NORMAL MODE BENDS FOR CIRCULAR ELECTRIC WAVES 1299 



The losses in the dielectric coat increase the attenuation constants by: 



// 



TM„m - — = — h, 



I3nm e ^ 



TE„OT - — = - — ^ 1 ~W\ 2^ ^' ^^^^ 



with n5>^0 pnm Pnm ^ € i-i i'nm ) 



2 // 



i -b^Orn -^ = -^- :j ^ . 



pOm O i — J-Om 



For the circular electric waves the dielectric coat increases the wall cur- 

 rent attenuation by 



TEom — = (e' - 1) H 5^ (18) 



OCOm VDm" 



The various symbols in (16), (17) and (18) are: 



^nm = plain guide phase constants of TM„m and TE„TO respectively; 

 Vnm = wth root of Jn(a:) = forTM„^ , andmthrootof /„'(a;) = 

 for TE„m waves respectively; 



Vnm = — = ^^ cutoff factor in plain waveguide of radius a; 



8 = - relative thickness of dielectric coat; 

 a 



e = e — je" relative dielectric permittivity of dielectric coat; 



aom = attenuation constant of TEom in the plain waveguide. 



The coupling coefficient between the straight guide modes in a curved 

 waveguide is c = c'/R in which : 



TEoi ^ TMii c = 0.18454 I3a, 



, 0.09319(^a)2 - 0.84204 , 



TEoi ^ TEn c = /^ \ + 0.09319 V(3o,a^ua, 



TF ^ TT^ ' 0-15575(/3a)^ - 3.35688 ^-^ (19) 



TEoi ^ TEi2 c = / ^ ^ + 0.1557O V^ovajSna, 



Vi8oiai8i2a 



, 0.01376(/3a)2 - 0.60216 , 



TEoi ^ TEi3 c = y ' ^ + 0.01376 Vl3oial3,za, 



where jS = free-space phase constant. 



We consider the bend configuration of Fig. 1, with the curvature being 

 a trapezoidal function of length. The maximum power loss due to con- 

 version to one of the unwanted modes in the first transition is, by (13), 



I ^2(2:1) 



A 2 



,2 _ 4 Co 



max 



(A/32i)2A/32" 



I 



