1---
2app_version: 0.7.0
3precision: 3
4form_title: Feedline Electrical Length & Quarter-Wave Transformer
5form_description: How many electrical degrees is this run of coax — and how far off the nearest quarter-wave are you? Also sizes a quarter-wave matching transformer.
6form_inputs: Frequency (MHz)|freq_mhz, Velocity factor|vf, Physical length (m)|physical_length_m, Impedance to match (Ω)|z_in, Load impedance (Ω)|z_out
7form_outputs: Electrical length|electrical_length_deg, Nearest quarter-wave length (m)|nearest_quarter_m, You are off by (m)|off_by_m, Quarter-wave transformer impedance (Ω)|z_transformer
8---
9# Feedline Electrical Length & Quarter-Wave Transformer
10// "Is this feedline a quarter-wave — or way off?"
11//
12// A wave travels slower in a cable than in free space, by the cable's
13// velocity factor (vf) — typically 0.66 for solid-dielectric coax like
14// RG-58, up to about 0.82 for foam types.
15
16speed_of_light = 299792458 // m/s
17freq_mhz = 14.2
18vf = 0.66 // velocity factor of the cable, from its data sheet
19physical_length_m = 5
20
21wavelength_m = speed_of_light / (freq_mhz * 1e6) * vf
22electrical_length_wl = physical_length_m / wavelength_m
23electrical_length_deg = electrical_length_wl * 360°
24
25"Wavelength in this cable (m)": wavelength_m
26"Electrical length (wavelengths)": electrical_length_wl
27"Electrical length": electrical_length_deg
28
29// Nearest quarter-wave physical length, and how far off you are — handy when
30// building a quarter-wave matching stub or a phasing line for a two-element
31// array, where being a few centimetres short changes the whole match.
32quarter_wl_m = wavelength_m / 4
33n_quarters = round(physical_length_m / quarter_wl_m)
34nearest_quarter_m = n_quarters * quarter_wl_m
35off_by_m = physical_length_m - nearest_quarter_m
36
37"Nearest quarter-wave length (m)": nearest_quarter_m
38"You are off by (m)": off_by_m
39
40# Quarter-wave transformer
41// A quarter-wave line of impedance Z matches two resistive impedances:
42// Z = √(Zin · Zout) — the classic trick for feeding, say, a 200 Ω folded
43// dipole with 50 Ω coax.
44z_in = 50
45z_out = 200 // e.g. a folded dipole feed point
46z_transformer = sqrt(z_in * z_out)
47
48"Quarter-wave transformer impedance (Ω)": z_transformer
49"...physical length needed at this frequency (m)": quarter_wl_m
50