By W. J. Kleen

ISBN-10: 0123955580

ISBN-13: 9780123955586

ISBN-10: 0323153518

ISBN-13: 9780323153515

Electronics of Microwave Tubes

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27) 1 and 2. F I G . 5. Plane-parallel two-electrode system (the diode of the LlewellynPeterson equations). The t o t a l current density ? tot = i tot e x 3 P(/^). ( · •TOT • e - 2 8 ) the convection current density ϊ^, and the velocity ϋ2 a t the plane of electrode 2 will now be calculated. Under small signal conditions t t o >t ic> v} and Ϋ can be related b y linear equations. 30c) 32 3. 29). T h e second form [ 3 0 ] , E q s . 30), is often easier to apply, however. I t is obtained from E q s .

E x p e r i e n c e suggests t h a t the use of E q . ( 3 . 1 1 ) presents some difficulty. often Therefore, we will calculate as an example the induced current in a static homogeneous field Ε = — V/d, when the input convection current is Icl = Icl exp (jwtj. Since V = 0 , we have I[n<^ — -^tof which can be measured in the external circuit between the electrodes. We can also write ν — v1— and hence by Eq. 11), t Jind = JΚ t-T = — (elm)E(t — tj} exp ( / ω ^ ) dtx D ¥fe tt = t e x p «-i f-^r£ e x p « +(^ e x p «}] · (3 12) 25 3 .

3 . 2 9 ) are now functions of ϋνϋ2,ζ,τά, a n d Θά only. T h e y are given in T a b l e 3 . 1 * where, for generality, Θ is written instead of Θά. Here Θ = Θά = ωτά is the s t a t i c transit angle between electrodes 1 and 2 in F i g . 3 . 5 when the potential distribution is modified b y the space charge of the steady current; Eq. 15) or F i g . 2 . 3 . T h e functions can be determined fd Φ(/<9) used in T a b l e from 3 . 2 differ somewhat from those published elsewhere [15,30], where a different convention is used for the direction of positive current.

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Electronics of Microwave Tubes by W. J. Kleen


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