Assuming that a transmission line operates in a TEM or quasi-TEM mode, the phase velocity can be determined from the line parameters (R,L,C,G per meter assuming the RLCG model of a transmission line). Because $$V_p = \frac{\omega}{\beta}$$ and from Wikipedia it is clear that $\beta$ follows uniquely from the RLCG parameters.
However, I have found that for a coplanar waveguide, the quasi-TEM approximation does not give a sufficiently accurate approximation for my situation. Therefore, I did attempt do find some other expression which is able to go from the RLCG parameters to the phase velocity more accurately. This does not appear to exist, supposedly because the phase velocity also depends on the dimensions of the transmission line in addition to the RLCG parameters. But I was also unable to find any expressions that do take into account the physical dimensions. The focus was mainly to find some expression for the effective permittivity, because this can be related to phase velocity.
Does there exist such an analytical expression, or is the only way to go EM-simulations?
