FILTER-TYPE CIRCUITS 



215 



cient M. This enables us to make calculations in terms of fields and currents 



at the electron stream. 



The gap factor can be used in another way. A voltage appears across a 



gap, and the electron stream induces a current at the gap. At the electron 

 1 stream the power Pi , produced in a distance Z by a convection current 



i with the same ^-variation as the field component considered, acting on the 

 ■field componciit is 



Pi = -Ei*L 



= -j-(MV)i* 



(4.74) 



Fig. 4.32 — A system of two opposed sets of slots. 



At the circuit we observe some impressed current / flowing against the 

 voltage V to produce a power 



Po = vr 



(4.75) 



By the conservation of energy, these two powers must be the same, and we 

 deduce that 



/* = Mi* 

 or, since we take M as a real number 



I = Mi 



(4.76) 



(4.77) 



Thus, we have our choice of making calculations in terms of the beam 

 current and a field component or effective field, or in terms of circuit voltage 

 and an effective current, and in either case we make use of the modulation 

 coefficient M. 



Our gain parameter C^ will be 



a = (F/L)W2/o/8/32Fo 



