70 BELL SYSTEM TECHNICAL JOURNAL 



and filament) are again principally responsible, both Vg and r^ vary.^ 

 The quantity m is the amplification factor and is used with its usual 

 significance. It varies with battery potential but this variation is 

 ordinarily very small, though not to be neglected. 



It eventuates, from the above considerations, that if the reactive 

 elements of the frequency determining circuit are constant, a permis- 

 sible assumption, the frequency may be stabilized if adequate account 

 is taken of changes in battery voltages and load resistances. This it 

 is the purpose of the present paper to discuss. 



Hartley Oscillator 



Consider first the form of the Hartley oscillator shown in schematic 

 form without indicating any special method of introducing the bat- 

 teries, in Fig. 2. Figure 1 shows the circuit equivalent of several of 

 the oscillators in the following figures when the impedances are repre- 

 sented in generalized form, and therefore will be employed for an 

 analysis of the conditions necessary to secure independence of fre- 

 quency and battery or applied voltages, and the results of this analysis 

 will then be interpreted in detail in terms of the special circuit of Fig. 2. 

 In Fig. 1 the impedances, Z4 and Z5, are inserted for the purpose of 

 effecting the independence of frequency and battery voltages, and the 

 values which they should have in order to accomplish this result are 

 found by the following analysis: 



From Fig. 1 we have the circuit equations when the assumed cur- 

 rent conditions are as shown by the arrows: 



tie = hirr, + Zi -f Z5) + hiZi + Z,„) - hZm, 



= /i(Zi + Z„0 + /2Z0 - h{Z.2 -f Zm), 



= - /iZ,„ - /oCZo + Z„0 -I- h{r, -f Z2 + Z4), 



e = hr,. (1) 



These equations are expressions of Kirchkoff' s Law regarding the sum 

 of the potentials in a closed mesh. The equations (1) effectively com- 

 prise only three simultaneous equations because the network has only 

 three meshes. 



In the above equation Zq is symbolic of the series impedance of the 

 tuned circuit. Using the symbolism of Fig. 1, 



Zo = Zi -f Z2 -f Z. + 2Z„. (2) 



2 The appendix to this paper contains a further discussion of the significance of 

 rp and rg together with an analysis of the conditions under which oscillator net- 

 works may be treated by the use of linear circuit equations as is done in the following 

 analysis. 



