Source Calibration and Boundary Scans

Capacitance Source Frequency Three-Row Scan

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