322 BELL SYSTEM TECHNICAL JOURNAL 



This circuit is of the forward-acting type; that is, the control energy is 

 taken from the line ahead of the point of variable loss. The variable 

 loss consists of a high impedance pad connected in the circuit through 

 two high ratio transformers Ti and Ti. The high resistances Ri and R2 

 are shunted by a pair of control tubes connected in push-pull. The 

 push-pull arrangement is desirable for two reasons. It reduces the 

 even order non-linear distortion effects caused by the shunt path on 

 the transmitted speech and it balances out the control impulse and 

 un filtered rectified speech energy from the control path which might 

 otherwise add distortion to the speech. The impedances of these 

 tubes are controlled by the control voltage Eg, which is roughly pro- 

 portional to the envelope of speech energy and which is derived from 

 the line through a non-linear or "rooter" * circuit, a linear rectifier 

 and a low-pass filter which may have a cutoff frequency in the range 20 

 cycles to 100 cycles. In the following analysis it is assumed that the 

 delay due to this filtering is negligible: 



Let El = r.m.s. speech voltage at input 

 and £2 = r.m.s. speech voltage at output in same impedance 



Re = a-c. impedance of control tubes. 



Now if Re is kept small compared to the pad impedance, we have 

 approximately 



E2 = kiEiRc. (1) 



Let Eg he the control voltage applied to the grids of the control 

 tubes. With the plate voltage Eb just neutralized by the steady bias- 

 ing grid voltage Ec, then only Eg may be considered as determining 

 the space current and we may assume ideally that the space current 



Ib = kiEG'. 

 Then 



P cLEb dEc 1 .^x 



^'--dTB-^-dTB-hE^^' ^2) 



wheres 5 is determined by tube design and the ^s are constants for 

 constant ^l tubes. For variable /x tubes equation (2) can be used to 

 set requirements on the tube design. 

 FrorrL (1) and (2) 



^^ = w^- '^) 



Now let the rooter be a non-linear circuit such that the instantan- 

 eous voltage is the tth root of £1. After rectification and filtering we 

 * So called because the output is a root of the input; see equation (4). 



