11. Conclusions
In this project, the behavior of reactive obstacles in waveguides were studied. The obstacles under study was thin cylindrical metal posts of diameters 0.09, 0.125 and 0.25 inch. They were introduced via the use of two waveguide test jigs. One of them operated on the C-band frequency range (3.95 - 5.85 GHz) and the other one operated on the X-band frequency range (8.2 - 12.4 GHz). Thin metal irises with partial openings were also used. All of these obstacles and the two test jigs were made of brass, which had a high electrical conductivity. It was for this reason that ohmic losses were assumed negligible. And therefore any effects resulted had to be reactive.
Obstacles were used in waveguides as filter and tuning elements because conventional circuit elements such as resistors, capacitors and inductors tended to dissipate signal as radiation at microwave frequencies. Concerning the metal posts in waveguides, essentially they produced reflections, scattered the energy and converted it into higher order modes in the vicinity of the discontinuity. This changed the propagating characteristics of the electromagnetic wave. Therefore some disturbances to the field was resulted. The reactance introduced was frequency dependent. Concerning the thin irises, they created reactive effects by interacting with either the magnetic or the electric field of the incident wave or both, depending on its physical shape. Localized evanescent higher order modes were induced which resulted in a storage of energy locally.
To model the effects quantitatively, a T-equivalent circuit with two parameters - one ZA elements and two ZB elements - was used. The limitation to this circuit was that only obstacles which were symmetric along the propagating direction of the wave could be modeled. As distinct from other mathematically derived equivalent circuits, the values of the two parameters in question were determined experimentally. This meant the main objective of this project was to determine those two values accurately and efficiently. Mathematical theory had been developed to express ZA and ZB in terms of the reflection coefficient r and the transmission coefficient t. The reason for using impedance, rather than reactance, was to take care of the possible events of having resistive parts in the measurements.
In order to collect data on r and t, the advanced HP8510C Microwave Network Analyzer (NWA) was used take the measurements. The NWA measured and computed the scattering parameters. The four parameters were essentially r(s) and t(s) with respect to the two different ports.
By transferring the accuracy of known responses of standards to the device under test (DUT), measurement calibration was necessary prior to the measurement process. Two calibration procedures were used in this project. Calibration Method 1 did not involve the use of the waveguide test jig. It was used in the measurement for thin irises. Calibration Method 2 involved the use of the waveguide test jig in the calibration process. Port extensions were used to shift the measurement planes to the center of the metal posts. This method assumed that the distance over which the measurement planes were shifted was within a perfect waveguide. This second method was used to take measurements for the metal posts.
In order to facilitate the process of data acquisition, a program NWAMODEL had been developed using LabVIEW. This program was based on another NWA monitoring program called NWAV-1b. NWAMODEL allowed rapid capture and storage of the experimental data (in terms of ZA and ZB etc. against frequency) to a computer disk. The experimental data could be presented in a real-time fashioned on the screen. Most of the functions in NWAV-1b relevant to this project was kept.
On the basis of the results acquired, it was decided the best strategy to work out r and t was to take the average of S11 and S22 for r and that of S12 and S21 for t.
The experimental results, where possible, were compared with those published by Marcuvitz. For the two metal posts (0.125 and 0.25 inch in diameter), the results obtained closely followed Marcuvitz's ones. On the basis of the trends shown, it was deduced that XB was in fact the thickness (i.e. diameter of the post) terms. Thinner posts had smaller values for XB.
It turned out that there were indeed associate resistive terms along the reactive ones. However, they were discarded for three reasons. First, they were insignificant in magnitude. Second, they showed no trend. Lastly, the measured results of XA and XB followed Marcuvitz's results regardless of their existences. Therefore RA and RB were disregarded.
Power had been used to assessed the quality of the measured data. Since the physics dictated that power should be conserved in an reactive environment, power should have a magnitude of unity. However, it turned out that it was not quite so in some occasions. Power was less than 0.8 in some cases. Nevertheless, it happened again that power did not affect the quality of the results. It was for this reason that the matter was not pursued further.
It was found that the accuracy of the measurements depended on the ratio of the relative size of the metal post to the dimension of the waveguide. Results for the metal posts in the C-band waveguide test jig appeared to be better than those in the X-band one, in terms of the resistive-to-reactive component ratio and power.
Results on an off-centered post in the C-band waveguide was presented. These results had never been published before. Besides, results on the reactance of the irises had also been included.
Regarding the objectives of this project, all of the requirements had been fulfilled. The program and the measurement procedure developed had the capability to extend the measurement on other symmetrical waveguide obstacles.
Nevertheless, further investigations on two areas would be worthwhile. First, since the quality of the results appeared to depend heavily on the quality of the waveguide test jig, and since port extension was such an important part in this exercise, there were reasons to believe that a re-design of the test jig would be beneficial. In particular, provisions should be made so that calibration to the plane of the obstacle could be achieved. Or else at least the length of the test jig should be reduced. Second, although the program NWAMODEL developed could deliver what it was meant to do, if used properly. However, it seemed to fall short in its ability to handle operational errors by users. Measures should be taken to address this issue.
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