Shortened Vertical / Groundplane

Antenna Geometry

Frequency f MHz

Height h m

λ = 42.22 m · h/λ = 0.142

Wire / tube diameter d 2.0 mm

Ground loss R_ve Ω

user-supplied, typ. 10–25 Ω. No soil model here — setting R_ve=0 gives a misleadingly optimistic efficiency.

Loading Coil

Coil position b 2.00 m

distance from the feed point (0 = base of the vertical)

Coil Q factor 100

Capacity Hat (top loading)

Matching Network

Matching inductor Q

series L carries the full antenna current; its loss lowers efficiency directly.

Antenna Library

System Efficiency (incl. ground & match loss)

27%

−5.7 dB · antenna only: 31%

Shortening vs. full λ/4

43%

6.00 m instead of 10.56 m

SWR 1.00

Rs (radiation)

8.9 Ω

Rvf (coil loss)

0.0 Ω

Rve (ground)

20.0 Ω

XA (feed)

−398 Ω

Zm (char. imp.)

504 Ω

Coil L

8.9 µH

Coil XL

398 Ω

Hat C · X_tip

off

RA (total)

28.9 Ω

Power split (radiated vs. total loss)radiated / loss

27%

73%

L-Network Match to 50 Ω (series L · shunt C)

Series L_s

9.46 µH

Shunt C_p

320 pF

L_s loss R

4.2 Ω

SWR (ideal)

1.00

Matching bandwidth — SWR around the operating frequency (fixed component values)

Efficiency vs. coil position b/h (L re-tuned for resonance at each point)

The optimum is typically flat and sits around b/h ≈ 1/3–2/3: moving the coil up raises both the required L (more loss) and Rs (more radiation) — a non-monotonic trade-off.

How this works: the monopole is modelled as two cascaded transmission-line segments (feed→coil, coil→tip) using the King/Schelkunoff characteristic impedance Z_m = 60·(ln(4h/d) − 1). The feed reactance adds an empirical Janzen end-correction. Radiation resistance is computed exactly by numerically integrating the far field of the (possibly loaded) current distribution — the short-dipole 80π²(l/λ)² approximation is ~2× off at these heights. Validated against two worked examples from the source (Rs within ~0.1–1.7 %, reactance and Z_m to <0.5 %). Ground loss R_ve is user-supplied — the tool has no soil model. Treat results as a solid design starting point; final tuning belongs to a NanoVNA. Unofficial, independent re-implementation; not affiliated with the authors.

Optional capacity hat: modeled as a lumped capacitive termination at the tip (exact within the same transmission-line framework used elsewhere in this tool). The disc-capacitance formula (C[pF] ≈ 35.42·D[m]) is validated against two published sources; real open spoke hats will show less capacitance than the disc figure for a given span — there's no reliable simple formula for that correction (see W4RNL's NEC-calibrated discussion at antentop.org), so treat the disc number as an optimistic estimate, not a build spec.