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# 4.5 Coplanar Line

In a coplanar line a metallic strip (width w) runs between infinite ground planes separated by slots (slot width s) on the upper surface of a substrate. In real circuits the ground planes have a finite width wg > w. Strip and ground are located in the same plane, hence, the name coplanar. Figure 4.11a shows the geometry. The trace represents the signal conductor and the ground planes represent the return conductors. The distance d between the ground planes is

4.38

An electromagnetic wave is present in air and substrate (height h, relative permittivity εr), so the fundamental wave type is quasi-TEM (see Figure 4.11b), where the magnetic fields runs in closed loops around the centre conductor and the electric fields point from centre conductor to the ground planes.

## 4.5.1 Characteristic Impedance and Effective Permittivity

In the literature [7, 11, 13] and [14] we find formulas for the characteristic impedance that involves elliptic integrals of the first kind that cannot be solved directly. In order to have less accurate but more easily evaluated expressions we reproduce here two equations from [11] and restrict our discussion to thick substrates ...

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