ULTRA-HIGH-FREQUENCY VACUUM TUBES 653 



The transit angle dc = o^Tc may be written in terms either of the 

 voltage Va or the current /o, thus 



9500x, -126/ XrV" 



XV Va ^ 



( Y ) radians, (64)' 



where X is the free-space wave-length in centimeters of an alternating 

 current of angular frequency co. 



The slope of the static characteristic of a diode coinciding with the 

 cathode and the plane A may be expressed 



^Va 



2 Va 285,00Ox;'' - 3780;c,4/» 



= r^= - - -— = — = — ■ = — - — , (65) 



3 /o VF.4 ^0^' 



where Yc is the low-frequency resistance in ohms of a square centimeter 

 of area. 



From (64) and (65) it can be seen that 



r^ = 3OXa:<.0,. (66) 



A further expression that occurs frequently in following equations is: 



^ = 12r,. (67) 



Later we shall be able to show how the low-frequency plate resist- 

 ance of the triode is related to r^ and the amplification factor, as well 

 as how the inter-electrode capacitances of the " cold " tube are in- 

 volved in these quantities. A simple approximation for the transit 

 time ratio h will also be derived. 



First-Order Relations 

 In the picture shown by Fig. 1 an alternating current is assumed 

 to flow from the cathode to the plane A. This current /<; is related 

 to the quantity / in the general equations (41) or (41a) by the ex- 

 pression Jc — elc/kme, and the current includes both conduction and 

 displacement components. Complete space charge at the cathode 

 allows initial velocities and accelerations to be placed equal to zero, 

 so that the first order potential difference between cathode and plane 

 A is given by (41a) as follows: 



n=0 K'l' -\- ^) ■ 



In a similar way, the potential between plane B and the plate can 

 be written when the initial first-order acceleration at B has been found, 



