20 DELL SYSTEM TECHNICAL JOURNAL 



the requisite high precision the excess characteristic impedance of 

 the line; the complete network then consisting of either of these excess- 

 simulators in series with the basic resistance element R\ of Fig. 5a. 

 In any specific application the most suitable values for the elements 

 constituting either of the two excess-simulators in Fig. 7 depend 



(a) 



L 2 ^5 



n_ (Wodh-Tr 



wwHkj C 4 www 



r 3 c 3 r 5 



Fig. 7 — -Two Potentially Equivalent 3-Element Excess-Simulators Possessing High 

 Simulative Precision for Most Applications, Except at very Low Frequencies 



somewhat on the particular frequency-range involved, and also on 

 the weighting of the desired simulative-precision with respect to the 

 frequency. As might be expected, therefore, the work of determining 

 closely the best combination of values for the elements of the excess- 

 simulator can hardly avoid a certain amount of tentative detailed 

 design-work; but usually this can be reduced to a relatively small 

 amount by a semi-graphical method such as outlined in the latter 

 part of Appendix C. Moreover, first-approximation values that will 

 usually prove to be rather close, can be quickly found by means of 

 the following approximate design-formulas (32), . . . (37), which are 

 explicit except for containing the single undetermined parameter D. 

 These formulas are such that the excess-simulator will possess high 

 simulative-precision at large and even fairly large values of F, for all 

 physcially admissible values of D (O^D^l); and at the lower values 

 of F will have a considerable range of adjustment by means of D, whose 

 optimum value can be readily determined from inspection of Figs. 8 

 and 9, as described below. The above-mentioned approximate design- 

 formulas for the elements of the two excess-simulators in Fig. 7 are 11 : 



C 2 =^^, (32) 



D 2VLC 

 Cz ~7=D ^R~' (33) 



^3 = 2^, (34) 



11 The first part of Appendix C gives the derivation of these formulas, and also 

 the equation of the curves in Fig. 8. 



