Regardless of the mathematical form of the gain function GR, if substituting
the value of the 100a percentile of GR in Friis??™ equation gives power that is greater than
186 RFID Handbook: Applications, Technology, Security, and Privacy
the required activation power, then such a point can be read with at least 100a% read
accuracy. In other words, a threshold point T on any reader axis is such a point that the
received power equals the required activation power Pmin when GR assumes the 100a
percentile value. Based on the above analysis, we can obtain the following formula:
r2
GT(uT,fT) ??
PT GR 100al2
Pmin(4p)2 (1 jGTj2)(1 jGRj2)j^pT ^pRj (10:5)
In Equation 10.5, GR_100a is the 100a percentile value of receiver gain while Pmin is the
minimum receiver power to activate a tag. Therefore, the right-hand side of Equation 10.5
is a constant. Let C be the value of the constant in Equation 10.5. Then f(uT, fT, r)?? (r2=GT(uT, fT))??C de?¬?nes the boundary surface of the 100a% read accuracy powering
region.
If RFID tags use half-wave dipole antennas, then the antenna gain is a function of uR with
a period of p and is symmetric about uR??p=2, as shown in Figure 10.3. This is because the
shape of cos p2
cos uR = sin uR is similar to that of sin uR.
In the case of a half-wave antenna, the 100a percentile value of the receiver gain is
obtained when uR??903(1a) degrees.
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