CURVED WAVE GUIDES 9 



In this equation 1\ is the energy stored in circuit 1, F-, the energy stored 

 in circuit 2 and Pn is the energy- transferred from one circuit to the other. 

 One finds 



F.^ :i+'^ = ^ = ilK, 1.1-17 



1.1-18 



Pl2 = -~ = ?I2/2A'2 = ; , - + /21/lAi 1.1-19 



A2 Ai 



Equations 1.1-5 and 1.1-6 contain four ampHtude constants. Two of these, 

 for instance Eu and £26 , can be adjusted to satisfy boundary conditions. 

 The other two are fixed by the equation 



-fi2« A'l _ pa — Pi _ pb — p2 _ EibKi 

 ElaK2 pa - P2 pb - pi Elf,Ki 



The square root of this expression, 



2a /Ki _ Eib /Ki _ 



\a y K,- E,b V Ki~ '^ 



may be called the normalized amplitude ratio. It is a vector quantity 

 denoting the amplitude ratio and phase relation of each oscillation frequency 

 in the two circuits, assuming that they have been normalized to equal 

 resistances by an ideal transformer. The absolute value 



■EL A'l _ ,., _ 1 



7-2 ,- —Ha— ,., 

 iila A 2 *' b 



is the ratio of the energies stored in the two circuits oscillating at frequencies 

 pa and Pb respectively. 



From 1.1-14, 15, 16 and 18 



IVa 



Vl + k' - 1 



Vl + k' + 1 



4„ = Vl + K-- - K~ 



= If 



When the indexes are left off, II' < 1 and | .-1 [ < 1 by definition. One 

 sees that energy, amplitude and phase relations between the coupled 

 circuits at each oscillating frequency are governed by the coupling dis- 

 criminant. This also applies to the damping coefficients and frequencies 



