DISTORTION CORRECTION 457 



and their effects in a network do not alter appreciably the general 

 characteristics. However, to calculate accurate results for both the 

 propagation constant and the iterative impedance of the final design 

 of a physical network taking into account all factors, one should use 

 the general formulae given in Appendix III which have been simplified 

 to give accurate results quite readily. 



2.7. Network Solutions from Their Propagation Characteristics 

 It was assumed in the previous section that the recurrent network 

 elements are invariable and that inductances and capacities are non- 

 dissipative. On this basis general formulae for the propagation char- 

 acteristic were obtained in terms of these elements. The same assump- 

 tions are retained here but reverse processes will be carried through 

 which derive the elements from the propagation characteristic of the 

 recurrent network. Three methods will be outlined, necessarily in 

 general terms. 



Method 1. Solutions from the Attenuation Constant 

 Since attenuation is ordinarily of greatest importance, this method 

 is the one most frequently used with networks having an attenuation 

 characteristic and involves initially the determination of the attenua- 

 tion coefficients Pq, Qo, etc., from this characteristic. Using these 

 coefficients, one derives from algebraic relations, first, the impedance 

 coefficients ao, bo, etc., and finally the network elements in Zn. The 

 elements of 221 follow from the inverse network relation (10). 



The method is based upon the transformation of the attenuation 

 formula (21) to a linear equation in Pq, Qq, etc., whose number is equal 

 to or greater than the number of independent network parameters. 

 If we multiply equation (21) by the (2-polynomial, we obtain formally 

 the attenuation linear equation which holds at all frequencies, 



Po +/^P2 + ■■■ - FQo -PFQ2 - . • • = 0. (23) 



Introducing in this the attenuation constant, and hence F, at a number 

 of different frequencies equal to the number of independent network 

 parameters, there results a system of independent simultaneous linear 

 equations which can be solved for the coefficients. The simplest 

 practical procedure is perhaps that of the step-by-step elimination of 

 the coefficients. 



When the number of coefficients and independent network param- 

 eters, hence equations, are the same, the solution of the latter offers 

 no particular difficulty and results can readily be checked by substitu- 

 tion in the original equation (21). 



