Corollary 1: Along the reader axis, if there exists any point with 100a% read accuracy,
then there is always a point with 100a% read accuracy such that any point closer to the
reader has at least 100a% read accuracy while any point further away fails to meet 100a%
read accuracy.
Proof: In Friis??™ equation, let the transmitter gain along the reader axis be given by GT.
Suppose there areM(M!1) orientations for each tag position along the reader axis; andM
corresponding values of the receiver gain GR at each of these points. Let T be the threshold
point with distance rT such that exactly 100a% of the M orientations at point T can receive
power greater than or equal to the minimum activation power. Then for any point T0 on the
reader axis with distance r0 >rT, any of the Morientations will receive power that is greater
than the power received from the same orientation at point T. Therefore, at least 100a%ofM
orientations at point T0 can be activated with suf?¬?cient power.
Corollary 1 indicates that for the case of a single reader antenna there will be a threedimensional
boundary surface within which lies the 100a% read accuracy powering
region. In Ref. [2], instead of evaluating every point in the portal space, an algorithm is
developed to obtain such a boundary surface. At any given point on the reader axis for a
given tag position, all the parameters in Friis??™ equation are known except for the receiver
gain GR.
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