Smith chart problems and solutions3/10/2023 The electric charges accumulated at the interface between adjacent ‘capacitors’ can be modulated by the transverse voltage. Each layer in the multilayer thin film in the present approach is treated as a capacitor coupled to the next so that the multilayer film is modelled as an effective capacitor which is constructed by a series of coupled capacitors. Each layer in the thin film is modelled by a propagation matrix, while the coupling between any two adjacent layers at an interface is modelled by an interface matrix. In this paper, the polynomial approach will be adopted exclusively to model the optical responses of a multilayer thin film made of non-magnetic, lossless materials.Ī polynomial approach is adopted to simulate the optical-electrical response of a multilayer thin film subjected to an applied transverse voltage. 2011 Taflove and Hagness 2005 Taflove et al. 2001), and finite difference time domain (FDTD) (Joannopoulos et al. 1994 Vigoureux 1991 Taya and Shabat 2015), conjugate characteristic-impedance transmission line (CCITL) (Orfanidis 2016 Guru and Hiziroglu 2009 Worasawate and Torrungrueng 2006 Pozar 2012), bi-characteristic impedance transmission line (BCITL) method (Orfanidis 2016 Guru and Hiziroglu 2009 Pozar 2012 Knittl 1976 Heavens 1991 Vašiček 1960 Torungrueng and Thimaporn 2004 Torrungrueng 2007), plane wave method (Guo and Albin 2003 Sakoda 2001 Joannopoulos et al. 2010 Azzam and Bashara 1977 Fukuyama and Ando 2013 Shabat and Taya 2003 Waerden 1949 Waerden et al. 2004 Markos and Soukoulis 2008), polynomial approach (El-Agez et al. Well-known mathematical methods for analysing the optical responses of multilayer thin films include Transfer Matrix Method (TMM) (Zi et al. The electrical structure of a thin film can be modelled as a function of the physical characteristic of the constituent materials and geometrical dimensions (such as the thickness of each layer and number of layers). The original T-chart based on the geometric mean of char-acteristic impedances is found to be the most convenient graphical representation for solving CCITL problems. It is found that all T-charts for each normalization factor are strongly dependent on the argument of characteristic impedances of CCITLs in a complicated fashion. In this study, three more possible normalization factors related to char-acteristic impedances of CCITLs are investigated. By using other normalization factors based on characteristic impedances, different graphical representations can be obtained i.e., T-charts for CCITLs with passive characteristic impedances are not unique, and it depends on the associated normalization factor. Originally, the normalization factor used in defin-ing normalized impedances of the T-chart is the geometric mean of characteristic impedances of CCITLs, which is not only one possible choice. In addition, an example shows that Meta-Smith charts offer a simple approach for matching network design using open-circuited single-stub shunt tuners.Ĭonjugately characteristic-impedance transmission lines (CCITLs) implemented by lossless periodic transmission-line struc-tures have found various applications in microwave technology, and the T-chart was developed to perform the analysis and design of CC-ITLs effectively. Results show that stability regions on Meta-Smith charts can be determined, and source and load reflection coefficients can be selected properly to obtain desired operating power gain. In addition, Meta-Smith charts, a graphical tool developed for solving problems in the CCITL system, are employed to design matching networks to achieve desired amplifier properties. It is found that the bilinear transformation plays an important role in transforming circles in the reflection coefficient Gamma(0)-plane in the Z(0) system to the Gamma-plane in the CCITL system. This paper aims to generalize the CCITL system by demonstrating a theoretical study of CCITLs and their applications in the microwave transistor amplifier design. A typical Z(0) uniform transmission line is a special case of CCITLs whose argument of Z(0)(+/-) equal to 0 degrees. Conjugately characteristic-impedance transmission lines (CCITLs) are a class of transmission lines possessing conjugately characteristic impedances (Z(0)(+/-)) for waves propagating in the opposite direction.
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