CIRCULAR ELECTRIC WAVE IN SERPENTINE BENDS 



1285 



In case 1 the wave amplitude Ein is only affected by a slight change of 

 the propagation constant. The small additional term in the expression 

 for Ein can usually be neglected. The power in the wave E^n is small 

 compared to the A\„ power; Tu is usually of the same order of magnitude 

 as 2^21 . 



In case 2, however, a complete power transfer between Ein and E2n 

 occurs cyclically if the loss is sufficiently low. Consequently, condition 

 (18) has to be carefully avoided. Rather, condition (17) must always be 

 satisfied. 



IV. SERPENTINE BENDS FORMED BY ELASTIC CURVES 



A section of the waveguide line between two supports deforms like a 

 beam fixed at both ends. Under its own weight, w per unit length, such 

 a beam will bend and form an elastic curve. Fig. 1, whose deflection 

 from a straight line is given by: 



,2 



y = 



wl X 



24:EI P 



1 



X 



(19) 



in which E = modulus of elasticity of the beam, and / = moment of 

 inertia of the beam. Since we are concerned with small deflections y 

 only, we have x = z and 6 = dy/dx. Hence, 



* = <'(i-3p+4'! 



(20) 



in which d = wl /12EI. Introducing the elastic curve (20) into the trans- 

 mission matrix (10) and (14) and performing the integrations with sin 

 Cod = Cod we get for the elements of the transmission matrix : 



7^11 = exp 



T.,. = exp 



yj + A7/ 



+ ? Ay'f - 



— y-J — Ayl 



2 ,2-1 

 Cod 



l05 



105 



2 ,2 

 Cod 



105 



/i 



+ 



Co d 



9 



3A7'/' + A7V' 



4A7«/' 

 A77' - (3 - 3A7/ + A7'^')V^"' 

 Cod 



1 



1 + 



4A7«/« 



4,4 



y - 'SAy-l- + Ayl 



(21) 



A7 1 + ~ Ay'r - (3 + 3A7/ + A7-/")-e 



2,2\2 -2A7/ 



T12 = T,i = ./ . 



Cod 

 2AyH' 



105 



[(3 - 3A7/ + A7'/')e 



-72' 



- (3 + 3A7/ + A7''r)e"^^']. 



