Microstrip via hole

Figure 11.11: microstrip via hole to ground

According to Marc E. Goldfarb and Robert A. Pucel [45] a via hole ground in microstrip is a series of a resistance and an inductance. The given model for a cylindrical via hole has been verified numerically and experimentally for a range of $h < 0.03\cdot\lambda_0$.

$$L = \dfrac{\mu_0}{2\pi}\cdot\left(h\cdot \ln{\left(\dfrac{h + \sq... ... + h^2}}{r}\right)} + \dfrac{3}{2}\cdot\left(r - \sqrt{r^2 + h^2}\right)\right)$$ (11.232)

whence $h$ is the via length (substrate height) and $r = D/2$ the via's radius.

$$R = R\left(f = 0\right)\cdot \sqrt{1 + \dfrac{f}{f_\delta}}$$ (11.233)

with

$$f_\delta = \dfrac{\rho}{\pi\cdot \mu_0\cdot t^2}$$ (11.234)

The relationship for the via resistance can be used as a close approximation and is valid independent of the ratio of the metalization thickness $t$ to the skin depth. In the formula $\rho$ denotes the specific resistance of the conductor material.