530 BELL SYSTEM TECHNICAL JOURNAL 



expression (21) becomes: 



MKSitx + \y 



z. 



X 



(Z, + Zi)(Z/ + Z2) 



X 



IJ- 



M+ 1 



Z2 4" Zp 



M+ 1 



Z2 + Zp 



1 -F 



X 



i?o + mZ/ 

 Z2 + ZJ 



Z/+- 



1 + 



Ra + AtZff' 



i?o + mZ/ 

 Z2 + Z/ 



Z/ + 



1 + 



i?o + mZ/ 



1 + 



Z2 + z/ 



Zo + ZJ 



(24) 



(Wj— w,) 



1 + 



Ro + A1Z9' 



X 



Z/ + 



Z2 + Z/ 

 Ro 



1 + 



Z2 + Z/ 



("1-6)2) 



With no feedback present, that is when Z2 = <» , equation (24) 

 reduces to 



MKSfx^ 



But in this case K 



Zp + -^0 1 0), I Zp' + i^o UJ Zp' + Ro I (wi-coj) 

 Zi 



(25) 



Zx + Z 

 of frequency coi and similarly S 



is the peak value K' of the grid voltage 

 Zi 



is the peak value S' of the 



Zl + Z2 I 0)2 



grid voltage of frequency C02. Expression (25) may thus be written : 



I Zp 4 -/?0 I 0)J Zp' + -^0 I 0)2 I Zp + i?o I (0)1-0.2) ' 



which is the well known expression given by Carson.'^ 



For the purpose of getting an idea of the magnitudes involved let 

 us consider a numerical example. A Western Electric No. 101 D 

 vacuum tube may have the following constants when used as a modu- 

 lator: Ro = 9000 ohms; ix = 6; grid-cathode capacitance Ci = 10.5, 

 plate-grid capacitance d = 4.8, and plate-cathode capacitance C3 

 = 8.1 micromicrofarads. The impedances Zp and Zg are assumed to 

 be pure resistances at all frequencies with the values 9000 and 10,000 

 ohms, respectivel3^ The impressed e.m.f. is of the form given by 



' Carson: I. R. E. Proc, June, 1921, page 243. 



