WAVEGUIDE HYBRID RINGS FOR MICROWAVES 477 



II. Equivalent Line Sections 



The first method following evaluates the line sections between outlets. 

 The second views each line section as made up of the necessary number of 

 quarter-wave sections, each represented by its equivalent T. 



Method 1 — The equivalent T for a recurrent structure'^ of constants Z 

 (characteristic impedance) and P { = A -f jB) propagation constant per 

 unit length is as shown in Fig. 2b. 



There result the equivalences sketched in Fig. 2c. 



Once the circuit is diagrammed using the above equivalences, it can be 

 reduced to simpler form by successive combinations of Ts, by well known 

 formulae. 



Method 2 — Determinants. We now consider the line to be made up of the 

 appropriate number of quarter-wave sections, with series taps. Thus we 

 will have Fig. 3. 



The shunt impedances are identical; call each F. The series impedances 

 are made identical by first assuming a tap at each quarter-wave junction; 



Fig. 3— Re-entrant line as succession of equivalent (quarter wave) T networks and 

 series taps. 



call each series leg 5. Then the (skew symmetrical) circuit determinant 

 for the case where N = 10, (or a 2| wavelength ring) is 



Z>i 



Now, for the case of an exact integral number of quarter wavelengths 



around the ring, all W-n = -j^ and all 5i_n = /^o + 2jZ, so all 5 + 2F = 



Zo. 



"K. S. Johnson, "Transmission Circuits for Telephone Communication" Book 

 published by D Van Nostrand Co., New York, N. Y. 



