1302 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



equation (3) gives hole density in the base layer: 



p.{t,x) = p. + L 2 sinh (wo/L) J^ 



_ f pcO - Pn) - (peQ " Pn)e^''^ ~\ _x/L 



L 2:sinh (wo/L) J 



[— swo/^n 

 Pel — Peie sxlL+ioit 



2 sinh (swo/L) J 



Pel - Peie^^n _« 



(4) 



-[ 



2 sinh {swo/L)j 



-sx/L+iut 

 6 



Since up to this point w has been assumed constant [w = Wo] , equation 

 (4) does not include effects of voltage dependence of base layer thick- 

 ness. To introduce these, a new set of boundary conditions is used: 

 at X = 0, 



.^^ p = Peo -^ Peie'"^ (5a) 



and at x = wq -^ Wi e"^ , . ^ 



p = Pco + Pcie"" (5b) 



in which Wi ^ Wq and is a phasor. 



dw ^j, 

 w, = ^^ F. 



It can be seen that conditions are as before except that the collector 



side of the base layer swings about position Wo at angular frequency co. 



A solution of equation (31) with conditions (5a) and (5b) is given by 



Pi(t,x) = pQ{t,x) + p(t,x) (6J 



in which po{t,x) is given by equation (4) and p{t,x) is the perturbation 

 associated with Wie'''^\ 



If equations (5a) and (5b) are rewritten in terms of p(t,x), they be- 

 come, using first order expansions: 



pM = (7a) 



pit,Wo + Wie*"^) = [(peo - Pn) csch (Wo/L) 



- iPcO - Pn) COth (Wo/L)] ^ 6^"' ^^^^ 



Since p(t,x) is an ac solution of the continuity equation (2), it has 

 the form : 



P(t,x) = £-6-/^+*"* + /?Tg— /L+*.* (g^ 



