P 1 -P 3 are the power ratios, while A, C, and E are three real calibration constants, and B, D and F are three complex calibration constants, so there are nine unknowns. The purpose of the calibration is to calculate these unknowns (calibration constants). By using three positions of a sliding short circuit with a matched load (calibration procedure [4,11]), the above unknowns are obtained. When an unknown impedance is connected to the DUT port, the power reading at the four detector ports will represent three circles in a complex ⌫-plane. The intersection point of these three circles will give the reflection coefficient magnitude and phase (see Fig. 2). In fact, the intersection of the three circles in one point is theoretical, because real systems are not stable, so the related geometrical configurations never have a single intersection points. By considering the intersection region as a triangle, we have different solutions such as: the intersection point of the medians of the triangle, the intersection point of the perpendicular bisectors of the triangle sides, the intersection points of the bisectors of the triangle interior angles, the intersection point of the three altitudes of the triangle, and so on.
MEASUREMENT AND RESULTSThe above-realized six-port reflectometer was first calibrated in order to calculate the calibration constants. Then it was used to measure the reflection coefficient of different unknown impedances (especially different positions of sliding SCs) and good agreement with the measurements of the vector network analyzer (Agilent 8719ES), with error not exceeding 2.5% in magnitude and Ϯ3°in phase in the operating range 2.67-3.25 GHz, was obtained. Table 1 illustrates some measurements at the 3-GHz center frequency. A shift of 40 MHz in the center frequency was found, due to the mismatch of the intersection lines that connect the ring couplers to each other and some tolerance in fabrication.In fact, the overall dimensions of the realized six-port reflectometer is around 10 ϫ 10 cm, which is very large. To reduce the size, we can use modified ring couplers [12], which are only 15% of the conventional ring coupler's size, and replace the intersection between couplers by its corresponding T or ⌸ junctions [12]. Currently, some trials are being conducted in which no detectors are inside the construction and this design problem is under study.
CONCLUSIONA six-port reflectometer constructed from a 0°/180°ring coupler has been presented. Three different constructions with their q positions are given. One of these constructions was realized on an RT/Duroid 5880 at 3-GHz center frequency. The realized six-port reflectometer was first calibrated and then used to measure the reflection coefficient of different unknown impedances. The sixport reflectometer was in good agreement with the measurements of the vector network analyzer (Agilent 8719ES), especially in the microwave range 2.67-3.25 GHz.
ACKNOWLEDGMENTThe author would like to thank Prof. Esmat A.F. Abdallah, Electronics Research Institute, E...