In Radio Frequency Identification (RFID) applications, it is beneficial to know where in a three-dimensional space an RFID tag will operate with respect to the interrogating transmitter. It becomes a very complex problem containing numerous variables including transmitted power, antenna gains, orientation, etc. One well-known equation used to approximate the power that a tag can receive from an interrogating transmitter is the Friis Equation. However, the commonly used form of the Friis Equation contains assumptions that limit the validity to a single point, orientation, and polarization in space, which is usually the most favorable. These simplifications eliminate the reflection coefficients and polarization terms, and the gains lose their angular dependences. This dissertation will provide a mathematical model that describes the operation of a tag in the far-field from a more realistic perspective in a three-dimensional space. The complete form of the Friis equation will be used as the basic formulation to model the amount of power a tag can receive for any orientation at a given point in space. The dissertation will also include mathematical analyses of how the location of the data base station affects the performance of the system by applying the physics embodied in the complete Friis equation to the return transmission link from the tag to the data base station. The complete mathematical expression will be used to evaluate the performance of an RFID tag by depicting the three-dimensional area of operation. The functioning volume will be solved using the developed scaling factor method and will give an accurate portrayal of where a tag can be successfully read as a specified percentage of reads when all orientations and polarizations are examined.
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