Analysis and calibration theory of the general 6-port reflectometor employing four amplitude detectors

An analysis is carried out of the general 6-port reflectometer, employing four amplitude detectors, for the measurement of complex reflection coefficients without the direct measurement of phase. The analysis in based on the matrix-renormalisation technique employing voltage-wave S-parameters with complex normalisation. The conclusion is drawn that seven complex standards are needed to calibrate a truly arbitrary 6-port reflectometer. This leads to two sets of seven simultaneous calibration equations, with eleven unknowns, for the real and imaginary parts. The theory is tested using a theoretical model, first, with ideal detector responses and, secondly, with a number of imperfections introduced to simulate unwanted residual parameters. The analysis shows that when certain combinations of conventional coaxial standards are used, the 7 × 7 matrices of the calibration equations can be singular. The investigation is extended to establishing the nature of the standards needed to eliminate singularity and to obtain explicit solutions of the two sets of equations which give the eleven real constants needed to completely calibrate the reflectometer. Three of these constants are the same in the common denominator of the two equations for the real and imaginary parts when the matrices are nonsingular. A brief analysis of the 5-port reflectometer is also given, which confirms the current view that this technique shows little promise of future application.