Physical Principles of RFID Systems - RFID: Fundamentals and Applications in Contactless Smart Cards and Identification - page 133

Impedance
matching

C 1

C 2

D 1 R L

U in

U T

U chip

(a) Practical circuit: voltage doubler with impedance matching

Impedance
matching

U T

R j C j

Z A Z A * Z rect *

Z rect

(b) AC equivalent circuit

Figure 4.78 (a) Circuit of a Schottky detector with impedance transformation for power match-
ing at the voltage source and (b) the HF equivalent circuit of the Schottky detector

W) the detector is in the
range of square law detection. The following holds (Hewlett Packard, 986):

In the case of operation at powers below − 20 dBm (10

µ

u in ⇒ u chip ∼ P in

u chip ∼ ( 4 . 101 )

Schottky detectors in RFID transponders operate in the range of square law detection
at greater distances from the reader, but also in the transition range to linear detection
at smaller distances (Figure 4.79).
The relationship between the input power and output voltage of a Schottky detector
can be expressed using a Bessel function of the zeroth order (Hewlett Packard, 1088):

1 + ·

I 0

n 8 R g · P in

1 +

R g + R s
R L

· u chip
n

· R s · I b
n

I b
I s +

u chip
R L ·

+

= · e ( 4 . 102 )

I s

Where = q/(k · T) , q is the elementary charge, k is the Boltzmann constant, T
is the temperature of the diode in Kelvin, R g is the internal resistance of the voltage
source (in transponders this is the radiation resistance R r of the antenna), P in is the
supplied power, R L is the connected load resistor (transponder chip) and u chip is the
output voltage (supply voltage of the transponder chip).
By numerical iteration using a program such as Mathcad (n.d.) this equation can
easily be solved, yielding a diagram u chip (P in ) (see Figure 4.81). The transition from
square law detection to linear law detection at around

− 20 (10 µ W) to − 10 dBM

(0.1 mW) input power is clearly visible in this figure.
Evaluating equation (4.102), we see that a higher saturation current I s leads to good
sensitivity in the square law detection range. However, in the range that is of interest for
RFID transponders, with output voltages u chip of 0.8 - 3 V, this effect is unfortunately
no longer marked.