Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 32

Assaudourion and Rimai considered the microstrip in the quasi‐static limit. They assumed the TEM mode propagation on it. They applied, in 1952, the well‐established conformal mapping method to compute the characteristic impedance, dielectric, and conductor losses. Between the years 1954 and 1955, Cohn also used the conformal mapping method to get the design‐oriented results for the characteristic impedance, dielectric and conductor losses of the stripline. He further used the conformal mapping method to get the odd‐even mode impedances of the edge‐coupled strip lines in 1955 itself. He further obtained these results for the broadside‐coupled strip lines in 1960. Following the conformal mapping method, in 1964 and 1965 Wheeler produced more accurate and design‐oriented expressions for the computation of characteristic impedance of microstrip line. He extended his analysis to get further results in 1977 and 1978 [J.56–J.64].

In 1969 Cohn suggested another planar line, i.e. the slot line. It is a complementary structure of the microstrip line. He also presented the equivalent waveguide model of the slot line, and obtained the frequency‐dependent propagation parameters of the slot line. Next in the group of the planar lines is the coplanar waveguide (CPW) proposed by C.P. Wen. He obtained the initial quasi‐static line parameters of CPW using the conformal mapping method. Subsequently, the conformal mapping method was applied to analyze several variants of the planar lines [J.65–J.67].

Other quasi‐analytical and numerical methods were also used for the analysis of microstrip lines. For instance, in 1968 Yamashita and Mitra introduced the quasi‐analytical variational method in the Fourier domain to obtain the quasi‐static line parameters of the microstrip line. It was the prelude to the quasi‐analytical dynamic spectral domain analysis (SDA) of microstrip and other planar lines. The dynamic SDA is a full‐wave analysis method that considers the hybrid mode nature of planar lines. After a gap of nearly 10 years, Itoh used the concept of the discrete Fourier transform and Galerkin's method to get the static line parameters of suspended coupled microstrip lines, and also extended the method to suspended multiconductor microstrip structures. The Fourier domain method was significantly extended by many investigators to other planar structures such as the CPW [J.68–J.71, B.15, B.16].

In 1973 and 1974, Itoh and Mitra introduced the dynamic SDA to obtain dispersion characteristics of the slot line, and also microstrip line. Jansen extended the dynamic SDA to analyze the higher order modes in the microstrip. The method is very powerful and analytically elegant. It has been used and improved by other researchers in the field of planar resonators, antenna, and line structures. Other powerful methods, such as the method of moments, finite elements, finite‐difference time‐domain method, and so on have also been developed to analyze the 2D and 3D complex planar structures. The contemporary EM‐Simulators are based on these numerical methods. The closed‐form models for faster computation of the static and frequency‐dependent line parameters of planar lines have also been developed by several investigators. The closed‐form models of lines, discontinuities, and so on helped the development of the Circuit Simulators [J.72–J.75, B.15, B.16].