ADVANCES IN CARRIER TELEGRAPH TRANSMISSION 203 



is zero. At / = 0, the switch closes and current ib starts to flow. If 

 Qi is the charge on the condenser at / = 0, 



^ = E sin co/i + Eo. (3) 



The switch remains closed while e increases to its crest value at b and 

 then decreases until, at time / = /2, the grid goes negative. If Q^ is 

 the charge on the condenser bX t = h 



^ = E sin co{h + h) + Eo. ' (4) 



The switch now opens, and the condenser discharges through Re 

 until the switch closes once more at ^ = 7" to begin another cycle, T 

 being the carrier period lirjw. During this interval the charge on the 

 condenser is given by 



q = Q^^~(t~t2)iCRc^ (5) 



In order that steady-state conditions may prevail, that is, in order 

 that every cycle be the same as its predecessor, q must again equal 

 Qi when / — T. Hence 



or, setting 



£) = ^-{T-t2)ICRc 



Qi = Q2D. (6) 



In connection with equation (la) it has been pointed out that what 

 is sought is an expression for the average charge Q in terms of the 

 parameters. Referring to Fig. 26B, it will be seen that this average 

 lies somewhere between Qi and Q2, but since Qi is very large compared 

 with Q2 — Qi, we may take either Qi or Q2 as equal to the average 

 charge ^ in (la), when considering the effect of bias on the grid of the 

 detector tube in producing compensator action. For the sake of 

 definiteness, let: 



2 \2 C (^b) 



Equations 3, 4 and 6 contain the five unknowns E, Qi, Q2, ti, h; hence 

 one more relation must be established before we can get the desired 

 formulation between E and Qi. The circuit equations for Fig. 255 

 when the switch is closed (charging period) furnish the required 

 relation. Thus: 



I + Rc{ia - ib) = 

 (R + Rc)ib - Rda = E sin <^{t + h) + £0. 



