Standard Smith Chart Approach to Solve Exponential Tapered Nonuniform Transmission Line Problems

Abstract

In this paper, the analysis of standard Smith chart based on the theory of exponential tapered nonuniform transmission lines (ETNUTL in short) is presented. The approach using the standard Smith chart for ETNUTL is realized by a novel mathematical transformation. The standard Smith chart approach provides more flexibility to solve ETNUTL problems.

Equivalent Graphical Solutions of Terminated Conjugately Characteristic-Impedance Transmission Lines With Non-Negative and Corresponding Negative Characteristic Resistances

“…On the other hand, observing from the right one, waves propagating in the forward and reverse directions possess Z − 0 and Z + 0 , respectively. Thus, interchanging of Z + 0 and Z − 0 in (8) and (9) with Z L = 0, Z in,R can be written compactly as shown in (12). Solving (10), (11) and (12) simultaneously, Z + 0 , Z − 0 and β can be determined analytically as follows [6]:…”

“…By definition, a CCITL possesses conjugate characteristic impedances Z ± 0 of waves propagating in the opposite directions along the transmission line. Examples of CCITLs are reciprocal lossless uniform TLs, nonreciprocal lossless uniform TLs [8][9][10], exponentially tapered lossless nonuniform TLs [2,11,12] and periodically loaded lossless TLs operated in passband [13][14][15][16][17][18]. Using the ABCD matrix technique, it can be shown that the equation of the input impedance at each terminal of loaded finite lossless periodic structures is in the same form as that of CCITLs [4].…”

Theoretical Study of Microwave Transistor Amplifier Design in the Conjugately Characteristic-Impedance Transmission Line (Ccitl) System Using a Bilinear Transformation Approach

“…Practical amplifier design, on the other hand, heavily relies on trade-offs and compromises as it inevitably involves integrating different subcomponents with different characteristics. The graphical tool such as the Smith chart has then been developed for a graphical-aided design of high-frequency devices such as microwave amplifiers in the Z 0 system [1][2][3], where Z 0 is the characteristic impedance (usually with a real value) of a transmission line (TL) of interest. The mathematical expressions for the graphical solutions have been further formulated and optimized in an effort to achieve certain properties of amplifiers [4].…”

“…In particular, a large community of researchers has paid a great attention to interconnects or TLs between these high-frequency sub-components as the TLs can greatly alter characteristics of the traveling signals and ultimately, the properties of amplifiers. TLs can typically be classified into several types such as reciprocal lossless and lossy TLs, nonreciprocal lossless [5][6][7][8] and lossy [2] TLs, and exponential tapered lossless nonuniform TLs [3,[9][10][11]. Some of these have already been employed for practical applications, while some novel ones have been modeled and fabricated; i.e., metamaterial TLs possessing negative refractive index and permeability [12][13][14][15][16][17].…”

Non-Uniqueness of T-Charts for Solving Ccitl Problems With Passive Characteristic Impedances

“…Examples of CCITLs are reciprocal lossless uniform transmission lines (TLs), nonreciprocal lossless uniform TLs, exponentially tapered lossless nonuniform TLs [3,8] and periodically loaded lossless TLs operated in passband [10][11][12][13][14][15]. In general, CCITLs are lossless and possess different characteristic impedances, which are complex conjugate of each other, for waves propagating in opposite directions.…”