component values. A reactance is not a component until you name a frequency. For the low-pass arrangement the series inductor is L = X_S/ω and the shunt capacitor is C = 1/(ω·X_P); for the high-pass arrangement the series capacitor is C = 1/(ω·X_S) and the shunt inductor is L = X_P/ω, with ω = 2πf throughout. That is why changing the design frequency on this page moves the component values but leaves Q and both reactances untouched.

A check you can run on any result here, and one this calculator's test suite runs on every design it produces. Put the network back together in complex arithmetic and look into it: for the low-pass case, the input impedance is jX_S in series with the parallel combination of R_high and −jX_P. At the worked example that parallel combination is 50 − j86.6025403784 Ω, and adding the series +j86.6025403784 Ω leaves exactly 50 + j0 — the source impedance, with the reactance cancelled to nothing. The suite asserts the same round trip for both arrangements at four different impedance ratios. It is a stronger check than any citation, because it proves the network does what it claims rather than that the algebra was copied correctly.

The mismatch metrics. Steer's transmission-lines volume gives Γ = (Z_L − Z_0)/(Z_L + Z_0) at Eq. (2.3.7) and the reflected power as P_R = |Γ|²P_I at Eq. (2.6.13). From those, the fraction of power actually delivered is 1 − |Γ|², so the mismatch loss in decibels is −10·log₁₀(1 − |Γ|²) and the return loss is −20·log₁₀|Γ|. Ellingson's Electromagnetics I §3.14 supplies SWR = (1 + |Γ|)/(1 − |Γ|), with SWR defined as the ratio of the maximum to the minimum magnitude of the standing wave. All four of these describe the unmatched pair; they are what the network is worth, not what it achieves.

The transformer alternative. OpenStax §15.6 gives the transformer relations V_S/V_P = N_S/N_P and i_S = (N_P/N_S)i_P, from which the primary sees a reflected resistance R_P = (N_P/N_S)²R_S. Inverting for the turns ratio needed to make a load look like a source gives n = √(Z_s/Z_l), which is the figure reported here. A transformer matches over a wide band where the L-network matches at a point, which is the fundamental trade this page puts side by side.

Rounding stage. All arithmetic is carried at full decimal precision and rounded once, at the return boundary — ten decimal places for values of one and above, ten significant digits below one. The second rule matters here: a sub-picofarad shunt capacitor and a nanohenry-scale series inductor both round to exactly zero under a fixed ten-decimal-place rule, and zero is a finite number that an ordinary output check would let through.

What this does not model. Component losses: real inductors have finite Q, and at high network Q the loss in the matching components can exceed what the mismatch was costing. Parasitics: an inductor's self-resonance and a capacitor's series inductance both matter at the frequencies where L-networks are most used. Complex impedances, which is the largest omission and the one stated beside the result. Bandwidth: the page reports Q, from which fractional bandwidth follows, but it does not compute a response curve. And component tolerance, which at a Q of 10 or more can move the match further than the network moved it.

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.