Coplanar waveguide short

There is a similar simple approximation for a coplanar waveguide short-circuit, also given in [54]. The short circuit is inductive in nature.

Figure 12.4: coplanar waveguide short-circuit

The equivalent length extension $\Delta l$ associated with the fringing fields is

$$\Delta l_{short} = \dfrac{L_{short}}{L'} \approx \dfrac{W + 2s}{8}$$ (12.29)

Equation (12.29) is valid when the metalization thickness $t$ does not become too large ($t < s/3$).

The short end inductance $L_{short}$ can be written in terms of the inductance per unit length and the wave resistance.

$$L_{short} = L'\cdot \Delta l_{short} = \dfrac{\sqrt{\varepsilon_{r,eff}}\cdot Z_L}{c_0} \cdot \Delta l_{short}$$ (12.30)

According to W.J.Getsinger [55] the CPW short-circuit inductance per unit length can also be modeled by

$$L_{short} = \dfrac{2}{\pi}\cdot \varepsilon_0 \cdot \varepsilon_{... ...frac{\pi\cdot Z_{F0}}{2\cdot Z_L\cdot \sqrt{\varepsilon_{r,eff}}}\right)\right)$$ (12.31)

based on his duality [56] theory.