NOISE FIGURE 



429 



10.2 The Diode Equations 



Llewellyn and Peterson have published a set of equations governing the 

 behavior of parallel plane diodes with a single-valued electron velocity. 

 They sum up the behavior of such a diode in terms of nine coefficients A *-/*, 

 in the following equations 



V^- Va = A* I + B* qa + C*r„ (10.6) 



qb= D* I + E* qa + /''*Z'„ (10.7) 



V, = G* I + H* qa+ I*v., (10.8) 



VOLTAGE DIFFEReNCE_ 

 (Vb-Va) 



CURRENT DENSITY 



lo + I 



INPUT CONVECTION 

 CURRENT DENSITY 



l^D + qa 



INPUT VELOCITY 

 LLa+Va 



OUTPUT CONVECTION 

 CURRENT DENSITY 



ID + Qb 



OUTPUT VELOCITY 

 Llb+Vb 



a b 



Fig. 10.1 — Parallel electron flow between two planes a and b normal to the flow, show- 

 ing the currents, velocities and voltages. 



These equations and the values of the various coefficients in terms of cur- 

 rent, electron velocity and transit angle are given in Appendix V. The diode 

 structure to which they apply is indicated in Fig. 10.1. Electrons enter nor- 

 mal to the left plane and pass out at the right plane. The various quantities 

 involved are transit angle between the two planes and: 



It) d-c current density to left 



/ a-c current density to left 



qa a-c convection current density to left at input plane a 



qb a-c convection current density to left at output plane b 



Ua d-c velocity to right at plane a 



Ub d-c velocity to right at plane b 



I'a a-c velocity to right at plane a 



Vb a-c velocity to right at plane b 



Vb-Va a-c potential difference between plane b and {)lane a 



' F. B. Llewellyn and L. C. Peterson, "Vacuum Tube Networks," Proc. I.R.E., Vol. 

 32, pp. 144-166, March, 1944. 



