172 BELL SYSTEM TECHNICAL JOURNAL 



Here Tc is cathode temperature. We see u and u^ are 



Jo 



u = 



r 



U€ 





■(mu^l2kT 



[ 3 -imu^ 

 I U € 



-^ Jq 



l2kTc) 



'^^ du 



I 



U€ 



■(mu^likTc) 



du 



kTc 

 m 



(61) 



(62) 



Accordingly 



.2 1 /A \ f^J- c 



. = i(4 - x) ^ 



Combining (63) with (59) we obtain 



B 



{dxor = ^ (4 



kT. 



m 



(63) 



(64) 



Combining (62) with (53) and remembering that Iq = Ne we find the mean 

 square open circuit noise voltage to be 



!;2 = 3(4 - tt) kTcRB 

 = (.644) UTcRB. 



(65) 



This is the chief contribution to noise in a space charge limited diode. 



Usually R is substantially equal to the plate resistance of the diode (it 

 does not include effects on the cathode side of the potential minimum). 

 Hereafter R will be treated as the total plate resistance of the diode. 



VI. Noise in Triodes and Pentodes 



Consider the triode shown in Fig. 6. Here we have a cathode, a grid, 

 and a plate. The input admittance of the tube is represented in the di- 

 agram by the grid-cathode capacitance Ci and the grid-plate capacitance d . 

 The resistance Rn is a fictitious noise resistance which will be evaluated 

 later. It is assumed to act between the input admittance of the tube and 

 the controlling action of the grid; no current can flow in Rn because the grid 

 as indicated in the diagram is presumed to present an open circuit. 



We will regard the cathode-grid region of the triode as an ''equivalent 

 diode '* The anode voltage of the diode is taken as 



V, = iV, + K,/m). 



(66) 



