Capacitance and inductance of IC wires

This post answers the question “What are capacitance and inductance of IC wires?”. Wiring loop (depicted below) makes the most common type of parasitic inductance.

The inductance of the IC wire with parameters depicted on the figure can be calculated by formula $L={\mu }_{0}R\left(\ln \right(\frac{16R}{d})–2)$.

Let’s calculate capacitance and inductance of IC wires of different shapes. Let’s consider the combination of IC wiring depicted on the figure below. Here $W\gg G$ . Conductor is insulated with dielectric with permittivity $\epsilon >{\epsilon }_0$ and permeability ${\mu }_0$.

Then for the unit length of the wire, capacitance $C$ and inductance $L$ for flat conductor can be found as $C_f=\frac{\epsilon W}{G}, L_f=\frac{{\mu }_{0G}}{W}$.

The unit length of wire capacitance $C$ and inductance $L$ for cylindrical conductor (depicted below) can be found as $C_c=\frac{2\pi \epsilon }{\ln ({\displaystyle \frac{H}{R}}+\sqrt{{\displaystyle \frac{H^2}{R^2}}–1})}$ and $L_c=\frac{{\mu }_0}{2\pi }\ln (\frac{H}{R}+\sqrt{\frac{H^2}{R^2}–1})$.

In both cases $CL=\epsilon {\mu }_0$.

More educational content can be found at Reddit community r/ElectronicsEasy.