516 BELL SYSTEM TECHNICAL JOURNAL 



method of circuit design as well. Robertson found that the input circuit 

 structure of the LS53 produces a measurable impairment in its gain-band 

 product, which redesign of both tube and circuit may be able to improve. 

 Comparison of his results with the theory has given a better understand- 

 ing of the limits of high-frequency performance, and has lent some sup- 

 port to the following set of rules of thumb which have been in use for 

 some time: 



1. The input loading arising from the returning electrons is consider- 

 able, the input conductance of these tubes at 4000 Mc being about 

 double the theoretical value of Llewellyn and Peterson. 



2. The input noise of these close-spaced tubes checks well with what 

 one would expect of a low-frequency diode with Maxwellian veloci- 

 ties, whose solution is known. In high-frequency noise calculations, 

 therefore, one can use with some confidence Rack's suggestion that 

 cathode noise can be regarded as an effective velocity fluctuation at 

 the virtual cathode.^'' 



3. Single velocity theory seems to hold well when velocities are much 

 larger than Maxwellian, drift times are not more than a few cycles, 

 electron beams are short compared to their diameter, and no exact 

 cancellations of large effects are predicted. In particular it holds well 

 for the 1553 output space and for calculations of the high-frequency 

 trans-admittance. 



Extensive calculations of signal and noise behavior in planar multigrid 

 tubes have been made by L. C. Peterson, using the single-velocity theory 

 except for an empirical value of input loading, and using Rack's sugges- 

 tion for cathode noise." The results so far checked have agreed well with 

 experiment. 



In short, the optimum design for the tube is still given fairly closely 

 by the figures of merit based on the approximate theory, but the per- 

 formance will fall somewhat short of the predictions of the simple theory; 

 performance can be estimated with the aid of the experimental measure- 

 ments and rules of thumb just described. 



Summary 

 From the foregoing calculations we draw a number of conclusions: 



1. The figures of merit can be validly analyzed into their dependence 

 on more elementary properties like transadmittance, circuit capaci- 

 tance, input loss resistance, and so on. 



' loc. cit. 



'" A. J. Rack "Effects of Space Charge and Transit Time on the Shot Noise in Diodes," 

 B. S. T. J., 17, 592-619 (October 1938). 



" L. C. Peterson "Space Charge and Noise in Microwave Tetrodes," Proc. I. R. E., 35, 

 1202-1274 (November 1947). 



