1306 THE BELL SYSTEM TECHNICAL JOUENAL, SEPTEMBER 1957 



To fiiid the optimum bend geometry for a given dielectric coated guide 

 and a specified bending angle we calculate r from (38). If r > 1 the opti- 

 mum geometry is 



I = 2 



with X from Fig. 3. If r < 1, 



and 



Zi = 



and 



A numerical example, the 90° bend of a |-inch I. D. copper pipe, is 

 shown in Fig. 4. The total bend loss in the optimally designed bend de- 

 creases steadily mth increasing thickness of the dielectric coat. This 

 indicates that there is also an optimum coat thickness, which minimizes 

 the total loss of the normal mode bend of optimum total length and taper 

 length. Unfortunately, however, several approximations made in calcu- 

 lating phase constants and coupling coefficients in the dielectric-coated 



0.20 



0.18 



0.02 



10 20 30 40 50 60 70 80 



FREQUENCY IN KILOMEGACYCLES PER SECOND 



100 



Fig. 5 — 90° normal mode bend of |-inch I.D. copper pipe with a dielectric coat 

 €.0075 inch thick (e' = 2.5, e" = 2.5 X 10~^), designed for optimum performance 

 at X = 5.4 mm (55.5 kmc). 



