Balun & Broadband Transformer Designer

Sources & verification

Power v1: bare copper diameter and DC resistance are from The ARRL Handbook for Radio Communications, 2023, 100th edition, Ch. 22, p. 22.39, Table 22.44 (Jason’s supplied scans, pp. 22.39–22.40). The resistance column is headed 25°C; values are used as printed. No open-air ampacity is used. Wound length only; no lead allowance, skin/proximity effect, temperature correction or ampacity assumption. All current/voltage stress maps are an EE-reviewed ideal model: EMRFD pp. 3.33–3.35, Figs. 3.74–3.80 (errata checked, wording only); Sevick pp. 1-6, 8-13, 8-18, 9-27. Includes the reviewed tapped trifilar split. Matched resistive loads only; no arbitrary phase, common-mode model or insulation ratings. Conventional primary copper loss includes quadrature magnetizing current from L_min at the lowest frequency. DC copper loss is a lower-bound screening estimate, excluding skin and proximity effect, temperature, leads and joints. Conventional mix 61 only: effective geometry comes from the linked Fair-Rite part page; 25°C sinusoidal loss-curve points are interpolated log-log without extrapolation. The frequency-specific B limit uses Fair-Rite’s 500 mW/cm³ general guideline; it is a core-only screening ceiling at the lowest frequency, not a thermal guarantee, saturation rating or full-band build rating. No numeric core ceiling is computed for TLTs, mix 43 or BN cores. Sevick Table 11-2 stays a separate advisory; nothing is combined into a build-power number.

Topologies and the design rules come from four books. Hayward, Campbell & Larkin, Experimental Methods in RF Design (EMRFD), ARRL, 1st ed. (2003): coupling from measurement (p. 3.33, Eq 3.43), turns ratio (Eq 3.44), the 5× reactance rule and the leakage limit X_leak ≤ R/5 (p. 3.34), the bifilar 1:1 (Fig 3.75), the 4:1 step-up balun and step-down unun (Figs 3.76, 3.77), the trifilar 1:1 (Fig 3.78), the two-core 9:1 (Fig 3.79), the Guanella 1:4 (Fig 3.80) and the λ/8 to λ/4 line length and 25 Ω paralleled-pair example (p. 3.35); the EMRFD errata for pp. 3.33–3.35 change wording only. Hayward, Introduction to Radio Frequency Design, ARRL, 1st ed. (1994), pp. 147–151 (Figs 4.27–4.31): the pseudobalun, the 4:1 as an autotransformer, the “real” 1:1 balun and the λ/8 line length. Hayward & DeMaw, Solid State Design for the Radio Amateur (SSDRA), ARRL, 1986 (3rd printing): Z₀ = √(R1·R2), the ≈ 50 Ω #24 enamel and ≈ 100 Ω hookup-wire lines and paralleled pairs (p. 55, Figs 11–14), and the 4–5× reactance rule (p. 60). Sevick (W2FMI), Transmission Line Transformers, ARRL, 2nd ed. (2nd printing, 1991): Guanella and Ruthroff names and Eqs 1-1 to 1-3 (pp. 1-5 to 1-7), the trifilar 1:9 and its tap (Figs 8-10, 8-17, Eq 8-2, pp. 8-13 to 8-20), the 10× TLT-mode rule (pp. 9-10, 9-11), the 1:1 names (p. 9-9), the Guanella 1:9 (p. 9-27, Fig 9-17), permeability guidance (p. 11-13), the power ratings (Table 11-2, p. 11-14) and the Z₀ tolerance and measurement notes (pp. 12-16 to 12-18). Core data are the Fair-Rite values in the Ferrite Core Turns calculator; wire diameters are heavy-build magnet wire. QRPedia design choices, approved by Jason (NT7S): turns are rounded up at the low end of the A_L tolerance, and 4:1, 9:1 and 1:9 windings are sized on the low-impedance side (IntroRF pp. 150–151, Fig 4.30c, for the Ruthroff 4:1 and 9:1; Sevick §2.3, p. 2-5, for the Guanella 1:4; Jason’s design choice for the Guanella 1:9 and, with Sevick p. 8-13, the trifilar 1:9). Unsourced and labeled where shown: VF = 1 (free-space λ), counting every strand toward the fit, the Table 11-2 band reading, more than two paralleled enamel pairs, any paralleled hookup-wire pairs, and the trifilar Z₀ estimate and taps on the Fig 8-17 wiring. Automated tests check the engine against the spec’s worked examples. Engine: .