Analytical expression of the impedance of a CPW ground

[pal74]

Hi,
I am trying to understand the calculation of the characteristic impedance of a CPW ground. I need to get an analytical expression for the impedance. My first step was to read the book: "Coplanar_waveguide_circuits__components__and_systems"
Here is what I don't understand: the characteristic impedance of the coplanar waveguide is function of the effective capacitance of the CPW, that can be calculated using conformal mapping transformation. Correct?
However, the equivalent circuit model of the CPW includes R, L, G and C.
So how come the characteristic impedance not a function of the CPW inductance L too?
Thank you.

 

[Valerie Park]

The characteristic impedance of the CPW is a function of the capacitance, not the inductance. The inductance is related to the physical dimensions of the CPW, such as the width of the signal trace and the spacing between the ground plane and the signal trace. The capacitance, however, is determined by the dielectric constant of the material. The capacitance is then used to calculate the characteristic impedance using the equation: Z0 = sqrt(L/C).