464 BELL SYSTEM TECHNICAL JOURNAL 



for the composite network equals the sum for the separate sections is 

 furnished by two sections of Network la or of 2a, Appendix IV, both 

 having four coefficients. On the other hand, a composite network of 

 la and 2a, one of each, has five attenuation coefficients. Finally, a 

 composite network of two sections of Network 2>a has only five attenua- 

 tion coefficients contrasted with a sum of six for the separate networks. 

 In the latter case we can obtain only five linear equations from the 

 attenuation characteristic which are not sufficient to determine the 

 six series elements. This probably means that for the same attenua- 

 tion characteristic the resistances in series with the two inductances 

 can be given any ratio to each other from zero to infinity. A sixth 

 relation can then be supplied by assuming the practical condition 

 which makes the ratio of resistance to reactance the same in the 

 inductance branches of both sections. This composite network can 

 have an attenuation constant whose increase with frequency is approxi- 

 mately linear over a wide internal frequency range. 



Composite phase networks of simple structure also lend themselves 

 readily to such treatment as a single unit. 



2.85. Composite Lattice Networks Having Uniform Attenuation 



To a lattice type network of a certain class having a finite non- 

 uniform attenuation characteristic there corresponds a single infinity 

 of complementary ones, such that when any one of the latter is com- 

 bined with it, the composite network has a uniform total attenuation 

 constant and a zero total phase constant over the entire frequency 

 range. The separate attenuation constants are complementary while the 

 phase constants are equal, hut opposite in sign. Such a conposite net- 

 work we have seen would be absolutely distortionless. It is a relatively 

 simple matter to obtain the necessary relations which such a comple- 

 mentary network must bear to the first if we impose these propagation 

 conditions on the combination. Two sets of relations may be derived, 

 each corresponding to a particular structure for the first network, 

 with the following results. 



If the given section (A, B) has series impedances 



zn = Rs + Zs, (38) 



where Rs is a resistance and Zs is any impedance, any equivalent trans- 

 formation of which does not contain series resistance, and if a com- 

 plementary network {A', B') is added such as to give a composite 

 network {A,, B,) with the propagation constant 



Ac = A + A' = constant, 



