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Basic

Recipes: RF

Eight everyday RF calculations, each worked with the crate and checked exactly. They are the questions a bench or a firmware asks: is the antenna matched, does the link close, how noisy is the receiver, which register values give this channel. Each page starts with the task and the numbers, and ends with a "Going deeper" section on what is exact, what is not, and why.

The example 19_rf does all eight in one program, one function per page, and tests/props/rf.rs holds the properties that check them against exact references.

  1. Mismatch: Γ, VSWR and return loss: a load on 50 Ω, a VSWR spec, and why Γ = ½ is exactly 20·lg 2 dB of return loss.
  2. Link budget: EIRP, the free-space path loss \(20 \lg(4\pi d/\lambda)\), dBm and dBW, and dBi against dBd.
  3. Friis noise cascade: noise figures in dB through a receiver chain, certified, and the −174 dBm/Hz that is a rounding.
  4. Fractional-N PLL: a synthesizer's register values, its frequency error and its integer-boundary spur, exact.
  5. Two-ports: S, Z, Y and ABCD: an L-match that matches exactly, attenuator pads in cascade.
  6. Free-space impedance: \(\eta_0 = \mu_0 c\) from a named CODATA set, and where 120π matters and where it doesn't.
  7. Skin depth and line input impedance: \(\delta = \sqrt{\rho/(\pi f \mu_0)}\) as an exact scale, and a stub's reactance through tan.
  8. Phase noise to jitter: a clock's phase noise integrated over a band, and its RMS jitter.

The API these pages use is described in the RF chapter: Impedance, Reflection, Levels and dBm. The rules behind "exact" are on What exact means.

Where the crate has no place yet

These pages found five gaps. The example writes what it needs and says so where it does:

  • CPX-8: no complex rational, so S, Z, Y and ABCD are exact only in the example's own Cq.
  • LVL-17: no certified level (dB) of an Exact or a Magnitude at run time; to_level works in f64.
  • LVL-18: no level of a spectral density (dBm/Hz, dBc/Hz) and no integral of one over a band.
  • LVL-19: no antenna gain against a named reference (dBi, dBd).
  • NUM-45: no public interval, so the example brackets tan and lg with a few lines of its own.