456 BELL SYSTEM TECHNICAL JOURNAL 



Accuracy 



There are three important sources of error. The first is lack of proper 

 adjustment. The second is that due to the detector attenuator calibration. 

 The third is that due to multiple reflections. 



Experience and care can almost eliminate the first source. The second 

 source may have a magnitude of twice the detector attenuator calibration 

 error. In equations (1) and (17) this is readily apparent. The evaluation 

 of W using equations (16) introduces negligibly more error provided IFs — Wi 

 is made large by proper choice of the magnitude of the reflection coefficient 

 of the termination Z. The possible errors due to multiple reflections be- 

 tween the waveguide impedance discontinuity being measured and an 

 imperfect termination are discussed in Appendix A. If the impedance 

 presented by the arm B of the hybrid junction is not perfect, energ>^ re- 

 flected from the hybrid junction will be partly absorbed in the termination 

 and cause an error in the measurement. If the magnitude of this reflection 

 coefficient is known, the maximum error may be computed. 



If a detector attenuator calibration error of ±0.1 db is assumed to be the 

 only contributing error, it is possible to measure the W due to an impedance 

 mismatch to an accuracy of ±0.2 db provided the W is greater than 26 db. 

 These numbers correspond to measuring a standing wave ratio of any value 

 less than 0.86 db to an accuracy of ±0.02 db or reflection coefficients of any 

 value less than 0.05 to an accuracy of ±2.5%. 



APPENDIX A 



Maximum Probable Error Due to Magnitude of Reflection 



Coefficient Being Measured When Measuring a 



Waveguide Coupling 



The purpose of this appendix is to derive equations so that the maximum 

 probable error due to multiple reflections may be calculated. The assump- 

 tions may not be rigorous but the mathematical treatment appears to 

 represent a reasonable approximation. It is assumed that there is no dissi- 

 pation in waveguide EF, waveguide GH and in coupling FG. 



The electrical relations of the coupling FG and the movable termination 

 Z might be represented as in Fig. 9, where Ka = characteristic impedance 

 of waveguide EF and Kh = characteristic impedance of waveguide GIL 

 The first few multiple reflections from the two discontinuities, coupling 

 FG and termination Z, can be illustrated as in Fig. 10. 



Evaluation of the magnitudes of the reflections can be accomplished as 

 outlined in paragraph 7.13, page 210 in the book "Electromagnetic Waves"* 

 by S. A. Schelkunoff. 



* Published by D. Van Nostrand, Inc., New York City, 1943. 



