De?¬?nition 2: Given some suitably de?¬?ned fraction a, the 100a% read accuracy powering
region is de?¬?ned as the space within which a tag can be read with at least 100a% read
accuracy.
Maximizing Read Accuracy by Optimally Locating RFID Interrogators 183
10.2.2 Friis??™ Equation and Antenna Gains
It can be shown [1] that the power received by an RFID tag is determined by the version of
Friis??™ equation that is listed below that takes into account the relative positions of the tag
and the reader??™s antennas:
PR ?? PT
GT(uT,fT)GR(uR,fR)l2
(4pr)2 (1 jGTj2)(1 jGRj2)j^pT ^pRj2, (10:2)
where
(uT, fT) are the spherical coordinates to de?¬?ne transmitter antenna orientation
(uR,fR) are the spherical coordinates to de?¬?ne receiver antenna orientation
PR is the received power
PT is the transmitted power
GR(uR, fR) is the receiver (tag) gain
GT(uT, fT) is the transmitter gain
GR is the receiver re?¬‚ection coef?¬?cient
GT is the transmitter re?¬‚ection coef?¬?cient
^pR is the receiver polarization vector
^pT is the transmitter polarization vector
r is the distance between the transmitter and the receiver
l is the wavelength
The re?¬‚ection coef?¬?cients GR and GT account for the impedance mismatch between the
antenna and circuitry [2] that are introduced in the simple modulation of the backscatter. In
an ideal situation, its value is 0, which means no power will be re?¬‚ected back because of
the mismatch.
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