Coplanar waveguide open

The behaviour of an open circuit as shown in fig. 12.3 is very similar to that in a microstrip line; that is, the open circuit is capacitive in nature.

Figure 12.3: coplanar waveguide open-circuit

A very simple approximation for the equivalent length extension $\Delta l$ associated with the fringing fields has been given by K.Beilenhoff [54].

$$\Delta l_{open} = \dfrac{C_{open}}{C'} \approx \dfrac{W + 2s}{4}$$ (12.27)

For the open end, the value of $\Delta l$ is not influenced significantly by the metalization thickness and the gap width $g$ when $g > W + 2s$. Also, the effect of frequency and aspect ration $W / (W + 2s)$ is relatively weak. The above approximation is valid for $0.2 \le W / (W + 2s) \le 0.8$.

The open end capacitance $C_{open}$ can be written in terms of the capacitance per unit length and the wave resistance.

$$C_{open} = C'\cdot \Delta l_{open} = \dfrac{\sqrt{\varepsilon_{r,eff}}}{c_0\cdot Z_L} \cdot \Delta l_{open}$$ (12.28)