MEASUREMENT OF IMPEDANCE MISMATCHES 459 



In order to evaluate vector 0-3 in Fig. 11 (the vector difference of vectors 

 0-2 and 2-3) one calculates their difference T. 



T = 32.92 - 4.90 = 28.02 db (39) 



For T = 28.02 db, F^ = 0.36 db (40) 



therefore TFo-3 = 4.90 dz 0.36 = 5.26 db = TF4 (41) 



In order to evaluate vector 0-2 in Fig. 12 (the vector difference between 

 vectors 0-1 and 1-2), one uses T from equation (36). 



For T = 1.92 db, Fo = 14.10 db (42) 



therefore I['o-2 = 10.00 + 14.10 = 24.10 db (43) 



In order to evaluate vector 0-3 in Fig. 12 (the vector difference between 

 vectors 0-2 and 2-3), one calculates their difference T. 



T = 32.92 - 24.10 = 8.82 db (44) 



For T = 8.82 db, F. = 3.93 db (45) 



therefore TF0-3 = 24.10 + 3.93 = 2S.03db = IF3 (46) 



Using equation (16) 



Ws-Wi= 22.77 db, r = 1.24 db, Fi = 5.40 and therefore W = 9.66 db. 



Since we started by assuming Wr = 10 db, the error amounts to 0.34 db. 



References 



1. Page 120, "Transmission Networks and Wave Filters," T. E. Shea. Published by D. 



Van Nostrand, Inc., New York City, 1929. 



2. "Hyper-frequency Waveguides — General Considerations and Experimental Results," 



G. C. Southworth, Bell System Technical Journal, April, 1936. 



3. "Directional Couplers." W. W. Mumford, Proceedings of the Institute of Radio Engineers, 



Februar>' 1947. 



4. "Hybrid Circuits for Microwaves," W. A. Tyrrell. A paper accepted for publication 



in the Proceedings of the Institute of Radio Engineers. 



5. "Note on a Reflection -Coefficient RIeter," Nathaniel I. Korman, Proceedings of the 



InstiliUe of Radio Engineers and Waves and Electrons, September 1946. 



6. "Probe Error in Standing-Wave Detectors," William Altar, F. B. Marshall and L. P. 



Hunter, Proceedings of the Institute of Radio Engineers and Waves afid Electrons, 

 January 1946. 



7. Pages 20 to 24, "Practical Analysis of UHF Transmission Lines — Resonant 



Sections — Resonant Cavities — Waveguides," J. R. Meagher and H. J. Markley 

 Pamphlet published by R. C. A. Service Company, Inc., in 1943. 



8. "Microwave Measurements and Test Equipments," F. J. Gaffney, Proceedings of the 



Institute of Radio Engineers and Waves and Electrons, October 1946. 



