[leavesofgrass]

PR 1 of 3 in the radio-toolset series. Stacked PRs follow for RF exposure (MPE/SAR) and the Smith chart/accessibility upgrade.

Why

abax's RF layer did not cover the circuit math of the FCC Amateur Extra (Element 4) exam. The 2024–2028 pool is effective 2024-07-01 through 2028-06-30, and this PR works from the copy that includes the fourth errata (2026-02-04). The missing pieces:

• time constants
• phase angle and admittance
• ERP chains
• link margin
• op-amp gain
• modulation index
• CW/FSK bandwidth
• ADC bits
• sideband band edges
• stub reactance

I extracted the pool text and inventoried every question that needs arithmetic: 45 questions reducing to about 20 distinct relations. This PR covers all of them.

What

59 new formula functions (Radio & RF category):

Area	Functions
Ohm's law & power	OHMV OHMI OHMR POWERVI POWERIR POWERVR
Series / parallel	RSERIES RPARALLEL LSERIES LPARALLEL CSERIES CPARALLEL (values or ranges)
Time constants	TAURC TAURL TCCHARGE TCDECAY TCTIME
Impedance & power	ZSERIESRLC ZPARALLELRLC ZMAG PHASEANGLE POWERFACTOR ADMITTANCE CONDUCTANCE SUSCEPTANCE POLAR2RECT REALPOWER REACTIVEPOWER APPARENTPOWER QSERIES QPARALLEL
Link & power chain	ERPW EIRPW RXLEVEL LINKMARGIN BWNOISEDB
Op-amps, FM, bandwidth	OPAMPINV OPAMPNONINV MODINDEX DEVRATIO CARSONBW CWBW FSKBW
Sampling	ADCBITS ADCLEVELS ADCLSB ADCSNR NYQUIST
Band edges, lines, antennas	USBMAXFREQ LSBMINFREQ LINELEN ELECDEG STUBX ANTEFF
Receiver	IMD3LO IMD3HI IP3 SFDR IMAGEFREQ

• Impedance arguments accept either an Excel complex string ("75+25j") or separate R, X numbers.
• Complex results are complex strings that the existing IMREAL, IMAGINARY and IMABS functions read.
• Backed by new pure-stdlib modules core.science.circuits and core.science.radio_calc.

Worked examples: docs/examples/radio/extra-class-formulas evaluates all 45 calculation questions as formulas. It exits non-zero if any result disagrees with the answer key, so tests/test_examples.py enforces it. I also checked the answer letters and wording in the script against the pool text programmatically.

Circuit calculator (Tools → Radio), with four tabs:

• Ohm's law: enter any two of E, I, R and P.
• RC/RL time constant, with a graph.
• RLC resonance: f0, Q and −3 dB bandwidth, with a graph.
• Impedance, phase and admittance.

Fields accept engineering notation (50u, 40 pF, 3.5 MHz).

Accessibility of the graphs:

• The chart canvas is keyboard-focusable and draws a visible focus ring.
• It has an accessible name, and an accessible description written from the plotted numbers. That description is the same text as the visible summary, and it fires DescriptionChanged when the values change.
• Reference lines and points are labeled with text, never color alone.
• Each graph is paired with the same data as a table, plus a Data → new sheet button.
• Colors come from the theme palette, so the high-contrast themes apply.

Sources and caveats

• CW/FSK necessary bandwidth follows 47 CFR § 2.202(g): Bn = B·K, and Bn = 2M + 2DK. The rule states no general WPM → baud conversion. CWBW uses 0.8 baud per WPM, the ratio in the rule's own worked example (25 WPM with B = 20), and the pool uses the same ratio (E8C05). This is documented.
• Coverage gaps:
  • The pool asks no numeric Smith chart or MPE questions; PRs 2–3 address those tools.
  • A few functions here go beyond the pool as practical station tools: Carson's rule, IP3/SFDR and image frequency.

Verification

• ruff check . passes.
• pytest -n auto: 4647 passed, 196 skipped. The skip count was unchanged by this PR; none of the new tests skip.
• mkdocs build --strict passes.
• python make_pyz.py builds, and abax.pyz --version runs.
• The coverage ratchet was run locally with the CI command: core 84.35% (floor 83), engine 63.26% (floor 62), both within slack.
• The new tests were mutation-checked:
  • Breaking the FSK formula, the phase-angle argument order, the ADC floating-point guard, or the complex-result cleanup each turns tests red.
  • The ADC guard mutation first slipped through, so a real floating-point edge case was added.
• Registry-size and description-coverage pins were raised (614 → 673 and 625 → 688) with comments.

🤖 Generated with Claude Code

https://claude.ai/code/session_0157FDmhHjtSvT3pWABUTvmX

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Generated by Claude Code