SHOT NOISE IN DIODES 611 



to solve. The difificulty in these equations arises from the fact that 

 tangential as well as radial initial velocities must be considered in 

 obtaining the total anode current. Since it was shown for the planar 

 diode that the effective temperature of the plate resistance is 0.644 

 times the cathode temperature for practically all operating conditions, 

 all that is really desired in the cylindrical diode solution is the limiting 

 value of the effective tube temperature. This may be found rather 

 easily from a comparison of the cylindrical diode with the planar tube 

 in the following manner. 



For a very large space charge, and a high plate potential the radius of 

 an equipotential surface near the potential minimum will be very 

 nearly equal to that of the cathode. Hence, for these operating 

 conditions, the planar diode equations may be applied to this region 

 of the cylindrical diode. In the planar tube, it was shown that for 

 770' > 3, 770 had to be of the order of unity to obtain the limiting value 

 of 0.644 for X. If the space charge and plate potential are sufficiently 

 large in the cylindrical diode, the radius of the equipotential surface 

 for which 170 is greater than unity will practically be equal to that of 

 the cathode. The cylindrical diode may then be divided into two 

 parts, a planar diode between the cathode and the equipotential 

 surface for which rjo > 1, and a cylindrical diode formed from the 

 remainder of the tube. In any diode, the only source of noise energy is 

 the cathode from which the noise power is transferred to the anode and 

 external circuit through the mechanism of the initial electronic 

 velocities. Furthermore, the same total noise power must be trans- 

 ferred across any equipotential surface between the cathode and anode. 

 In the planar portion of the cylindrical diode as described above, the 

 total noise power crossing any equipotential surface was shown to be 

 2.576kTdf. This same noise power must be transferred across any 

 other equipotential surface in the cylindrical diode. Hence, the 

 effective plate resistance temperature for the cylindrical electrode tube 

 must also be 0.644 times its cathode temperature. From this line of 

 reasoning, it may be shown that the limiting value of the effective 

 temperature for any shape diode is the same as that for the planar tube 

 with the same cathode temperature. 



From the experimental data given in his paper, Pearson definitely 

 recognized that the limiting value of the diode plate resistance temper- 

 ature should be between 0.59 and 0.65 of that of the cathode.^ The 

 writer understands that North and Thompson of the R.C.A. in an 

 unpublished paper have obtained the same general result for the effect 

 of space charge upon shot noise in diodes. 



