Physical Principles of RFID Systems - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 94

90

120 60

Im in Ω

150 30

f RES > f TX

R Lmax

Re in Ω

180 0

0 5 10 15

R Lmax

R Lmin

f RES < f TX

210 330

240 300

270

f RES = f TX
f RES = f TX + 3%
f RES = f TX − 1%

Locus curve of Z T ( R L Figure 4.35 0 . 3-3k ) in the impedance plane as a function of the

load resistance R L in the transponder at different transponder resonant frequencies

=

Figure 4.35 shows the corresponding locus curve for Z T = f(R L ) . This shows that
the transformed transponder impedance is proportional to R L . Increasing load resistance
R L , which corresponds with a lower(!) current in the data carrier, thus also leads to a
greater value for the transformed transponder impedance Z T . This can be explained by
the influence of the load resistance R L on the Q factor: a high-ohmic load resistance
R L leads to a high Q factor in the resonant circuit and thus to a greater current
step-up in the transponder resonant circuit. Due to the proportionality Z T ∼ jωM ·
i 2 — and not to i RL — we obtain a correspondingly high value for the transformed
transponder impedance.
If the transponder resonant frequency is detuned we obtain a curved locus curve
for the transformed transponder impedance Z T . This can also be traced back to the
influence of the Q factor, because the phase angle of a detuned parallel resonant
circuit also increases as the Q factor increases ( R L ↑ ), as we can see from a glance at
Figure 4.34.
Let us reconsider the two extreme values of R L :

ω 2 k 2 · L 1 · L 2

R 2 + jωL 2

Z T (R L → 0 ) = ( 4 . 53 )