1---
2app_version: 0.7.0
3precision: 3
4form_title: L-Network Matching
5form_description: Match two resistive impedances with two components. Enter both impedances and the frequency — get the exact coil and capacitor values, the network Q and the bandwidth you get with it.
6form_inputs: Source impedance (Ω)|Zs, Load impedance (Ω)|Zl, Frequency (MHz)|freq, Topology|topology[Low-pass (L series, C shunt):1,High-pass (C series, L shunt):2]
7form_outputs: Network Q|Q, Series reactance (Ω)|Xs, Shunt reactance (Ω)|Xp, Inductor (µH)|ind_uh, Capacitor (pF)|cap_pf, Bandwidth (MHz)|bandwidth
8---
9# L-Network Matching
10// Two components, one match. The classic tuner section.
11//
12// The rule that makes it work: the SERIES element always sits on the
13// low-impedance side, the SHUNT element across the high-impedance side.
14// Swap them and the network transforms the wrong way.
15//
16// Both impedances are taken as purely resistive here — cancel any
17// antenna reactance first, then match what is left.
18
19# What you want to match
20Zs = 50 // Ω, source (your rig or line)
21Zl = 450 // Ω, load (the antenna feed point)
22freq = 14.2 // MHz
23topology = 1 // 1 = low-pass, 2 = high-pass
24
25R_high = max(Zs, Zl)
26R_low = min(Zs, Zl)
27w = 2pi * freq * 1e6 // rad/s
28
29# Network
30Q = sqrt(R_high / R_low - 1) // loaded Q — fixed by the ratio
31Xs = Q * R_low // series element, low-Z side
32Xp = R_high / Q // shunt element, high-Z side
33
34"Transformation ratio": R_high / R_low
35"Network Q": Q
36"Series reactance Xs (Ω)": Xs
37"Shunt reactance Xp (Ω)": Xp
38
39# Component values
40// Reactance to component: L = X/ω, C = 1/(ωX).
41// Low-pass (1): series coil, shunt capacitor — also attenuates harmonics.
42// High-pass (2): series capacitor, shunt coil — blocks DC and static.
43ind_uh = Xs / w * 1e6 if topology == 1 else Xp / w * 1e6
44cap_pf = 1e12 / (w * Xp) if topology == 1 else 1e12 / (w * Xs)
45
46"Inductor (µH)": ind_uh
47"Capacitor (pF)": cap_pf
48
49// A wound air-core coil can be trimmed to the exact value, but a bought
50// choke or capacitor can't — e12()/e24() round to the nearest value from
51// the corresponding preferred-number series.
52"Inductor, nearest E12 (µH)": e12(ind_uh)
53"Capacitor, nearest E24 (pF)": e24(cap_pf)
54
55# Bandwidth
56// A higher transformation ratio forces a higher Q — and a higher Q
57// narrows the range over which the match holds.
58bandwidth = freq / Q
59"-3 dB bandwidth (MHz)": bandwidth
60
61// Check: shunt C across R_high, then series L, must land back on R_low.
62// Parallel combination of R_high and −jXp, real part:
63r_after = R_high * Xp^2 / (R_high^2 + Xp^2)
64"Check — resistance after the shunt element (Ω)": r_after
65