DESIGN FACTORS OF THE 1553 TRIODE 507 



3. The dimensions of the grid are iniinitesimal compared to the elec- 

 trode spacings. 



4. The electrode dimensions are small compared to the wavelength. 



It can be shown that the intrinsic gain-band product may be expressed 

 in the following two ways: 



Mi = K 

 = K' 



LdiFsidi), 



(5) 

 [diF^\dWv;i 



} where K, K' are parameters which are functions only of frequency. 

 i 



Xi is the cathode-grid spacing in cm 



di is cathode-grid transit angle and di — { ^ ) 



^ \j / 



' j = cathode current density in amp/cm''^ 



6300 X2 

 do = grid-anode transit angle and 6^ — - — j—f 



and Fi (di), 7^2(^2) and F^idi) are complicated functions of their respective 

 transit angles. 



Consider frequency to be given as part of the specifications on the tube. 



Variation with Current Density, j 



In the first formulation the current densitv is involved only in the 



second factor. This factor is a function only oi di — i " r ) and is shown 



plotted in Fig. 6. If Xi and X are considered to be held fixed for the moment 

 the first maximum at ^1 ^ requires j to be as large as possible consis- 

 tent with emission limitations and life. For the 1553 the cathode current 

 density is set at 180 ma/cm-. 



The other maxima at larger values of di (and smaller values of j), 

 where Fz{di) goes through zero, correspond to transit angles where Gn — » 

 in the single-valued velocity theory. These maxima cannot be taken at 

 face value, however, to indicate maxima in the unequal-() gain-band 

 product since they violate the assumption that Qi << Q2 for which the 

 formula was developed. To make a study of gain-band variation in this 

 region therefore entails a study of gain-band product as a function of 

 bandwidth, as was pointed out previously in connection with comparison 

 of the equal-() and unequal-(3 cases. Such maxima are of interest pri- 



