674 BELL SYSTEM TECHNICAL JOURNAL 



If we use this as the surface resistivity in (i5) we obtain 



G = 1.99 X 10"' (fj \/N/X/D*\'d\ (i8) 



It is a somewhat remarkable fact that if we work out the loss for a pair 

 of grids with surface resistivity R in one direction and infinite resistivity 

 in the other direction (parallel wire grids) we get just twice the conductance 

 given by (i5). Thus, it appears to be roughly true that if we have a given 

 parallel wire grid, adding wires between the original wires and adding wires 

 perpendicular to the original wires should have about the same effect in 

 reducing circuit loss. 



APPENDIX X 



Starting of Pulsed Reflex Oscillator 



If a reflex oscillator is turned on gradually, the voltage from which the 

 oscillations build up is certainly that due to shot noise in the electron stream. 

 However, if the current is turned on as a pulse of short time of rise, it might 

 be that the microwave voltage produced by the high frequency components 

 of the pulse would be larger than the voltage produced by shot noise, and 

 hence that oscillations would build up from the transient produced by the 

 pulse and not from shot noise. This would be important because presum- 

 ably the voltages produced by the pulse are always the same and related in 

 the same manner to the time of application of the pulse; thus, in buildup 

 from the transient of the pulse there would be no jitter. 



In an effort to decide from which voltage the oscillations build up, we 

 will consider Johnson noise and shot noise voltages. 



Associated with a mode of oscillation of the resonator there is a mean 

 stored energy kT. If L and C are the effective inductance and capacitance 

 of the mode and P and V^ are the mean square current and voltage 



kT = Yl/I + 'v^C/2. ' (jl) 



On the average, half of the energy is in the capacitance and half in the in- 

 ductance; thus 



7^= kT/C 



(J2). 

 = kTuo/M. 



Here M is the characteristic admittance of the mode and con is the resonant 

 radian frequency. 



As an equivalent circuit for the mode we may use conductance (/ in shunt 

 with an inductance L and a capacitance C. The impressed Johnson noise 



