Physical Principles of RFID Systems - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 141

4.2.6.6 Modulatedbackscatter

As we have already seen, the transponder antenna reflects part of the irradiated power
at the scatter aperture σ (A s )ofthe transponder antenna . In this manner, a small part
of the power P 1 that was originally emitted by the reader returns to the reader via the
transponder as received power P 3 .
The dependence of the scatter aperture σ on the relationship between Z T and Z A
established in Section 4.2.5.4 is used in RFID transponders to send data from the
transponder to the reader. To achieve this, the input impedance Z T of the transponder
is altered in time with the data stream to be transmitted by the switching on and off
of an additional impedance Z mod in time with the data stream to be transmitted. As
a result, the scatter aperture σ , and thus the power P S reflected by the transponder,
is changed in time with the data, i.e. it is modulated. This procedure is therefore also
known as modulated backscatter or σ - modulation (Figure 4.87).
In order to investigate the relationships in a RFID transponder more precisely, let
us now refer back to equation (4.82), since this equation expresses the influence of the
transponder impedance Z T = R T + X T on the scatter aperture σ . In order to replace U 0
by the general properties of the transponder antenna we first substitute equation (4.90)
into equation (4.88) and obtain:

G · R r
π · Z F ·

G · R r · S
π

S · Z F = λ 0 ·

U 0 = λ 0 · ( 4 . 106 )

We now replace U 0 in equation (4.82) by the right-hand expression in

equation (4.106) and finally obtain (PALOMAR, 18000):

λ 0 2 R r · · G

σ = ( 4 . 107 )

π · [ (R r + R V + R T ) 2 + (X A + X T ) 2 ]

where G is the gain of the transponder antenna.
However, a drawback of this equation is that it only expresses the value of the scatter
aperture σ (PALOMAR, 18000). If, for the clarification of the resulting problems, we
imagine a transponder, for which the imaginary component of the input impedance Z T
in unmodulated state takes the value X Toff =− X mod , but in the modulated state

(modulation impedance Z mod connected in parallel) it is X Ton =− X A − X mod .We
further assume that the real component R T of the input impedance Z T is not influenced
by the modulation. For this special case the imaginary part of the impedance during
modulation between the values ( + X mod ) 2 and ( − X mod ) 2 is switched. As can be
clearly seen, the value of the scatter aperture σ remains constant. Equation (4.81), on
the other hand, shows that the reflected power P S is proportional to the square of
the current I in the antenna. However, since by switching the imaginary part of the
impedances between − X mod and + X mod we also change the phase θ of the current
I , we can conclude that the phase θ of the reflected power P S also changes to the
same degree.
To sum up, therefore, we can say that modulating the input impedance Z T of the
transponder results in the modulation of the value and/or phase of the reflected power
P S and thus also of the scatter aperture σ . P S and σ should thus not be considered

X A +