line parameters.
1.2.1 Development of Planar Transmission Lines
The waveguide is a low‐loss transmission medium capable of handling high power transmission. However, it is a bulky structure with limited bandwidth. The fabrication of waveguide‐based components is a complex and expensive machining process. The limitations of the waveguide provided an impetus for the growth of planar lines, and technology based on the planar lines. H.A Wheeler, in 1936, developed a low‐loss coplanar stripline, and in 1942 created parallel plate strip transmission line on a high permittivity substrate. The line structure was compact and suitable at low RF frequency from 150 MHz to 1500 MHz. However, properly documented stripline was reported by R.M. Barrett only in 1951. Just next year, i.e. in 1952, Grieg and Engelmann reported microstrip line. Both structures competed with each other. Initially, the stripline in the homogeneous medium was a preferred line, as it is a dispersionless line with a larger bandwidth. It supports the TEM mode propagation. As it is a shielded line, so it also has a higher Q‐factor. Whereas, the microstrip in the inhomogeneous medium is a dispersive line as it supports the dominant hybrid mode. It has a smaller bandwidth and lower Q‐factor. During 1960, solid‐state components started appearing, and microstrip became the preferred line structure for the MIC environment. The microstrip is an open structure that provided easier access for the interconnections. It led to the development of miniaturized microstrip integrated circuit (MIC) technology. Gradually, the discrete active devices were combined with the planar passive microwave components, and the hybrid MIC (HMIC) came into existence. The sixties were a very creative period for the planar line technology. In 1968, Cohn reported the slot line followed by the coplanar waveguide (CPW) that became the medium of MMIC. C.P. Wen in 1969 developed the CPW. It is an interesting and unusual coincidence that the abbreviation of both the line name and inventor's name is CPW. The integration of the slot line with waveguide took place in 1972 when Meier reported the quasi‐planar fin line [J.40–J.44].
Further compactness in the microwave circuits and systems took place through the development of the monolithic MIC (MMIC) circuit concept in the year 1964. At this stage, the MMIC was based on silicon technology. Unfortunately, the program was not successful due to the very lossy Si‐substrate. The semi‐insulating Si‐substrate deteriorated in the process of the formation of active devices, such as bipolar junction transistors (BJTs) on a Si‐substrate. The next phase of MMIC development took place for the GaAs substrate‐based technology in 1968. It required nearly 10–12 years for its more meaningful development. The span of 1980–1986 was a period of rapid growth for MMIC technology. In 1990s, SiGe based technology was developed that permitted operation of high‐efficiency circuits at higher frequencies. The MMIC technology achieved its maturity for the MMIC based on the silicon and indium–phosphide (InP) substrates apart from the GaAs substrate. At the core of the development were the multilayer planar lines and new varieties of active devices [J.45].
Another kind of Si‐based technology, namely the micro‐electro‐mechanical system (MEMS) gradually came to the fields of RF and microwave. Petersen's reported the MEMS membrane‐based switches in July 1979. However, after a long gap, Yao and Chang developed the surface MEMS switch for DC‐4 GHz operation and high‐quality MEMS inductor chip could be realized in 1997. Subsequent years witnessed a reduction in operating voltage of MEMS switches. The operation of MEMS in the microwave and mm‐wave ranges expanded their applications in the field of the antenna and other microwave systems [J.46–J.48].
The robust and compact multilayer ceramic tape‐based microwave technology, called the low‐temperature co‐fired ceramics (LTCC) gradually acquired significance for the development of the hybrid integrated circuits. It started in 1950–1960 to develop more robust capacitors. The several layers of different materials are used in a single multilayer laminated package to design multi‐functionality circuit‐blocks. The planar lines in the LTCC are used in the multilayer and multilevel formats as a medium to develop the components and interconnect [J.49, J.50].
Further innovations in the planar microwave technology were added by incorporating the periodic reactive loading of planar lines and planar surfaces resulting in the electronic band‐gap (EBG) lines and EBG surfaces for a wide range of applications. Long ago, the theoretical basis for the analysis of the periodic structures was summarized by L. Brillouin [B.14]. The theoretical concept of the metamaterial as a double negative (negative permittivity and negative permeability) material medium, and its radical impact on behaviors of the electromagnetic phenomena were worked out by Victor Veselago in 1967. The practical development of the metamaterials is an outcome of a long history of artificial dielectrics and mixture medium. However, only in 1996–1999, Pendry and co‐workers suggested, and further experimentally demonstrated, the artificial negative permittivity below the controlled plasma frequency. It was realized by using the periodic arrangement of thin conducting wires. Further, in 1999 Pendry and co‐workers suggested and experimentally produced resonance type magnetic behavior in the split coaxial conducting cylinders. However, only Smith and co‐workers worked out the simultaneous negative permittivity and negative permeability in 2000, and experimentally verified it in 2001. Gradually, the concept of metamaterials was added to the planar lines and surfaces resulting in the realization of metalines and metasurfaces. These artificial structures have significantly influenced the design and development of unique antenna, components, and circuits with new characteristics and multifunctionality. Present researches in these fields are in progress in many directions [J.51–J.55].
1.2.2 Analytical Methods Applied to Planar Transmission Lines
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
