ST AN1806 APPLICATION NOTE
AN1806
APPLICATION NOTE
Antenna (and Associated Components)
Matching-Circuit Calculation for the CRX14 Coupler
In the basic RFID system (as shown in Figure 1):
1. The Reader generates an electromagnetic field. This field is rectified to generate the
supply voltage inside the Tag.
2. The Reader transmits information to the Tag by modulating the carrier wave.
3. The Tag back-scatters the carrier wave, by modifying its own impedance thereby
perturbing the field, in order to transmit back information to the Reader.
Figure 1. Basic RFID System
Signal (2)
Reader/Writ er
Ante nna
Power (1)
Signal (3)
Tag
February 2006 Rev. 3 1/37
www.st.com
Contents AN1806 - APPLICATION NOTE
Contents
1 CRX14 Contactless Coupler Chip from ST . . . . . . . . . . . . . . . . . . . . . . . 6
2 Short Range Contactless Memories from ST . . . . . . . . . . . . . . . . . . . . . 7
2.1 Low-end SR Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Secure SRIX Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Basic concepts and fundamental equations . . . . . . . . . . . . . . . . . . . . . 8
3.1 Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Inductance, L, and the Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Inductance of a Planar Rectangular Coil . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.4 Magnetic Coupling Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.1 Matching Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Current Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.3 VR Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4 Current Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Designing an RFID application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1 Using the Excel Spreadsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 Step 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.3 Step 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.4 Step 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.5 Step 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Appendix A Calculation details of serial-to-Parallel Conversion . . . . . . . . . . . . 26
5.6 Calculation of the Impedance of Equivalent Circuit
at the Second Resonance Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Appendix B Calculation Details of Current Calculation . . . . . . . . . . . . . . . . . . . 30
5.7 VR Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.8 Current Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2/37
AN1806 - APPLICATION NOTE Contents
Appendix C Demo kit board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6 Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3/37
List of tables AN1806 - APPLICATION NOTE
List of tables
Table 1. K1 and K2 values according to layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Table 2. Main Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Table 3. Values of Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Table 4. Calculation steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Table 5. Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Table 6. Parameter values for tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Table 7. Computed read range as a function of K and the H field . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Table 8. Summary of the Main Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Table 9. Values of the Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Table 10. Bill of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Table 11. Document Revision History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6
4/37
AN1806 - APPLICATION NOTE List of figures
List of figures
Figure 1. Basic RFID System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Figure 2. Circular Loop Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 3. Magnetic Field as a Function of the Distance of the Tag from the Reader. . . . . . . . . . . . . . 9
Figure 4. Magnetic Field as a Function of the Antenna Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure 5. Round Planar Spiral Coils. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 6. Planar Square, Hexagonal and Octagonal Spiral Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 7. User Interface Screen of the Planar Rectangular Coil Inductance Calculator . . . . . . . . . . 13
Figure 8. Real Circuit for the Antenna System on the Board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Figure 9. Series-to-Parallel Circuit Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 10. Parallel Equivalent Circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 11. Equivalent Impedance (Z) Plotted against Frequency (f) . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 12. Coupling between One Tag and One Reader Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Figure 13. Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure 14. Excel Configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Figure 15. Basic Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Figure 16. Coupling factor model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Figure 17. Equivalent circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 18. Layout of Demo-kit Board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Figure 19. Component Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4
5/37
CRX14 Contactless Coupler Chip from ST AN1806 - APPLICATION NOTE
1 CRX14 Contactless Coupler Chip from ST
ST has designed the CRX14, a short range contactless coupler chip, compliant with the
ISO14443 type B proximity standard. The CRX14 generates a 13.56MHz signal. Designed
to deliver an RF power of 100mW, it operates in the Short Range on contactless memory
tags (provided that they, too, are compliant with ISO14443 type B).
The CRX14 features the ST anti-collision mechanism, which allows the reader to detect and
identify all the tags that are present in the operating range, and to access them individually.
Because the CRX14 implements the France Telecom-proprietary anti-clone function, the
reader can also perform authentication of tags that are equipped with the France Telecom
anti-clone capability.
The CRX14 coupler interf aces between:
● the memory tags, on one side, through input /output buffers and the ISO14443 type B
radio frequency protocol, and
● the system master processor, on the other side, through a 400kHz I
Operating from a 5V power supply, and delivered in a SO16N package, the CRX14 coupler
chip is an excellent solution for building contactless readers, embedded in the final
equipment, and offering a good co mpromise between operating range and cost.
2
C bus.
6/37
AN1806 - APPLICATION NOTE Short Range Contactless Memories from ST
2 Short Range Contactless Memories from ST
All devices from the ST Short Range Contactless series are compliant with the ISO14443
type B standard. They a re accessible via a 13.56MHz carrier frequency, and support a data
transfer rate between tag and reader of 106kbit/s in both directions. All of them are totally
compatible with each other, in terms of tag protocol access. The series is sub-divided into
two families:
● Low-end SR Family
● Secure SRIX Family (equipped with anti-clone and anti-collision capabilities).
2.1 Low-end SR Family
SR176 is the first member of ST low-end short range family. It contains:
● 176 bits of EEPROM, organized as eleven 16-bit blocks, that can be write-protected
● a 64-bit UID, and
● a fixed 8-bit chip identifier.
2.2 Secure SRIX Family
SRIX is a family of highly secure devices that support the anti-clone capability, allowing tag
authentication. The system master processor sends an authenti cation request to ea ch of the
tags present in the CRX14’s field. Each tag runs its anti-clone algorithm to compute a
signature, and sends it back to the reader for an authentication check. The anti-clone
function helps fight against fraud, since any tag that does not belong to the system will
answer with a wrong signature.
The first member of the SRIX family is the SRIX4K, featuring 4096 bits of EEPROM
organized as 128 words of 32 bits. These are, in turn, organized in five main areas:
● One 5-word OTP z one , accessib le in user mode , whose bit s can only be s witche d from
1 to 0
● Two 32-bit binary counters that can only be decremented
● 121 words of user EEPROM, of which 9 can be individually write protected
● One 8-bit chip identifier that allows a reader to identify uniquely each tag present in its
field during the anti-collision operation
● One 64-bit read-only unique identifier (UID), programmed on the manufacturing line.
The family will be later extended to include a lower density, 512-bit, device.
7/37
Basic concepts and fundamental equations AN1806 - APPLICATION NOTE
3 Basic concepts and fundamental equations
To calculate the characteristics of a RFID system, we need some definitions and
assumptions:
● The reader generates a tension
● This tension supplies the inductive antenna L
● A current I
flows through the antenna and creates a magnetic field defined at
R
distance x.
● This field is transformed into a supply voltage in the tag.
● When the tag is near the reader antenna, it modifies the antenna tuning.
● To calculate the real current, we need to calculate the mutual inductance M and the
coupling factor between the reader antenna L
● We can also calculate the range within which the tag receives enough magnetic flux to
work well.
3.1 Electromagnetic Field
To generate an electromagnetic field, we can assume a circular loop antenna (Figure 2.)
by the tuning circuit.
R
and the tag antenna LT.
R
Figure 2. Circular Loop Antenna
I
r
R
x
~
The Electromagnetic field is given by Equation 1.
Equation 1
IRNR× r
Hrx()
-------------------------------------------------=
2x2
2r
×
R
Where:
● I
is the current in the loop antenna
R
● N
● r
● H
is the number of turns of the loop antenna
R
is the coil radius
R
(x) is measured in A/m
r
H
2
×
R
32⁄
+()
AI09013
8/37
AN1806 - APPLICATION NOTE Basic concepts and fundamental equations
An inductive coupling is possible in the near field, the limit between a near field and a far
field is given by Equation 2.
Equation 2
λ
-------------
x
≤
2 π×
Where:
● λ =c/f
In this application note, we use only Tags with a working frequency of 13.56MHz. So, the
limit between a near field and a far field is:
● x ≤ 3.52m
Figure 3 illustrates the magnetic field as a function of the distance of the tag from the reader,
for giv en values of the number of turns, N, the current, I, and the antenna radius, r.
Figure 3. Magnetic Field as a Function of the Distance of the Tag from the Reader
H ( x )
8
7
6
5
4
H [A/m]
3
2
1
0
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16
Distance [m]
With:
r=2cm
N=2
I=0.2A
H ( x )
AI09022
Figure 4 illustrates the magnetic field as a function of the antenna radius, r, for given values
of the number of turns, N, the current, I, of reader antenna, and the distance between tag
and antenna reader, x.
9/37
Basic concepts and fundamental equations AN1806 - APPLICATION NOTE
Figure 4. Magnetic Field as a Function of the Antenna Radius
H( r )
4,5
4
3,5
3
2,5
2
H [A/m]
1,5
1
0,5
0
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16
radius r[m]
In this example we can see that the field decrease when the radius goes beyond an op ti mal
value.
3.2 Inductance, L, and the Antenna
To tune the reader antenna, we need to be able to calculate its inductance.
With:
x=2cm
N=2
I=0.2A
H( r )
AI09023
Equation 3: Inductance of a Circular Loop
L µ0N
× r×
Where:
● r is the mean coil radius
● r
is the wire diameter
0
● N is the number of turns
● µ
● L is measured in H
= 4π10-7H/m
0
1.9
ln×=
r
-----
r
0
10/37
AN1806 - APPLICATION NOTE Basic concepts and fundamental equations
Figure 5. Round Planar Spiral Coils
d
AI09024
Equation 4: Inductance of Round Planar Spirals
d
L 31.33 µ0× N2×
------------------------------------ -
×=
8d⋅ 11 c⋅+
Where:
● d is the mean coil diameter
● c is the thickness of the winding
● N is the number of turns
● µ
● L is measured in H
= 4π10-7H/m
0
Figure 6. Planar Square, Hexagonal and Octagonal Spiral Coils
d
d
in
d
out
in
d
out
d
in
d
out
Equation 5: Inductance of Planar Square, Hexagonal and Octagonal Coil
LK1µ0× N2×
×=
1K2ρ⋅+
d
--------------------------- -
Where:
● d is the mean coil diameter: (d
–d
is the outer diameter
out
–d
is the inner diameter
in
●
● K
ρ = (d
and K2 depend on the layout (as summarized in Table 1.)
1
out–din
)/(d
out+din
)
out+din
)/2
AI09025
11/37
Basic concepts and fundamental equations AN1806 - APPLICATION NOTE
Table 1. K
and K2 values according to layout
1
Layout K
Square 2.34 2.75
Hexagonal 2.33 3.82
Octagonal 2.25 3.55
1
K
2
3.3 Inductance of a Planar Rectangular Coil
We have developed a convenient software tool, using the Grover method (Equation 6) for
calculating the inductance of rectangular planar antenna. The user interface is shown in
Figure 7.
We have found that the software gives a good approximation of the inductance L, in
comparison to measurements of the inductance of a real antenna on an impedance meter.
Equation 6: Grov er Method
LL0M
+=
∑
Where:
● M is the mutual inductance between each of the segments of the antenna
● L
is as defined in Equation 7
0
Equation 7
s
L
=
0
∑
L
j
j1=
Where:
● s is the number of segments
● L
is the self inductance of each segment
j
12/37
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