Data Integrity - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 212

command. In this manner the number of iterations necessary for the selection of an
individual transponder can be gradually reduced if a large number of transponders are
'waiting' for processing in the interrogation zone of the reader. In our example, run-
ning the anticollision algorithm again would thus automatically lead to the selection
of one of the previously processed transponders 1, 3 or 4.
The average number of iterations L that are required to detect a single transpon-
der from a large number depends upon the total number of transponders N in the
interrogation zone of the reader, and can be calculated easily:

log (N)
log ( 2 ) + 1

L(N) = ld(N) + 1 = ( 7 . 7 )

If only a single transponder is located in the interrogation zone of the reader, pre-
cisely one iteration is required to detect the serial number of the transponder — a
collision does not occur in this case. If there is more than one transponder in the inter-
rogation zone of the reader, then the average number of iterations increases quickly,
following the curve shown in Figure 7.23.

Dynamic binary search procedure In the binary search procedure described above,
both the search criterion and the serial numbers of the transponders are always trans-
mitted at their full length. In practice, however, the serial numbers of transponders do
not consist of one byte, as in our example, but, depending upon the system, can be
up to 10 bytes long, which means that a large quantity of data must be transferred in
order to select an individual transponder. If we investigate the data flow between the
reader and the individual transponders in more detail (Figure 7.24) we find that:

5

4

3

2

1

0

0 2 4 6 8 10 12 14 16

N

Figure 7.23 The average number of iterations needed to determine the transponder address
(serial number) of a single transponder as a function of the number of transponders in the
interrogation zone of the reader. When there are 32 transponders in the interrogation zone an
average of six iterations are needed, for 65 transponders on average seven iterations, for 128
transponders on average eight iterations, etc.