NOISE FIGURE 



435 



Then we find that 



L = [(.V2.V3)- + (y.y,)- + (.V2J3)- + (x,y,y]P^ 

 + 2[x3(v^ + A-;) + x.(xl + yl)]P 

 + (-vo + .V3)- + (y2 + ys)- 

 This has a minimum value for P — Pm 



— [x^ixl + yl) + Xiixl + 3'3)] 



P,„ = 



(10.35) 



(10.36) 



(xiXsY + (yoysY + (xzysY + (xs^'o)^ 

 We note that, as we are not deahng with the increasing wave, Xo and .V3 



1.0 

 0.8 

 0.6 



0.1 



0.08 

 0.06 



Fig. 10.3 — According to the theory presented, the overall noise figure of a tube with a 

 lossless helix and no space charge is proportional to L. Here we have a minimum value 

 of L,a , minimized with respect to P, which is dependent on gun transit angle, and also 

 the corresponding value of F, Fm . According to this curve, the optimum noise figure 

 should be lowest for low electron velocities (low values of b). It may, however, be impos- 

 sible to make F equal to P^ . 



must be either negative or zero, and hence Pm is always positive. For no 

 space-charge and no attenuation, Xs is zero for all values of b and 



P _ -^^ 



-£ m — 2 I 2 



^2 + X2 



From (10.36) and (10.35), the minimum value of L, Lm , is 



Lm = {x2 + XiY + iy-i + jif 



_ [x-iiyl + xo) + X2(x3 + yl)Y 



{xiXz)- + {y-iy^y + {x'iy-iY + {x^yiY 



When X3 - 0, as in (10.37) 



2 2 

 Lm = X2 + ^2 + ^yty-i + 



2 , 2 



X2 + yt 



(10.37) 



(10.38) 



(10.39) 



