FERROMAGNETIC DISTORTION OF A WAVE 353 



respectively, on account of hysteresis and variable permeability, II 

 being the maximum of the applied magnetizing force. The total non- 

 linear reactance is then 



X{oi, H) ^ Xo + AX(co, H) 

 with 



Xq = Cj^Lq, 



the constant part, representing the reactance the coil would have if 

 the permeability remained constant at its initial value. 



The distortion voltages for a two-frequency input may be written 

 in terms of these non-linear impedances. With some simplication 

 this is done in Table II for special cases, using equation (56) and the 

 relations 



0.47riV7 0.47riV/ 



I ' ^ I ' 



TABLE II 



Case la Case 16 



<c<<C 1 « = 1 



k<^\ k = \ 



En 0.960 ^R{p - 2g, Q)J 0.870 ^R{p - 2q, Q)J 



En 0.375 LR{p + 2g, Q)J 0.340 ^R{p -f 2g, Q)J 



E21 1.28 AR{2p-q,Q)I 0.870 ARi2p - q, P)I 



£21 0.500 AR{2p + q, Q)I 0.340 AR{2p + q, P)I 



E30 0.200 ARiSp, P)I 0.068 Ai?(3/>, P)I 



Eo3 — 0.068 AR{3q, Q)J 



Case \c Case 2 



fe » 1 -c « 1 



«»! fe»« 



£12 1.28 AR{p - 2q, P)J 0.212 kX{P - 2q, 2P + 307 



£12 0.500 AR{p -f- 2q, P)J 0.212 kX{P + 2q, IP -f- 307 



£21 0.960 A7?(2^ - 2, P)I 1.06 kAR{2P - q, P - 0.94407 



£21 0.375 A7?(2^ + q, P)I 1.23 KAR{2p + q, P + 2.7307 



£30 — [0.425 kZo(3/>) - 0.200 AT? (3/>,P)]7 



£03 0.200 A7?(3^, 0/ 0.200 AR{2,p, Q)J 



The general formulae of case 1 can be similarly represented, but not 

 as concisely. Besides exhibiting the connection between intermodu- 

 lation products and impedance changes, this table provides a con- 

 venient means for computing voltage components directly from data 

 obtainable by single-frequency bridge measurements. 



