Microstrip - Characteristic Impedance

Characteristic Impedance

A closed-form approximate expression for the quasi-static characteristic impedance of a microstrip line was developed by Wheeler:

where is the effective width, which is the actual width of the strip, plus a correction to account for the non-zero thickness of the metallization:

Here Z₀ is the impedance of free space, ε_r is the relative permittivity of substrate, w is the width of the strip, h is the thickness ("height") of substrate, and t is the thickness of the strip metallization.

This formula is asymptotic to an exact solution in three different cases

1. , any (parallel plate transmission line),
2. , (wire above a ground-plane) and
3. ,

It is claimed that for most other cases, the error in impedance is less than 1%, and is always less than 2%. By covering all aspect-ratios in one formula, Wheeler 1977 improves on Wheeler 1965 which gives one formula for and another for (thus introducing a discontinuity in the result at ). Nevertheless, the 1965 paper is perhaps the more often cited. A number of other approximate formulae for the characteristic impedance have been advanced by other authors. However, most of these are applicable to only a limited range of aspect-ratios, or else cover the entire range piecewise.

Curiously, Harold Wheeler disliked both the terms 'microstrip' and 'characteristic impedance', and avoided using them in his papers.