COUl'LKD WAVE TIIEOKY AND WAVEGUIDE APPLICATIONS ()()9 



(O 10 



^1 1 0.454 LI I* 



I 0.454 LI 

 0.273 L—>| I*— -*| 



0.273 L 



Fig. 7 — Discrimination versus Q/-K for two uniform couplings superposed. 



the discrimination is greater than 38 db for ^/tt between 1.95 and 3.0, 

 and is greater than 50 db for ^/tt larger than 3. Below QJ-k = 1.95 the 

 discrimination is similar to that shown in Fig. 6. 



Linear superposition of two uniform coupling distributions yields a 

 structure which is easy to fabricate and, in cases where the requirements 

 are not too complex, may provide satisfactory discrimination. The third 

 line of Fig. 4 gives the general relation, and Fig. 7 shows the discrimina- 

 tion plot for a case of interest. Discriminations on the order of 30 db are 

 available in a broad region between d/ir equal to 1.3 to 2, an attractive 

 abscissa value compared to the d/ir = 8 required for simple uniform 

 coupling. 



Linear superposition of a linear taper and uniform coupling also yields 

 a structure which is easy to fabricate, and the theoretical discrimination 

 plot for an interesting set of conditions is shown in Fig. 8. High discrim- 

 inations are provided over greater ranges of 6 than for the case of two 

 uniform coupling functions superposed. 



The general relations involved in the superposition of coupling func- 

 tions may be summarized as follows: Let c/)i(.r), 4>2{x) • • -ipnix) be kno^^'n 

 coupling functions and let 



(f)r = <^i + </>2 + 



(7) 



Let the maximum length of the coupling interval be L. Then, designating 

 the transforms of 01 , 02- • •</>„ by Fi and Fi- • -Fn respectively, Avhere 



.L/2 



''-L 



LI2 



(t>n(x). 



.i(2fl/L)i-' 



dx, 



(8) 



