L-Network Impedance Match
Two-component L-match between resistive source and load — Q, L, and C at your frequency.
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The engineering
The minimum hardware that makes one resistance look like another: a series reactance on the low-impedance side and a shunt reactance on the high side. This card gives the low-pass flavor (series L, shunt C) — the usual choice because it also swallows harmonics. Swap L and C for the high-pass mirror if you need DC blocking instead.
Q is not chosen — it is forced by the transformation ratio, which is the L-network's weakness and its honesty. 50 → 200 Ω locks Q at 1.73 and roughly a 58% bandwidth; bigger ratios get narrower. Need a specific Q? Cascade two Ls through an intermediate resistance or move to a Pi/T network.
Where this math comes from
Matching begins with Moritz von Jacobi's 1840 maximum-power-transfer theorem, but reactive matching became an industry inside the Bell System — George Campbell's loading coils and image-parameter theory treated every junction as an impedance to be negotiated rather than endured.
Radio made the L-network folk hardware: every 1930s transmitter output stage and every modern antenna tuner is one or two of these, and Phillip Smith's 1939 chart exists mostly so engineers could walk L-network arcs with a pencil.
- 1840Moritz von JacobiMaximum power transfer theorem — why matching matters.
- 1920George Campbell / Bell SystemImage-parameter design; matching becomes systematic.
- 1939Phillip H. SmithSmith chart — L-network design as geometry.
See the full timeline of the math behind every calculator →
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