ANALYSIS OF MICROSTRIP COUPLERS USING THE MEASURED EQUATION OF INVARIANCE AND THE MOMENT METHOD

Abstract

Numerical techniques in electromagentics can be classified into two mam categories, differential equations techniques and integral equation techniques. Each category has its own advantages and disadvantages. In the microstrip structures the main disadvantage of the differential equation techniques is the need of artificial boundary conditions that should be put at some distance far from the structure which results in a great increase in the computational domain and consequently the required storage memory and computational time. The integral equation techniques on the other hand do not suffer from this problem as the computational domain is on the metallic part of the structure (i.e. the microstrip conductors laying over the dielectric). The main disadvantage of the integral equation technique is that it produces full matrices that require large memory storage and time to solve them as well as the need of Green's function. In 1993, Kenneth Mei and his research team at University of California, Berkley invented a new method, which is a mixture between the differential equation techniques and integral equation technique, namely the Measured Equation oflnvariance (MElt In this thesis the problem of finding the characteristic impedance of a single

microstrip line was studied and solved numerically using the . finite difference technique, which belongs to the first category, the differential equations techniques. The same problem was approached using the moment method, which belongs to the second category. After that the same problem was solved using the measured equation of invariance and a comparison between the three methods showing the required memory, time and accuracy was introduced. A study ofthe sources of error in the measured equation of invariance was carried out and this led us to propose a different scheme for discretizing the computational domain, which results in an increase in the accuracy while decreasing the required computational time to half its value. The problem of two symmetrical coupled lines was studied using the moment method and the measured equation of invariance. It was shown that the technique of the measured equation of invariance is applicable only if we make use of the even and odd modes property of the structure. If we tried to solve the problem without this property the measured equation of invariance gives incorrect results.