WAVEGUIDE HYBRID RINGS EOR MICROWAVES 483 



Evaluating, we find d^^s) = 0, showing D is isolated from S. The other 

 two expansions give 



^5(^,) = (+iZj[2Z' - Z'ZI] 

 and 



d^E,) = (+iZ)[Z'Zo - 2Z'l. Ill— 5.4 



So the difference between the voltages at Ei and £2 is transmitted to D. 

 Hereafter we will operate on a single voltage at 5. Note, incidentally, 

 that if the S arm were not terminated the Zo in column 1, row 1 of f/5(ij) 

 and dhCk.) would be zero, in which case 



df,CE„ = - (+yZ) ilZ") and ^5(^,) = + {^-jZ) (2Z') III— 5.5 



To study frequency shift on current from S^ at ^ we can write III — 5.1 

 as 



.(A) = 



-\-jZ Zo+2jAZ -\-jZ 



-\-jZ 2jAZ +jZ 



+yz 2jAZ 



-^-jZ +jZ 



-\-jZ Zo+2jAZ 



III— 6 



= 2Z2(-Z'jAZ + 2ZoAZ' + 4jAZ') = -IZ'^Z. Ill— 7.1 



Match Condition. The impedance match condition is readily shown to be 

 -s/lZ = Zo as for the three-arm 1 JX ring. 



Construction of Test Samples 



From the drawing of the hybrid circle (Fig. 1), it will be seen that the 

 multiple soldering of guides into the ring can present difficulty in fabrica- 

 tion, especially where numerous branches are required. In addition, early 

 measurements indicated the necessity of accurate dimensions, both linear 

 and angular. As a consequence, the experimental hybrid circles which were 

 used in the measurements reported herein were milled from brass cylinders. 

 Figure 8 shows a 4-branch ring opened so that interior detail can be seen. 

 This form of experimental construction enables dimensions to be held to 

 average values of about half a thousandth of an inch and ten minutes of arc. 

 The mating surfaces are fiat to within this tolerance. However, no currents 

 resulting from the held tend to flow in the direction crossing the gap and no 

 loss ensues from this source. These mechanical tolerances are essential 

 only to a basic experiment of the nature here described; larger tolerances 

 could undoubtedly be specified in practice. 



