Source Calibration and Boundary Scans

Capacitance Source Frequency Three-Row Scan

This scan keeps inductance fixed and changes only the capacitance source, so the LC product is easy to see row by row. Capacitance values 1, 2, and 4 make reciprocal mode-square values 1, 1/2, and 1/4, showing the checked mode slowing as capacitance grows. Real frequency calibration depends on component tolerances, parasitic capacitance, temperature, readout loading, fitting choices, and uncertainty.

Keeping inductance fixed isolates how capacitance changes the LC reciprocal square. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Capacitance row 1 sets reciprocal mode square

Row 1 keeps inductance at 1 and reads capacitance 1. The checked LC product sets the displayed reciprocal square.

LC=1⋅1=1,ω⋅ω=1L C=1\cdot1=1,\quad \omega\cdot\omega=1
Capacitance source row 1The LC check binds L, C, product, and reciprocal mode square.inductance=1 Hcapacitance=1 FlcProduct=1 s^2omegaSquared=1 1/s^2

Capacitance row 2 sets reciprocal mode square

Row 2 keeps inductance at 1 and reads capacitance 2. The checked LC product sets the displayed reciprocal square.

LC=1⋅2=2,ω⋅ω=12L C=1\cdot2=2,\quad \omega\cdot\omega=\frac{1}{2}
Capacitance source row 2The LC check binds L, C, product, and reciprocal mode square.inductance=1 Hcapacitance=2 FlcProduct=2 s^2omegaSquared=1/2 1/s^2

Capacitance row 3 sets reciprocal mode square

Row 3 keeps inductance at 1 and reads capacitance 4. The checked LC product sets the displayed reciprocal square.

LC=1⋅4=4,ω⋅ω=14L C=1\cdot4=4,\quad \omega\cdot\omega=\frac{1}{4}
Capacitance source row 3The LC check binds L, C, product, and reciprocal mode square.inductance=1 Hcapacitance=4 FlcProduct=4 s^2omegaSquared=1/4 1/s^2

Capacitance alone slows the checked mode

The scan changes only capacitance. The product follows that source, and the reciprocal square falls in the same checked rows.

CLCωω11122124414\begin{array}{c|c|c}C&L C&\omega\omega\\1&1&1\\2&2&\frac{1}{2}\\4&4&\frac{1}{4}\\\end{array}
Capacitance source scanThe middle row is displayed while the table keeps all rows.C=2 gives omega-square=1/2