ST AN2866 APPLICATION NOTE
AN2866
ai15802
Antenna
Chip
Application note
How to design a 13.56 MHz
customized tag antenna
Introduction
RFID (radio-frequency identification) tags extract all of their power from the reader’s field.
The tags’ and reader’s antennas form a system of coupled inductances as shown in
Figure 1. The loop antenna of the tag acts as a transformer’s secondary.
The efficient transfer of energy from the reader to the tag depends on the precision of the
parallel resonant RLC loop antennas tuned to the carrier frequency (usually 13.56 MHz).
The purpose of this application note is to give a step-by-step procedure to easily design a
customized tag antenna.
Figure 1. RFID tag coupled to a reader’s magnetic field
Tag
Reader
Figure 2. An antenna designed for a specific chip and frequency
ai15802
January 2009 Rev 1 1/24
www.st.com
Contents AN2866
Contents
1 Simplified equivalent inlay circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Equivalent inlay circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Calculating the antenna coil inductance . . . . . . . . . . . . . . . . . . . . . . . . . 8
4 Designing the antenna coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 Inductance of a circular loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Inductance of a spiral coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.3 Inductance of an antenna with square coils . . . . . . . . . . . . . . . . . . . . . . . 10
5 Contactless measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1 Antenna coil prototype verification with an analyzer . . . . . . . . . . . . . . . . 14
5.1.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 14
5.1.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.2 Antenna coil prototype verification without an analyzer (first
method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.2.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 15
5.2.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6 Non-contactless (contact) measurement method . . . . . . . . . . . . . . . . 18
6.1 Without an analyzer (second method) . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
6.1.1 Preparing the equipment and connections . . . . . . . . . . . . . . . . . . . . . . 18
6.1.2 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.1.3 Example using an LRI2K device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
7 Frequency versus application: recommendations . . . . . . . . . . . . . . . 22
8 Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2/24
AN2866 List of tables
List of tables
Table 1. Antenna coil inductances for different C
Table 2. K1 & K2 values according to layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Table 3. Document revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
values at a given tuning frequency . . . . . . . . . . 8
tun
3/24
List of figures AN2866
List of figures
Figure 1. RFID tag coupled to a reader’s magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Figure 2. An antenna designed for a specific chip and frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Figure 3. Equivalent circuit of a chip and its antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Figure 4. Equivalent circuit of a chip, its antenna (modeled with a series
resistance) and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Figure 5. Equivalent circuit of a chip, its antenna (modeled with a parallel
resistance) and connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Figure 6. Simplified equivalent circuit of a chip, its antenna and connections . . . . . . . . . . . . . . . . . . . 7
Figure 7. Antenna design procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Figure 8. Spiral coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Figure 9. Square coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Figure 10. User interface screen of the planar rectangular coil inductance calculator. . . . . . . . . . . . . 12
Figure 11. Rectangular planar antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Figure 12. Measurement equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Figure 13. Resonance traces of the prototype at different powers . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Figure 14. ISO standard loop antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 15. Without an analyzer: first measurement method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Figure 16. Oscilloscope views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 17. Synthesis of resonance traces for different voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 18. Measurement circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Figure 19. Determining the resonance frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure 20. Coil samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Figure 21. Coil characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Figure 22. New coil samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 23. Second coil characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 24. Best antenna coil prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4/24
AN2866 Simplified equivalent inlay circuit
ai15804
R
chip
C
tun
A
B
R
ant
C
ant
L
ant
Chip Antenna
1 Simplified equivalent inlay circuit
The chip and its antenna can be symbolized using their equivalent electrical circuit.
Figure 3 shows the equivalent electrical circuit of the chip (parallel association of a
resistance which emulates the current consumption of the chip and a capacitance added to
the chip to ease tuning).
The antenna is a wire, so its equivalent electrical circuit is a wire with a resistance
symbolized by R
C
is the representation of parasitic elements (produced by the bridge).
ant
Figure 3. Equivalent circuit of a chip and its antenna
. The antenna also has an inductance denoted by L
ant
. The capacitance
ant
5/24
Equivalent inlay circuit AN2866
ai15805
R
chip
C
tun
A
B
R
s_ant
C
ant
L
ant
Chip Antenna
R
1con
C
con
R
2con
Connection
ai15841
R
chip
C
tun
A
B
R
p_ant
C
ant
L
ant
Chip Antenna
R
1con
C
con
R
2con
Connection
2 Equivalent inlay circuit
The schematic shown in Figure 3 is but a first approach to the problem because it does not
take into account the connection between the chip and the antenna. The assembly phase of
the chip onto the antenna may lead to the introduction of parasitic elements. These parasitic
elements are symbolized by two resistances and a capacitance as shown in Figure 4 and
Figure 5.
The equivalent circuit of the antenna may include either a series (see Figure 4) or a parallel
(see Figure 5) resistance.
Figure 4. Equivalent circuit of a chip, its antenna (modeled with a series
resistance) and connections
Figure 5. Equivalent circuit of a chip, its antenna (modeled with a parallel
resistance) and connections
The symbols in Figure 4 and Figure 5 correspond to:
R
: current consumption of the chip for a given power value
chip
C
: tuning capacitance of the chip
tun
R
: equivalent parasitic resistance generated by the connection between the chip and
con
the antenna
C
: equivalent parasitic capacitance generated by the connection between the chip and
con
the antenna
C
: equivalent parasitic capacitance of the antenna coil
ant
: Antenna coil series resistance
R
s_ant
R
: Antenna coil parallel resistance
p_ant
L
: Antenna coil inductance
ant
6/24
AN2866 Equivalent inlay circuit
ai15806
C
tun
L
ant
R
eq
R
eq
R
chipRp_ant
×
R
chipRp_ant
+
------------------------------------- -=
R
p_ant
R
s_ant
1
L
ant
ω×
R
s_ant
-------------------- -
⎝⎠
⎛⎞
2
+
⎝⎠
⎛⎞
×=
This equivalent circuit (Figure 4) can also be simplified as illustrated in Figure 6 (use the
simplified circuit for calculations).
Figure 6. Simplified equivalent circuit of a chip, its antenna and connections
R
is calculated as follows:
eq
with where ω is the angular frequency.
7/24
Calculating the antenna coil inductance AN2866
f
0
1
2π L
antCtun
⋅
---------------------------------------- -=
L
ant
1
2πf
0
()2C
tun
⋅
------------------------------------- -=
Q
R
eq
2π f0L
ant
⋅⋅
------------------------------------=
L
ant
1
2π 13.56 MHz×()
2
21 pF⋅
------------------------------------------------------------------------ - 6.56 µH==
3 Calculating the antenna coil inductance
The resonant frequency f0 of a parallel resonant LC circuit can be calculated by:
The coil inductance at the carrier frequency resonance is: .
The quality factor Q of the simplified circuit is calculated as follows: .
Example of the calculation of an antenna coil inductance:
Table 1. Antenna coil inductances for different C
frequency
values at a given tuning
tun
Product C
tun
(pF)
Tuning frequency
(MHz)
Antenna coil inductance (µH)
21 13.56 6.56
28.5 13.56 4.83
LR (long-range)
23.5 13.56 5.86
97 13.56 1.42
64 13.56 2.15
SR (short range)
64 14.40 1.90
Figure 7 describes the steps of the antenna design procedure that gives an easy and
reliable method of designing an antenna coil prototype.
This procedure uses the C
capacitance of the chip, a software tool called antenne.exe,
tun
and tools to produce antenna coil prototypes.
By determining dimensions and values, the execution of the first run gives the best out of
three coils meeting the requirements. Usually, the best results appear after the second run.
8/24
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