How this calculator works
Build a lossless network between positive resistive port components, then compensate source and load series reactances at the design frequency. Pi and T networks split the transformation through a virtual resistance; their chosen Q must exceed the minimum imposed by the resistance ratio. The component table lists source-to-load order, including separate compensation when it cannot be combined. The sweep assumes each supplied port reactance behaves as an ideal inductor or capacitor. Source reactance is external to the plotted input impedance, whose target at design is the complex conjugate of the source.
Formula
L match: Q = sqrt(Rhigh/Rlow - 1); series X = Q Rlow; shunt B = Q/Rhigh. T virtual R = min(Rs,Rl)(1+Q²). Pi virtual R = max(Rs,Rl)/(1+Q²). L = X/(2 pi f); C = -1/(2 pi f X) for series X < 0.
Worked example
Matching 50 to 200 ohms at 100 MHz with a low-pass L network gives Q = sqrt(3), a series reactance of 86.6025 ohms and a load shunt susceptance of 0.00866025 S. The components are about 137.832 nH and 13.7832 pF.
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Frequently asked questions
Does this include component loss?
No. Inductor Q, capacitor ESR, self-resonance and layout parasitics need a circuit simulation or measurement.
Why can a DC path be rejected?
Compensating a complex port may require a series capacitor or shunt inductor, which conflicts with a requested DC-through path.
Is the match broadband?
The exact match is at the design frequency. The optional sweep shows how the ideal input impedance changes nearby.