Identification and Sign-Ambiguity-Free Calculations of Reciprocal Characteristic Parameters in Microwave Applications

Various microwave circuit characterizations and measurements, such as extracting forward and backward propagation factors in thru-reflect-line calibration and choosing the correct reflection coefficient in the transmission/reflection method for material characterization, involve the calculation of complex reciprocal characteristic parameters. The calculation procedure is generally obstructed by assignment between the real physical parameters and the calculated values and sign choice of square roots. This letter shows that the complex reciprocal characteristic parameters can be explicitly differentiated by the relative magnitudes of their moduli, and the problems of parameter identification and sign choice can be eliminated by proper rearrangement of the operands in the square root function and the aid of complex hyperbolic functions. Therefore, the calculation formula for each of the reciprocal roots is fixed without undetermined signs and conforms to the passive or active conventions.