Question 2.1: Find the relationship between the surface impedance Zs and t......
Find the relationship between the surface impedance Z_s and the per-unit-length parameters of a conductor of periphery p.
From the definition, the surface impedance Z_s is the impedance of a metal patch of width w and of length l = w (often expressed in \Omega / \square, ohm per square). For a conductor of periphery p and length l = p the total input impedance will be:
Z= Z l= Z p= R l+ j \chi l \equiv Z_s; \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \text{(2.14)}
it follows that the p.u.l. impedance of the conductor Z is:
Z=\frac{Z_s}{p}.\hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \text{(2.15)}
For example, for a circular wire of radius r (p = 2π r) and for a strip of width w and thickness t (p = 2t + 2w) we have, respectively:
Z _{\text {wire }}=\frac{Z_{ s }}{2 \pi r}, \quad Z _{\text {strip }}=\frac{Z_s}{2(w+t)}.\hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \text{(2.16)}
The same law holds for the p.u.l. resistance:
R=\frac{R_s}{p}. \hspace{30 pt}\hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \hspace{30 pt} \text{(2.17)}