Accurate analytical determination of quasi-static microstrip line parameters

Abstract

In the design of microstrip components, the analytical equations of Wheeler have an advantage in handling-speed and simplicity over alternative quasi-static analyses involving complex computation by numerical methods. Wheeler equations can produce excessive errors, however, unless care is taken particularly in the choice of changeover point between equations for narrow or wide strips. This paper shows that for alumina-type substrates with 8 < εr < 12, the Wheeler analysis and synthesis equations produce results within 1% of those given by selected numerical methods, when the changeover points are correctly chosen. Additional new and modified formulae are presented for the direct calculation of microstrip effective permittivity from either W/h or Z0, also to an absolute accuracy of less than 1%. These complete an accurate set of analytical equations for quasi-static analysis or synthesis of microstrip lines.