460 BELL SYSTEM TECHNICAL JOURNAL 



similar to that used in dealing with equation (23) can be applied and 

 will not be repeated here. This process, apparently new, of obtaining 

 linear equations for the impedance coefficients which contain powers 

 of frequency and the impedance components, was applied by the 

 writer to non-dissipative two-terminal networks in this Journal, 

 January, 1923, p. 21, also in U. S. Patent No. 1,509,184, dated Septem- 

 ber 23, 1924; and to dissipative networks which simulate a smooth 

 line impedance in U. S. Patent Application, Serial No. 134,515, filed 

 September 9, 1926. It is merely outlined here. 



2.8. Useful Properties and Relations 



The following discussion covers a number of points concerning these 



networks which have been found quite useful. They can be verified 



readily from the fundamental formula and so need not be derived 



in detail. 



2.81. Analytical Simplifications 



Let it be desired to design a given network from its attenuation 

 characteristic in a frequency range when the number of attenuation 

 coefficients is one greater than the number of independent network 

 elements. As previously stated, it is usually possible in such cases 

 to choose as part of the attenuation data the attenuation constant at 

 a particular frequency, such as zero or infinite frequency, and make 

 the resulting number of attenuation coefficients and independent 

 elements equal in number, with consequent ease of solution. Another 

 method of simplifying the analysis might be to slightly alter the form 

 of the given Zu by adding to it, or subtracting from it, a resistance 

 element in series or in parallel. This may have the effect of making 

 the resulting attenuation coefficients and independent elements equal 

 in number without appreciably altering the general attenuation char- 

 acteristic in the desired frequency range. 



2.82. Uniform Attenuation Change 



According to principles developed above, if the attenuation constant 

 of a given network is changed uniformly over the entire frequency 

 range without altering its phase constant, its distortion producing 

 characteristics are not affected. 



Let zu correspond to a given lattice type network and Zu' to a 

 derived one in which the attenuation only has been changed by a 

 uniform amount Aq ait all frequencies. Then one form of structure 

 for Zii is 



1 



Sii = 



' + ' 



(27) 



WiZu + m-iR m-iR- 



