Simplified calibration equations for the unidirectional and bidirectional computer-corrected network analyser

Circuit analysis of network analysers has previously been carried out employing flowgraphs based on Mason´s rule, and error networks at each measurement port to simulate imperfections of the measurement system. None of these techniques is necessary in circuit analysis by matrix renormalisation. The renormalisation transforms give directly the calibration and measurement equations in terms of the actual S parameters and port mismatches of the system hardware instead of symbols representing flowgraph parameters. An earlier analysis by this method, employing the 3-port transforms, is extended to a reanalysis using the newly developed 4-port transforms which leads to a very much simpler and explicit solution, both for the unidirectional and bidirectional network analyser. Because all the calibration constants are expressed in terms of the system parameters, the matrix renormalisation technique gives not only a much clearer insight into how system imperfections affect overall accuracy, but also an explicit solution without the need for a matched load as one of the standards. The technique adopted should also be of academic interest to those concerned with network analysis because an explicit solution is obtained, in a rigorous manner, of four nonlinear equations involving a minimum of algebraic manipulation.