A METHOD OF IMPEDANCE CORRECTION 831 



extra element considerably increases the admittance of the final shunt 

 arm, and therefore the attenuation of the network, at frequencies 

 remote from the cutoff. In spite of these modifications the analogy 

 to standard sections is a fairly trustworthy guide to the attenuation 

 of the networks. Several examples are given in the accompanying 

 paper. 



Since the ideal pure reactances contemplated by the theory are not 

 physically available these conclusions must be modified somewhat in 

 practical designs. As we might expect, however, unavoidable dis- 

 sipation of energy in the network elements will alter the transmission 

 characteristic of the correcting device about as it would that of an 

 ordinary filter. In the attenuating range the effect can be neglected. 

 In the nominal transmission band absorption of energy in the termina- 

 tion will reduce the transmitting efficiency of the circuit somewhat, 

 but the loss in efficiency is no more serious than it would be in standard 

 filter sections having the same general configuration. 



Parasitic resistances in the network elements may of course affect 

 the impedance as well as the transmission properties of the circuit. 

 Since the structure is used primarily because of the impedance char- 

 acteristic it furnishes, possible changes in impedance, caused by varia- 

 tions in the phase angles of the network elements, are of particular 

 interest. Changes in impedance produced by dissipation of energy 

 in the correcting networks, are easily estimated when the complete 

 circuit with whose impedance we are concerned can be considered as a 

 network of ordinary resistances, inductances and capacities and when 

 dissipation affects the phase angles of all reactive elements equally. 

 It can be shown that in such a network the change produced by dissipa- 

 tion in the resistance of the structure is proportional, to a first approxi- 

 mation, to the derivative of its reactance characteristic with respect 

 to frequency, and that conversely the change in the reactance character- 

 istic is proportional to the frequency derivative of the resistance 

 characteristic. The explicit formulae are: 



AX=-/.f, 



where /is frequency and d the dissipation constant (defined as ratio of 

 resistance to reactance) for each reactive element. 



A filter, with its terminating sections and load resistance, is a net- 

 work of resistances inductances and capacities to which the theorem 

 applies. It seldom happens of course, that all of the reactive elements 



