The end-fed question: where do the watts go in a 49:1?

The end-fed half-wave is the most argued-about antenna in portable radio. Its fans point at the convenience — one wire over a branch, feed it at the bottom, no feedpoint dangling mid-air. Its critics point at the black box that makes it possible: the little 49:1 transformer, plus the counterpoise question, plus whatever the coax is quietly doing. The argument is usually conducted in folklore because the system is hard to reason about piecemeal — every piece interacts.

wire.efhw_sloper models the whole chain at once: ~9.5 m of thin wire sloping down at ~63° (the slope_deg knob — the apex, ≈10 m at the defaults, is derived from it) to a feed point at 1.5 m, into a step-down unun with a real magnetizing branch and core loss, a compensation capacitor, a short counterpoise, and 5 m of RG-58 to the rig. Every stage is a knob, and the power budget itemizes each one.

Why a transformer at all

The end of a half wave is a voltage antinode: the model’s feedpoint impedance at resonance is ~2.2 kΩ — no rig drives that directly. unun_ratio picks the classic step-downs (49:1, 64:1, or 225:4); at the stock 49:1 the rig sees 58 − 3j Ω, SWR 1.17, on 14.1 MHz. The transformer composition is exact in the network layer: idealize the unun (huge magnetizing L, no comp cap, zero-length line) and the rig impedance is the feedpoint divided by turns² to numerical precision — an oracle the test suite pins. Flip the ratio dropdown and the differences are honest too: 64:1 lands SWR 1.40 and 225:4 lands 1.26 on this particular wire, because the “right” ratio depends on a feed impedance the antenna’s height and slope keep moving.

Anti-resonance trivia worth knowing: an ideal-wire end-fed is a numerically nasty solve — the impedance peak at the half-wave point is a near-singularity. The real wire loss modelled since v0.23 damps it, which is both why this design solves cleanly and why physical EFHWs are more forgiving than lossless theory suggests.

Where the watts go

At the stock operating point the budget reads (fractions of input power):

stage	share
unun core loss (magnetizing branch)	~0.6 %
5 m RG-58	~6.0 %
wire loss (I²R), 28 AWG PVC	~6.1 %
structural efficiency	~87 %

One label deserves care: that ~87 % is structural efficiency — the input power not burned in components and conductors — and it is the number this page’s knobs can move. It is not the fraction that leaves as sky wave: this sloper runs steep and low, and over average ground the dirt takes its share of what the structure delivers. The pattern integral puts radiated (incl. ground) at ~32 % for the stock 20 m setup (~39 % for the 40 m variant below — the flatter 30° slope gives back more from the dirt’s ledger than its extra wire loss costs). Both numbers are true, in different ledgers — the accounting is the subject of Three ledgers of efficiency.

Three readings worth taking home:

1. The wire is the transformer’s equal. The scary lossy-looking ferrite box burns under a percent at mid-band with the stock magnetizing Q; the innocent-looking 28 AWG wire burns six times that, because the half-wave’s current maximum lives in the middle of the thin wire. Flip wire_type to 18 AWG PVC and the wire row drops to ~1.9 % (structural efficiency 91 %) — the same gauge story as wire gauge for POTA, amplified by the end-fed’s current distribution. The whole antenna still weighs 18 g in 28 AWG.
2. The counterpoise is load-bearing. The stock 1.05 m is the classic 0.05 λ. Shrink it to 0.3 m and the match collapses to SWR 4.3; stretch it to 3 m and it detunes the system the other way (SWR 1.5). “The coax shield is my counterpoise” works precisely because a short deliberate one like this is all the return path the feed needs.
3. Loss buys bandwidth, again honestly. The stepped-down 2.2 kΩ feed plus the wire loss flatten the SWR curve: the model holds the entire 20 m band under 2:1. That’s the EFHW’s famously friendly SWR curve — and the budget shows what it costs.

The unun defaults (lmag_uH = 8, qlmag = 10) put the core in the 85–90 % efficiency range bench-measured for FT240-43-class 49:1 builds. The model is deliberately minimal — a magnetizing branch with finite Q, not a full transformer characterization — so treat the (mag) row as the shape of the loss, and tune qlmag against a measurement if you have one: Q = 5 doubles the core’s share, Q = 20 halves it.

The 40 m variant

wire.efhw_sloper:band40 is the same POTA box — unun, comp cap, and coax untouched — with twice the wire: ~19 m of 28 AWG PVC retuned to put the rig-side SWR minimum at 7.1 MHz (SWR 1.36, and the whole band under about 2:1). Two things change with the band, and both are honest physics rather than knob-turning:

• The slope comes down. A 63° rise would put the apex at ~18 m; the variant’s 30° lands it near 11 m — a tall mast or a friendly tree limb. At ~0.26 λ up the pattern is near-NVIS (takeoff ≈ 78°, essentially omnidirectional), which is exactly how 40 m POTA operates: regional skywave, not DX.
• The wire loss doubles. The longer high-current half wave burns ~10 % in I²R (vs ~6 % on 20 m), for 84 % structural efficiency. The 100 pF comp cap is a 20 m-flavored compromise, too — ~200 pF would buy SWR 1.19 here, if you’d rather rebuild the unun than accept 1.36.

Try it

Open wire.efhw_sloper in the simulator with the sweep locked to 20 m. Flip unun_ratio and watch the match move; drag cp_len_m and watch it matter more; flip wire_type to bare wire and watch resonance jump up the band (retune with length_factor — insulated wire is a few percent electrically longer). Then drag the measurement frequency across the band and watch the power budget re-divide itself between the coax, the core, and the wire — the end-fed question, answered per watt.