230 BELL SYSTEM TECHNICAL JOURNAL 



For purposes of future discussion it is convenient to express this 

 requirement in precise form. If the network functions ideally its loss 

 must be given by an equation of the following type: 



d = F,{c^) + F.{c^)Fs{R), (1) 



where R is the variable resistance. The function F^iui) corresponds to 

 the temperature characteristic. It must evidently be under our control. 

 The function Fi(a)) represents a fixed loss, analogous to that of an 

 ordinary equalizer. It is of less importance since it can always be 

 changed by the addition of separate fixed networks. In several of the 

 structures to be described, however, it also is under our control, so that 

 the networks can be used as combined fixed equalizers and temperature 

 correcting devices. The function F^iR) expresses merely the calibra- 

 tion of the controlling element with respect to temperature, and its 

 exact form is consequently of minor importance. 



It is not difficult to find circuits which function broadly in the 

 manner described by equation (1). In most instances, however, the 

 desired proportionality in the set of variable characteristics is realized 

 only very approximately. A simple circuit, which it is hoped is both 

 a fair and a plausible example, may illustrate the sort of performance to 

 be expected. 1 The structure consists of a condenser in series with a 

 variable resistance, bridged across a resistance circuit, as shown by 

 Fig. 1. For high values of the variable resistance we may anticipate 

 that the attenuation will be low at all frequencies, while at lower values 

 a characteristic rising with frequency should be obtained. The net- 

 work should then behave much like a radio "tone control." An inspec- 

 tion of the actual characteristics, also shown on Fig. 1, indicates, how- 

 ever, that although this general behavior is in fact obtained, the curves 

 change shape rapidly in every range except that corresponding to high 

 resistances and high frequencies, where they are almost constant. 



The distortion exemplified by the curves of Fig. 1 is the greatest 

 obstacle in the design of variable equalizers to satisfy the specifications 

 of equation (1). To a certain extent it is unavoidable. It is easily 

 shown for example, that the transfer admittance from generator to load 

 impedance in any network containing a single \-ariable resistance can be 

 written as 



Y = ^^f±^, (2) 



1 More elaborate circuits have, of course, been devised in the past. Mention 

 should be made in particular of the structure described in U. S. Patent No. 2,019,624. 

 issued to Mr. E. L. Norton. For moderate ranges of variation, the characteristics 

 of this network are somewhat similar to those of the structure exempHfied later by 

 Fig. 6. Another method of attack is shown by U. S. Patent No. 2,070,668, issued 

 to Mr. W. R. Lundry. 



