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AESTECHNO
L-MATCH

RF impedance matching calculator: L, Pi and T

To match a complex source Zs = Rs + jXs to a complex load ZL = RL + jXL, enter the four values and the frequency. We compute the L-network (one inductor, one capacitor) that presents the conjugate Zs* back to the source, which is the condition for maximum power transfer. The result gives ideal values, values rounded to your chosen preferred-value series, Q, bandwidth, and the return loss those buyable parts actually deliver.

Inputs

Network

Topology

An L-network fixes its own Q. Pi and T let you choose it, but only upward: they narrow the band, never widen it.

Must stay above the minimum Q the resistance ratio dictates.

Up to four networks match equally well. They are ranked most robust first against component tolerance.

We recompute the actual match after rounding to buyable values.

Source impedance

Negative if capacitive.

Load impedance

As measured on a VNA. Negative if capacitive.

From a VNA sweep (.s1p)

Drop a one-port Touchstone file and we read the impedance at your design frequency, interpolating between samples. S-parameters only, and never outside the measured band.

Source Zs

No file loaded.

Load ZL

No file loaded.

Schematic of the matching network Circuit diagram of the chosen matching network. The source impedance is on the left, the load on the right, joined by a signal path. Series elements sit on the path and shunt elements run from it down to ground. The arrangement of those elements changes with the topology: an L-network has two, a Pi network has a series element between two shunts, and a T network has a shunt between two series elements. Each element is labelled with the preferred-value component to fit. L 7.5 nH L 10 nH Zs = 50 + j0 Ω ZL = 12.5 - j30 Ω
The network to build, with preferred-value components. Where the shunt elements tap the signal path is what decides the impedance seen looking in.
Smith chart of the matching trajectory Smith chart normalised to the real part of the source impedance. A filled dot marks the load, a hollow dot the impedance after the element nearest the load, a cross the conjugate target Zs*, and a diamond where the rounded preferred-value components actually land. Two arcs join them: a series element rides a constant-resistance circle, a shunt element a constant-conductance circle.
  • ● load
  • ○ after each element
  • ✕ target Zs*
  • ◆ with rounded parts
  • ␷ constant VSWR
  • ␷ constant Q
  • ◉ worst case over tolerance
Normalised to Rs. A series element rides a constant-resistance circle, a shunt element a constant-conductance circle. The target sits at the centre only when the source is purely resistive.
Result

7.5 nH

Breakdown

shunt L = 10 nH · Q = 0.831 · match -37.9 dB

Network 1 (active) series L, shunt L · Q 0.831 · -37.9 dB · -24.8 dB worst
Network 2 series L, shunt L · Q 1.73 · -26.2 dB · -22 dB worst
Network 3 series C, shunt L · Q 0.831 · -29.6 dB · -18.2 dB worst
Network 4 series L, shunt C · Q 1.73 · -22.6 dB · -15.3 dB worst
Arrangement series at source, shunt across load
Series L ideal 7.615 nH
Series L E24 7.5 nH
Shunt L ideal 9.873 nH
Shunt L E24 10 nH
Q 0.831
-3 dB bandwidth 1.045 GHz
Return loss -37.9 dB
Return loss, worst case ±5% -24.8 dB
Mismatch loss 0.000703 dB
VSWR 1.03

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Ideal lossless network, exact at the design frequency only. Pi and T narrow the band relative to an L, never widen it. Networks are ranked by the worst match inside the component tolerance box, so the default is the most robust rather than the best on paper. Inductor Q, capacitor ESR and package parasitics shift the real tuning further: confirm on a VNA.

RF // MATCHING

An approximate match is paid for in lost range and in certification margin. We design and measure RF chains from HF to multi-gigahertz: book a free 30-minute audit through our contact page.

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Frequently asked questions

FAQ

Why target the conjugate Zs* rather than the real part Rs?
Maximum power transfer requires the impedance seen by the source to be the conjugate of its own, that is Rs minus jXs. Matching only the real part leaves the source reactance uncompensated, so power is reflected and the link budget suffers. As soon as Xs is non-zero, targeting Rs alone produces the wrong network. That is why this calculator asks for all four quantities rather than two resistances.
Why does the calculator offer several networks?
Depending on the impedances, up to four L-networks match equally well at the design frequency: series L with shunt C, series C with shunt L, and the two mixed pairs L-L and C-C. They differ on two things that matter in practice. Q, which sets the bandwidth: a lower Q tolerates component drift better. And DC behaviour: a series capacitor blocks bias, a series inductor passes it. The table compares them all and ranks them most robust first: the default is the network that holds up best when the components drift within tolerance, not the one with the best nominal figure.
What does the return loss after rounding actually mean?
Ideal values come from a continuous calculation, but you buy parts from a preferred-value series. We do not simply round each component to its own nearest value: the two errors can partly cancel, so we search neighbouring values for the best buyable pair. The network is then rebuilt with those values, the real input impedance recomputed and the resulting reflection coefficient shown. A perfect ideal match can fall below 20 dB once snapped to E12. That figure, not the theoretical one, is what you should check before ordering components.
When should I pick a Pi or T network over an L?
An L-network has no adjustable Q: it follows from the resistance ratio. Pi and T add a third element and make Q free, but in one direction only. Their minimum Q is still the one the resistance ratio dictates, so they narrow the band and never widen it. Choose them to filter deliberately, reject a harmonic, or hit a specific loaded Q. For a difficult match they do not help: the L-network remains the widest and the least sensitive to component tolerance.
What does the worst case beside the match mean?
An E24 part is a 5% part, E12 is 10%, E96 is 1%. So we sweep the tolerance box around the two chosen values and report the worst match found inside it: that is the performance you can guarantee in production, not the one an ideal sample gives. The degradation is far from marginal, typically 7 to 15 dB at plus or minus 5 percent. It also changes the ranking: a network that looks better on paper can be the more fragile of the two.
Does the calculation account for component losses?
No, the network is computed from ideal lossless elements. In practice an inductor's finite Q, a capacitor's equivalent series resistance and package parasitics shift the tuned frequency and reduce efficiency, and they matter more as network Q rises. We recommend treating the result as a starting point, then verifying with a vector network analyser on the actual board before committing the layout.
Why does Q rise when the impedances are far apart?
In an L-network Q is not a free parameter: it follows from the resistance transformation ratio. The wider the gap between source and load, the higher the Q, so the narrower the bandwidth and the more sensitive the network becomes to component tolerance. If the resulting bandwidth is too narrow for your application, the answer is a Pi or T network, or matching in two stages.
Can I enter an impedance measured on a VNA?
Yes, that is the intended use. A vector network analyser reports the real and imaginary parts of the impedance directly at your working frequency: enter them in the RL and XL fields, keeping the sign. A negative reactance is capacitive, a positive one is inductive. A real antenna is almost always complex, which is exactly what calculators limited to two resistances cannot handle.
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AESTECHNO is an electronics design house based in Montpellier, France. 10+ years of RF design experience, with a 100% success rate on CE/FCC certifications.