IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 99

The accuracy of (3-73) and (3-74) is reasonable, but two approximations made
during the derivation degrade the accuracy. First, we assumed that the signal
conductor is infinitely thin, which is not realistic because microstrip transmission
lines manufactured on printed circuit boards often have conductor thicknesses
of dimensions similar to the dielectric height. There is little benefit of deriving
a finite thickness formula here because the most useful method would employ
numerical solutions that are not covered in this topic. Second, the charge distri-
bution on the signal conductor is not uniform. The charge distribution near sharp
edges is derived in Section 3.4.4 and applied to this formulation.

3.4.4 Charge Distribution near a Conductor Edge

The approximation made in the analysis of Section 3.4.3 assumed that charge dis-
tribution on the signal conductor on the microstrip was uniform. Realistic charge
distributions tend to increase significantly near the corners on the conductors,
which will alter the capacitance and subsequently the effective permittivity of
the transmission line. To begin the derivation of the charge distribution, consider
Figure 3-19, which shows two intersecting planes at an angle of θ . The two cases
of interest are when θ = 270 ◦ , which will yield the charge distribution near a

sharp corner, and when θ =

360 ◦ , which will yield the charge distribution near
the edge of a very thin strip. The derivation assumes that the conducting planes
are kept at a potential V with respect to a point far away. Since we are interested

y

P

r

f

q

x

Φ = V

Edges of a conductor

Figure 3-19 Two conducting planes held at a potential V with respect to a far-off point
intersecting at an angle.