# Capacitance per unit length

CHAPTER 4

4.5 Capacitance per unit length

Most of the geometries of the cables and signals used have regular structure and their capacitance is specified in terms of per unit length. The capacitance per unit length of these well defined structures can be expressed as a formula.
4.6 Capacitance Per Unit length of a Coaxial Cable

The Capacitance per unit length of a coaxial cable is given by

Figure 4.5 - The Capacitance formed by a coaxial cable
4.7 Capacitance per Unit Length of a Microstrip

The structure of a microstrip resembles that of a parallel plate capacitor. Let w is the width of the trace of a microstrip and h is the separation between the trace and the ground plane. To feed our intuition, imagine a parallel plate capacitor similar to the microstrip as shown in the figure below.
The equation does not give any exact value of the capacitance per unit length of the microstrip. It however, reveals three important conclusions

1. The capacitance per unit length of a microstrip increases with the increase in trace width.
2. The capacitance per unit length of a microstrip decreases with the increase in the separation between trace and ground plane.
3. The capacitance per unit length of a microstrip increases with the increase in the dielectric constant of the material between the trace and the ground plane.

To get the precise value of the capacitance per unit length of the microstrip, a 2D field solver is used. There are some formulas that can be use to estimate the capacitance per unit length of the microstrip. These formula work well for certain ratios of w/h. But they give estimate of the capacitance per unit length as a first approximation. If higher accuracy is needed, 2D field solver should be used.

One of these formula is the one recommended by IPC, the Industry Association of Printed Circuit Board. According to this, the capacitance per unit length of the microstrip is given by

Many calculators are available online that use this formula for calculation of the capacitance per unit length. Here are two of them

http://referencedesigner.com/tutorials/si/si_06.php

http://emclab.mst.edu/pcbtlc2/microstrip.html

You can also create your own calculator using a spread sheet. The accuracy of these calculators is within 5% to 10%. The accuracy varies with w/h ratio.

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