448 BELL SYSTEM TECHNICAL JOURNAL 



the oscillator splits equally in paths AD and AB. The half in AD is com- 

 pletely absorbed in the perfect termination Z' . The half in AB is partly 

 reflected from the impedance mismatch due to the waveguide coupling BE 

 and the remainder is absorbed in the perfect termination Z. Again due to 

 the properties of the perfect hybrid junction, the impedance presented by 

 the arm B when arms A and C are perfectly terminated is also perfect, 

 and the reflected energy from waveguide coupling BE splits equally in 

 paths BA and BC. The part in BA is absorbed by the oscillator. The 

 part in BC representing the voltage reflected from the coupling BE is meas- 

 ured by the calibrated detector and indicator. The magnitude of the inci- 

 dent voltage may be measured when the waveguide piece EF is replaced 

 by the fixed shorting plate. 



It is convenient to measure voltages applied to the calibrated detector 

 and indicator in terms of attenuator settmgs in db for a reference output 

 indicator reading. Then the ratio expressed in db between incident and 

 reflected voltages (hereafter called W) is 



W2 (due to the coupling BE) = Ai - A2 (1) 



where Ai is attenuator setting for incident voltage and A2 is attenuator 

 setting for reflected voltage. 



Both reflection coefficient and standing wave ratio may be expressed in 

 terms of 11'. For if 



X = voltage due to incident power (2) 



and Y = voltage due to reflected power, (3) 



Y 

 then reflection coefficient = — (4) 



and voltage standing wave ratio = .—^. p— - (5) 



Since Widb) = 20 logio .^l (6) 



W 

 1 + antilog — 



then in db, standing wave ratio = 20 logio (7) 



W 

 -1 + antilog — 



Standing wave ratio plotted versus W is shown in Fig. 2. Reflection coeffi- 

 cient versus W can be found in any "voltage ratios to db" table. 



II. Termination Z Imperfect, Termination Z' Perfect, Only One 



Coupling on Hybrid Junction 

 In Fig. 1, if the termination Z is not perfect, there will be two reflected 

 voltages from branch B. The vector diagram of the voltage at C might be 



