Application of the T-chart for solving exponentially tapered lossless nonuniform transmission-line problems

Abstract

seven attenuator sets with the load resistances shown for the FET parameter extraction. The largest four data sets may then be utilized for the final equation solving. Note that the input powerlevel adjustments follow the rules of maximizing N-harmonic levels with higher-order terms in noise-flow levels for N-order coefficient evaluations. SOLUTION ACCURACY EVALUATIONThe extracted coefficients of the FET, shown in Table 2, use the four data sets selected according to the conversion-ratio rules and the additional graphical/numerical evaluations of solution qualities. Figure 2(a) shows the equation plots for the linear coefficients g m1 and g d1 in the four different attenuator cases. The solution quality is determined by the linear independence of the lines, that is, the slopes, and the intersections to the x-axis-the shifts in vertical or horizontal directions of the lines. Following the determining equation in [1], the line slopes are decided by the input/ output voltage ratio changed by the attenuators, while the righthand-side terms, determining the shifts of the lines, are the load resistances for the linear case and the measured harmonic powers for the higher-order coefficients. In summary, the attenuators affect all the behaviors of the lines.The 2 nd -and 3 rd -order extractions can also provide this kind of solution-quality observation, but more than two unknowns are involved ( g m2 , g m1d1 , and g d2 for the 2 nd order; g m3 , g m2d1 , g m1d2 , and g d3 for the 3 rd order), which the plane representation cannot support. Here, we choose g m2/3 and g d2/3 , as shown in Figures 2(b) and 2(c), where the other coefficients are fixed at the extracted values. All the plots in Figure 2 show that the extractions are qualified and robust.The additional solution-quality representations are given quantitatively by using the equation residual errors of the determining equations for more precise and accurate judgments. Table 3 shows the errors in percentages for the extracted values at the seven attenuator-set equations. The larger errors occur at the sets exactly as indicated by the graphical examples that assist users in choosing suitable data. The numerical mean is convenient for the automatic measurements, while the graphical one provide more physical understandings and interpretations. CONCLUSIONThis paper has presented theoretical, graphical and numerical observations for the solution accuracy of FET nonlinear currentcoefficient extractions used in Volterra series analysis. The selection of the attenuator sets is the most important issue that can be assisted by the conversion ratios of the output/input powers for different harmonic contents. The dependencies on the harmonic powers versus the attenuator sets have been demonstrated by the nonlinear current expressions in order to provide users with a clear mathematical interpretation of this phenomenon. The quality of the solution was evaluated by graphical and quantitative means as well as experiments using a commercial MESFET in order to show the validity and r...

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

“…One class of transmission lines (TLs), called conjugately characteristicimpedance transmission lines (CCITLs), has been introduced recently in the literature [1][2][3][4][5][6][7]. By definition, a CCITL possesses conjugate characteristic impedances Z ± 0 of waves propagating in the opposite directions along the transmission line.…”

“…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].…”

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

“…Conjugately characteristic-impedance transmission lines (CCITLs) have found various applications in microwave technology [1][2][3][4][5][6][7]. 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].…”

“…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.…”

“…In the analysis and design of CCITLs, the analytical approach usually provides quite complicated formulas. In contrast, a graphical approach based on the T-chart provides a simpler way to obtain solutions with more physical insight [1][2][3][4].…”