1---
2version: 0.1.0
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# draftply — 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 = 2 * pi * 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).
41if topology == 1:
42 # Low-pass: series coil, shunt capacitor. Also attenuates harmonics.
43 ind_uh = Xs / w * 1e6
44 cap_pf = 1e12 / (w * Xp)
45
46if topology == 2:
47 # High-pass: series capacitor, shunt coil. Blocks DC and static.
48 ind_uh = Xp / w * 1e6
49 cap_pf = 1e12 / (w * Xs)
50
51"Inductor (µH)": ind_uh
52"Capacitor (pF)": cap_pf
53
54# ── Bandwidth ──────────────────────────────────
55# A higher transformation ratio forces a higher Q — and a higher Q
56# narrows the range over which the match holds.
57bandwidth = freq / Q
58"-3 dB bandwidth (MHz)": bandwidth
59
60# Check: shunt C across R_high, then series L, must land back on R_low.
61# Parallel combination of R_high and −jXp, real part:
62r_after = R_high * Xp^2 / (R_high^2 + Xp^2)
63"Check — resistance after the shunt element (Ω)": r_after
64