LC Oscillators

Same LC Source Binds the Mode Label

A mode label is accepted only when it cites the same checked LC source that supplies the inductance, capacitance, and frequency-square value. The bookkeeping is exact for the stated source record and ideal lumped-element oscillator; real devices require separate metrology for wiring parasitics, resonator coupling, drift, loss, and readout calibration.

A mode label must cite the checked LC source. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A platform mode cites one LC source

The mode label is accepted only because the same source carries 1 henry, 1 farad, and frequency square 1.

L=1 H,C=1 F,ω2=1 s−2L=1\ \text{H},\quad C=1\ \text{F},\quad \omega^{2}=1\ \text{s}^{-2}
One source for one modeA copied mode label would fail source validation.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2

This is a frequency-square training model

The book keeps the exact square 1 and does not compute a rounded oscillation frequency.

ωchecked2=1 s−2\omega^{2}_{\text{checked}}=1\ \text{s}^{-2}
Training boundaryOnly the checked square is part of the claim.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2