GENERAL CIRCUIT CONSIDERATIONS 



231 



(or curve B. As {E^/^'^Py^ varies as {v/vgY^^, we must adjust the coupling 

 between resonators so as to make 



Vg = V(3.2)3 _ 031 z; 



in order to make {Er/^-Py^ the same for the resonators as for the helix. 

 I'Yom (5.12) we see that this means that a change in frequency by a frac- 

 tion .002 must change v by a fraction .06. Ordinarily, a fractional variation 

 of V of ±.03 would cause a very serious falling off in gain. At 3,000 mc the 

 total frequency variation of .002 times in v would be 6 mc. This is then a 

 measure of the bandwidth of a series of resonators used in place of a helix 

 lor which ^a = 3 and adjusted to give the same gain. 



Fig. 5.9 — The factor/ by which (£?//3^P)^'^ for a series of resonators such as those of 

 I ig. 5.4 is reduced because of wall thickness t, in relation to gap spacing L. 



5.4 Physical Limitations 



In Section 3.3b the resonators were assumed to be very thin and to have 

 walls of zero thickness. Of course the walls must have finite thickness, and 

 it is impractical to make the resonators extremely thin. The wall thickness 

 and the finite transit time across the resonators both reduce E'l^P. 



?.4a Effect of Wall Thickness 



Consider the resonators of Fig. 5.4. Let L be the spacing between resona- 

 tors (1/Z resonators per unit length), and / be the wall thickness. Thus, the 

 gap length is (L — /). Suppose we keep L and the voltage across each 



