ELECTRIC WAVE-FILTERS 331 



Simulation is within .7 per cent of the impedance over the continuous 

 range from 100 to 3000, within 2 per cent from 3000 to 5000, and within 

 4 per cent from 5000 to 5500 cycles per second; the per cent accuracy 

 is best in the case of the mid-section network. This upper frequency is 

 approximately 97 per cent of the critical frequency, 5635 cycles per 

 second. There is good simulation even considerably beyond the 

 critical frequency, as may be inferred from Fig. 16. 



For still greater precision, networks which originally have three or 

 more parameters and which are formed in a manner similar to those 

 of Fig. 15 may constitute the basic networks. 



4.6 Other Approximate Designs 



Alternative designs of networks simulating Ki and K-i can be made 

 with the networks of Fig. 15 as foundations. The method of doing 

 this will merely be outlined here since the networks do not appear to be 

 as practical as the ones already described in detail. 



This procedure assumes that the actual loaded line structure can be 

 quite accurately represented physically in the desired frequency range 

 by a ladder structure of series and shunt impedances, Zi and Zi, re- 

 spectively. Roughly, Zi would be series resistance and inductance and 

 So would be parallel resistance and capacity. Then throughout the 

 two networks of Fig. 15 the impedance of Zik is to be replaced by that 

 of 2i and the impedance of z-ik by that of z-z- Also the terminating 

 resistance R is to be replaced by V21Z2, the impedance of the corre- 

 sponding uniform line, which in this case might be approximately 

 simulated by a resistance in series with a network like the supple- 

 mentary network of Fig. 17. The resulting impedance networks 

 would then approximately represent Ki and K^. However, no design 

 formulas are needed to show that even if these networks give as good 

 simulation as the networks of Fig. 17 they would require more elements. 



Appendix I 



Reactance Frequency Theorems and Proofs of Frequency Relations in 

 M-Type or Higher Order Wave- Filters 

 There are certain simple frequency relations which hold in the 

 reactance characteristics of non-dissipative impedances. A statement 

 and proof of these relations will first be given. From them will follow 

 readily the proofs of the frequency relations in the characteristics of 

 M-type or higher order wave-filters, which are represented by formulas 

 (20) to (24), since they require a consideration of the "constant ^" 

 series impedance Su only. 



