Physical Principles of RFID Systems - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 89

Table 4.3 Parameters for line diagrams and locus curves,
if not stated otherwise

L 1 = 1 µ H L 2 = 3 . 5 µ H

C 1 = 1 /(ω TX ) 2

· L 1 (resonance) R 2 = 5

= 1 /(ω RX ) 2

C 2 · L 2 (resonance) R L = 5k

f RES = f TX = 13 . 56 MHz k = 15%

All line diagrams and locus curves from Section 4.1.10 are — unless stated other-
wise — calculated using the constant parameter values listed in Table 4.3.
Transmission frequency f TX Let us first change the transmission frequency f TX of
the reader, while the transponder resonant frequency f RES is kept constant. Although
this case does not occur in practice it is very useful as a theoretical experiment to help
us to understand the principles behind the transformed transponder impedance Z T .
Figure 4.30 shows the locus curve Z T = f(f TX ) for this case. The impedance vector
Z T traces a circle in the clockwise direction in the complex Z plane as transmission
frequency f TX increases.
In the frequency range below the transponder resonant frequency (f TX <f RES ) the
impedance vector Z T is initially found in quadrant I of the complex Z plane. The
transformed transponder impedance Z T is inductive in this frequency range.
If the transmission frequency precisely corresponds with the transponder resonant
frequency (f TX = f RES ) then the reactive impedances for L 2 and C 2 in the transponder

90

120 60

Im in Ω

150 30

f RES

180 0

0 10 20 30 40 50

Re in Ω

Z ′ (f TX )

210 330

240 300

270

k = 10%

k = 20%

Figure 4.30 The impedance locus curve of the complex transformed transponder impedance
Z T as a function of transmission frequency ( f TX

1 - 30 MHz) of the reader corresponds with
the impedance locus curve of a parallel resonant circuit

=