# Fringe effect and Capacitance

**CHAPTER 4**

**4.13 Fringe Effect and Capacitance of Combination of structure**

In case of a parallel plate capacitor, if we double the area of overlap, the capacitance of the parallel plate capacitor doubles.

We must note that in the case of the parallel plate capacitor, we ignore the fringe effect. Because of the fringe effect the capacitance of a parallel plate capacitor is more than the capacitance calculated by the formula. Fringe effect occurs when the electric field extends the area of the overlap. When we double the area of the parallel plate capacitance, the area of the overlap does double. However, the fringe effects do not double. Therefore in practical parallel plate capacitor the capacitance is not doubled when the area of the overlap is doubled. It is slightly less.

We therefore make two statements

1. The capacitance of a practical parallel plate capacitance is more than that calculated from the formula for the parallel plate capacitor due to the fringe effect.

2. If we join two practical parallel plate capacitors, so that their area of overlap doubles, the resulting capacitance is less than twice the capacitance of individual capacitors. This is because the fringe effect capacitance is less than double.

We can extend the concept of the fringe effect of capacitance in the case of the microstrip structure. In case of the microstrip structure, the capacitance per unit length does not double by doubling the width of the trace.

The Capacitance per unit length for the case of 5 mils trace width was calculated in the previous section. The rlgc matrix calculated from hspice for the 10 mils case is reproduced here.

*SYSTEM_NAME : demo * * Half Space, AIR * ------------------------------------ Z = 1.270000e-004 * diel_1 H = 1.016000e-004 * ------------------------------------ Z = 2.540000e-005 * //// Bottom Ground Plane /////////// * ------------------------------------ Z = 0 * L(H/m), C(F/m), Ro(Ohm/m), Go(S/m), Rs(Ohm/(m*sqrt(Hz)), Gd(S/(m*Hz)) .MODEL demo W MODELTYPE=RLGC, N=1 + Lo = 2.460224e-007 + Co = 1.431457e-010 + Ro = 2.690930e+000 + Go = 2.501310e-003 + Rs = 1.497919e-003 + Gd = 5.396465e-013 |

The Capacitance per unit length in this case is 1.431457e-010 farad per meter or 3.6359 pf/inch. We have earlier noted the capacitance of the 5 mils trace width was 2.407 pf/inch. If we apply the parallel plate capacitor analogy, the capacitance of the microstrip structure should double to about 4.814 pf/inch. However, it is observed to be 3.6359 pf/inch.

Some of the capacitance is resulted from the fringe effect of the structure. The electric lines of the forces come out of the side of the trace and propagates down to the ground layer. When we double the trace width we do not double this fringe effect. Therefore the capacitance is less than twice even if we double the trace width.

We can generalize this statement for any combination of structure.

“If two structures are joined, their resulting capacitance with respect to the ground is less than the sum of the capacitances of the individual structures with respect to ground”.

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