Readers - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 316

The antenna current i LS is of interest in this context, because this allows us to calculate
the magnetic field strength H that is generated by the antenna coil (see Chapter 4).
To clarify the relationships, let us now modify the matching circuit from Figure 11.18
slightly (Figure 11.22).
The input impedance of the circuit at operating frequency is precisely 50 .For
this case, and only for this case(!), the voltage at the input of the matching circuit is
very simple to calculate. Given a known transmitter output power P and known input
impedance Z 0 , the following is true: P

U 2 /Z 0 . The voltage calculated from this
equation is the voltage at C 2p and the serial connection of C ls ,R ls and X LS , and is thus
known. The antenna current i 2 can be calculated using the following equation:

=

√ P · Z 0

i 2 =

( 11 . 7 )

1
ωC 1s

R Ls + jωL s − j

11.4.3 The influence of the Q factor

A reader antenna for an inductively coupled RFID system is characterised by its res-
onant frequency and by its Qfactor . A high Q factor leads to high current in the
antenna coil and thus improves the power transmission to the transponder. In contrast,
the transmission bandwidth of the antenna is inversely proportional to the Q factor.
A low bandwidth, caused by an excessively high Q factor, can therefore significantly
reduce the modulation sideband received from the transponder.
The Q factor of an inductive reader antenna can be calculated from the ratio of
the inductive coil resistance to the ohmic loss resistance and/or series resistance of
the coil:

2 π · f 0 · L coil
R total

Q = ( 11 . 8 )

The bandwidth of the antenna can be simply calculated from the Q factor:

f 0
Q

B = ( 11 . 9 )

50 Ω

i 2

Antenna coil

C 1s

i 1 R Ls X Ls

C 2p

U in Z A

Figure 11.22 The matching circuit represented as a current divider