130 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



Sf = Stiffness load of coupler and front volume in dynes per cm. 

 / = current in amperes 

 X = displacement of diaphragm in cms. 

 The solution of these equations for the displacement is 



tE 



^ " (i?o + i? + jo^L) {Sr + Sf) + icor' . 10"' ^^^ 



For an adiabatic change, the pressure p in the chambers in front of the 

 diaphragm due to a small displacement x is 



where y = ratio of specific heats of air = 1 .405 



Po = atmospheric pressure = 1.013 x 10^ dynes/cm- 

 A = effective area of diaphragm in cm^ 

 Vg == receiver front volume beneath the grid holes, in cm*"^ 

 Ft, = coupler volume = 6 cm^ 



Combining equations (3) and (4) we have 



yPpA tE 



^ Vg+Vc' (Ro + R){Sr + Sf) + Mr' 10"' + L{Sr + Sf)] 



(5) 



Substituting equation (5) in equation (1) and expressing 77 as a power ratio 

 we obtain 



'^ " F, + Vc'""'' {Ro + R)\Sr + Sfy + <.VlO-' + LiSr + Sf)f' ^^^ 



Let K = ^^^^^_^ ^^^ or r' = KL{Sr + ^/)10^ 



Then 



_ 47P0 .10^ Vc . 



RoKLiSr + Sf) 



(Ro + R)'{Sr + Sf)' + c^-^lKLiSr + Sf) + L(Sr + Sf)Y 

 and factoring 



^ 47P0 .10' Vc Sf K 



'^ coVc ' Vg + Vc ' Sr + Sf ' 1 + K 



R^L{1 + K) 



(7) 



(i?o -I- Rf + cu2L^(l + K)' 



(8) 



