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13.56mhz_天线设计.pdf
Introduction
Review of a Basic Theory for RFID antenna Design
Current and Magnetic Fields
FIGURE 1: Calculation of magnetic field B at location P due to current I on a straight conducting...
FIGURE 2: Calculation of magnetic field B at location P due to current I on the loop
FIGURE 3: Decaying of the magnetic field B vs. distance r
Induced Voltage in an Antenna Coil
FIGURE 4: A basic configuration of reader and tag antennas in RFID applications
FIGURE 5: Orientation Dependency of the Tag Antenna
Wire Types and Ohmic Losses
DC Resistance of Conductor and Wire Types
AC Resistance of Conductor
Resistance of Conductor with Low Frequency Approximation
TABLE 5: AWG Wire Chart
Inductance of Various Antenna Coils
Calculation of Inductance
FIGURE 6: A circular coil with single turn
FIGURE 7: A circular coil with single turn
FIGURE 8: N-turn multilayer circular coil
FIGURE 9: A spiral coil
FIGURE 10: N-turn square loop coil with multilayer
FIGURE 11: N-turn square loop coil with multilayer
FIGURE 12: A straight thin film inductor
FIGURE 13: Square loop inductor with a rectangular cross section
FIGURE 14: One turn Reader antenna
Example with dimension:
FIGURE 15: Two conductor segments for mutual inductance calculation
Configuration of Antenna Circuits
Reader Antenna Circuits
FIGURE 16: Various Reader Antenna Circuits
Tag Antenna Circuits
Consideration on Quality Factor Q and Bandwidth of Tuning Circuit
FIGURE 17: Various External Circuit Configurations
Bandwidth requirement and limit on circuit Q for MCRF355
Resonant Circuits
Parallel Resonant Circuit
FIGURE 18: Parallel Resonant Circuit
Series Resonant Circuit
FIGURE 19: Series Resonance Circuit
Tuning Method
FIGURE 20: Voltage vs. Frequency for Resonant Circuit
FIGURE 21: Frequency Responses for Resonant Circuit
Read Range of RFID Devices
FIGURE 22: Read Range vs. Tag Size for Typical Proximity Applications*
FIGURE 23: Read Range vs. Tag Size for Typical Long Range Applications*
Appendix A: Calculation of Mutual Inductance Terms in Equations 36 and 37
Appendix B: Mathlab program example for Example 8
References
Trademarks
Worldwide Sales
AN710
Antenna Circuit Design for RFID Applications
Author:
Youbok Lee, Ph.D.
Microchip Technology Inc.
REVIEW OF A BASIC THEORY FOR
RFID ANTENNA DESIGN
INTRODUCTION
Current and Magnetic Fields
Passive RFID tags utilize an induced antenna coil
voltage for operation. This induced AC voltage is
rectified to provide a voltage source for the device. As
the DC voltage reaches a certain level, the device
starts operating. By providing an energizing RF signal,
a reader can communicate with a remotely located
device that has no external power source such as a
battery. Since the energizing and communication
between the reader and tag is accomplished through
antenna coils, it is important that the device must be
equipped with a proper antenna circuit for successful
RFID applications.
An RF signal can be radiated effectively if the linear
dimension of the antenna is comparable with the
wavelength of the operating frequency. However, the
wavelength at 13.56 MHz is 22.12 meters. Therefore,
it is difficult to form a true antenna for most RFID appli-
cations. Alternatively, a small loop antenna circuit that
is resonating at the frequency is used. A current
flowing into the coil radiates a near-field magnetic field
that falls off with r-3. This type of antenna is called a
magnetic dipole antenna.
For 13.56 MHz passive tag applications, a few
microhenries of inductance and a few hundred pF of
resonant capacitor are typically used. The voltage
transfer between the reader and tag coils is accom-
plished through inductive coupling between the two
coils. As in a typical transformer, where a voltage in the
primary coil transfers to the secondary coil, the voltage
in the reader antenna coil is transferred to the tag
antenna coil and vice versa. The efficiency of the
voltage transfer can be increased significantly with high
Q circuits.
This section is written for RF coil designers and RFID
system engineers. It reviews basic electromagnetic
theories on antenna coils, a procedure for coil design,
calculation and measurement of
inductance, an
antenna tuning method, and read range in RFID
applications.
Ampere’s law states that current flowing in a conductor
produces a magnetic field around the conductor. The
magnetic field produced by a current element, as
shown in Figure 1, on a round conductor (wire) with a
finite length is given by:
EQUATION 1:
=
Bφ
µ
oI
---------
4πr
(
cos
α
2
–
cos
α
)
1
(
Weber m
⁄
2
)
where:
I = current
r = distance from the center of wire
µ
0 = permeability of free space and given
as 4 π x 10-7 (Henry/meter)
In a special case with an infinitely long wire where:
α
α
1 = -180°
2 = 0°
Equation 1 can be rewritten as:
EQUATION 2:
=
Bφ
µ
oI
---------
2πr
(
Weber m
⁄
2
)
FIGURE 1: CALCULATION OF MAGNETIC
FIELD B AT LOCATION P DUE TO
CURRENT I ON A STRAIGHT
CONDUCTING WIRE
Wire
Ζ
α
2
α
R
α
1
0
r
dL
I
P
X
B (into the page)
2003 Microchip Technology Inc.
DS00710C-page 1
AN710
The magnetic field produced by a circular loop antenna
is given by:
EQUATION 3:
FIGURE 2: CALCULATION OF MAGNETIC
FIELD B AT LOCATION P DUE TO
CURRENT I ON THE LOOP
=
Bz
=
µ
2
----------------------------------
)3 2⁄
oINa
2
2+
r
2 a
(
2
µ
------------------
oINa
2
1
-----
3
r
for
2
r
>>a
2
where
I = current
a =
r =
radius of loop
distance from the center of loop
µ
0 = permeability of free space and given as
4 π x 10-7 (Henry/meter)
The above equation indicates that the magnetic field
strength decays with 1/r3. A graphical demonstration is
shown in Figure 3. It has maximum amplitude in the
plane of the loop and directly proportional to both the
current and the number of turns, N.
Equation 3 is often used to calculate the ampere-turn
requirement for read range. A few examples that
calculate the ampere-turns and the field intensity
necessary to power the tag will be given in the following
sections.
X
α
a
coil
I
y
=
V
Vo
sin
ωt
R
r
P
Bz
z
FIGURE 3: DECAYING OF THE MAGNETIC
FIELD B VS. DISTANCE r
B
r-3
r
DS00710C-page 2
2003 Microchip Technology Inc.
AN710
INDUCED VOLTAGE IN AN ANTENNA
EQUATION 5:
COIL
Faraday’s law states that a time-varying magnetic field
through a surface bounded by a closed path induces a
voltage around the loop.
Figure 4 shows a simple geometry of an RFID applica-
tion. When the tag and reader antennas are in close
proximity, the time-varying magnetic field B that is
produced by a reader antenna coil induces a voltage
(called electromotive force or simply EMF) in the closed
tag antenna coil. The induced voltage in the coil causes
a flow of current on the coil. This is called Faraday’s
law. The induced voltage on the tag antenna coil is
equal to the time rate of change of the magnetic flux Ψ.
EQUATION 4:
V
–=
N
dψ
-------
dt
where:
N = number of turns in the antenna coil
Ψ = magnetic flux through each turn
The negative sign shows that the induced voltage acts
in such a way as to oppose the magnetic flux producing
it. This is known as Lenz’s law and it emphasizes the
fact that the direction of current flow in the circuit is
such that the induced magnetic field produced by the
induced current will oppose the original magnetic field.
The magnetic flux Ψ in Equation 4 is the total magnetic
field B that is passing through the entire surface of the
antenna coil, and found by:
ψ
∫=
B · Sd
where:
B = magnetic field given in Equation 2
S = surface area of the coil
• = inner product (cosine angle between two
vectors) of vectors B and surface area S
Note:
Both magnetic field B and surface S
are vector quantities.
The presentation of inner product of two vectors in
Equation 5 suggests that the total magnetic flux ψ that
is passing through the antenna coil is affected by an
orientation of the antenna coils. The inner product of
two vectors becomes minimized when the cosine angle
between the two are 90 degrees, or the two (B field and
the surface of coil) are perpendicular to each other and
maximized when the cosine angle is 0 degrees.
The maximum magnetic flux that is passing through the
tag coil is obtained when the two coils (reader coil and
tag coil) are placed in parallel with respect to each
other. This condition results in maximum induced volt-
age in the tag coil and also maximum read range. The
inner product expression in Equation 5 also can be
expressed in terms of a mutual coupling between the
reader and tag coils. The mutual coupling between the
two coils is maximized in the above condition.
FIGURE 4: A BASIC CONFIGURATION OF READER AND TAG ANTENNAS IN RFID APPLICATIONS
Tag Coil
V = V0sin(ωt)
Tag
B = B0sin(ωt)
I = I0sin(ωt)
Reader
Electronics
Tuning Circuit
Reader Coil
2003 Microchip Technology Inc.
DS00710C-page 3
AN710
Using Equations 3 and 5, Equation 4 can be rewritten
as:
EQUATION 8:
=
V0
2πfNSQBo
αcos
EQUATION 6:
=
–
V
N2
dΨ
21
-------------
dt
=
–
N2
(
d
----- B∫
dt
Sd⋅
)
where:
–=
N2
d
-----
dt
∫
2
µ
oi1N1a
2
2+
r
---------------------------------- · Sd
2 a
)3 2⁄
(
f = frequency of the arrival signal
N = number of turns of coil in the loop
S = area of the loop in square meters (m2)
Q = quality factor of circuit
Β
o = strength of the arrival signal
α = angle of arrival of the signal
In the above equation, the quality factor Q is a measure
of the selectivity of the frequency of the interest. The Q
will be defined in Equations 43 through 59.
FIGURE 5: ORIENTATION DEPENDENCY OF
THE TAG ANTENNA
B-field
a
Tag
The induced voltage developed across the loop
antenna coil is a function of the angle of the arrival
signal. The induced voltage is maximized when the
antenna coil is placed in parallel with the incoming
signal where α = 0.
–=
2
)
µ
-----------------------------------------
oN1N2a
(
2+
r
2 πb
(
)3 2⁄
2 a
2
di1
-------
dt
–=
M
di1
-------
dt
where:
V = voltage in the tag coil
i1 = current on the reader coil
a = radius of the reader coil
b = radius of tag coil
r = distance between the two coils
M = mutual inductance between the tag
and reader coils, and given by:
EQUATION 7:
M
=
)2
µ
πN1N2 ab(
o
--------------------------------------
)3 2⁄
(
2+
r
2 a
2
The above equation is equivalent to a voltage transfor-
mation in typical transformer applications. The current
flow in the primary coil produces a magnetic flux that
causes a voltage induction at the secondary coil.
As shown in Equation 6, the tag coil voltage is largely
dependent on the mutual inductance between the two
coils. The mutual inductance is a function of coil
geometry and the spacing between them. The induced
voltage in the tag coil decreases with r-3. Therefore, the
read range also decreases in the same way.
From Equations 4 and 5, a generalized expression for
induced voltage Vo in a tuned loop coil is given by:
DS00710C-page 4
2003 Microchip Technology Inc.
EXAMPLE 1: CALCULATION OF B-FIELD IN
EXAMPLE 3: OPTIMUM COIL DIAMETER
A TAG COIL
OF THE READER COIL
AN710
The MCRF355 device turns on when the antenna
coil develops 4 VPP across it. This voltage is rectified
and the device starts to operate when it reaches 2.4
VDC. The B-field to induce a 4 VPP coil voltage with
an ISO standard 7810 card size (85.6 x 54 x 0.76
mm) is calculated from the coil voltage equation
using Equation 8.
EQUATION 9:
An optimum coil diameter that requires the minimum
number of ampere-turns for a particular read range
can be found from Equation 3 such as:
EQUATION 11:
=
Vo
2πfNSQBo
cos
α
4=
NI
=
K
---
2
3
2
)
(
a
-------------------------
2+
r
2
a
and
=
Bo
⁄
4
)
2(
-----------------------------------
2πfNSQ
αcos
=
0.0449
(
µwbm
2–
)
where:
=
K
2Bz
---------
µ
o
where the following parameters are used in the
above calculation:
Tag coil size = (85.6 x 54) mm2 (ISO card
size) = 0.0046224 m2
Frequency = 13.56 MHz
Number of turns = 4
Q of tag antenna
coil
= 40
AC coil voltage to
turn on the tag
= 4 VPP
cosα = 1 (normal direction, α = 0).
By taking derivative with respect to the radius a,
)
(
d NI
--------------
da
=
K
)3 2⁄
3 2⁄
----------------------------------------------------------------------------------------------------
) 2a a
(
–
)1 2⁄
2+
r
2+
r
a
(
(
2
3
2
2a
4
a
=
K
2
)1 2⁄
(
a
--------------------------------------------------------
2+
r
2r
–
2
2
) a
(
3
a
The above equation becomes minimized when:
The above result shows a relationship between the
read range versus optimum coil diameter. The optimum
coil diameter is found as:
EXAMPLE 2: NUMBER OF TURNS AND
EQUATION 12:
CURRENT (AMPERE-TURNS)
Assuming that the reader should provide a read
range of 15 inches (38.1 cm) for the tag given in the
previous example, the current and number of turns
of a reader antenna coil is calculated from
Equation 3:
EQUATION 10:
a
2=
r
where:
a = radius of coil
r = read range.
3 2⁄
The result indicates that the optimum loop radius, a, is
1.414 times the demanded read range r.
2
)
(
2+
2Bz a
r
-------------------------------
µa
2
(
6–
)
)2
2 0.0449 10
---------------------------------------------------------------------------------------
×
) 0.1
(
+
) 0.1
(
7–
×
4π 10
0.38
(
)
(
2
2
3 2⁄
0.43 ampere - turns
(
)
(
)
NI
rms
=
=
=
The above result indicates that it needs a 430 mA
for 1 turn coil, and 215 mA for 2-turn coil.
2003 Microchip Technology Inc.
DS00710C-page 5
AN710
WIRE TYPES AND OHMIC LOSSES
EQUATION 14:
DC Resistance of Conductor and Wire
Types
The diameter of electrical wire is expressed as the
American Wire Gauge (AWG) number. The gauge
number is inversely proportional to diameter, and the
diameter is roughly doubled every six wire gauges. The
wire with a smaller diameter has a higher DC
resistance. The DC resistance for a conductor with a
uniform cross-sectional area is found by:
EQUATION 13:
DC Resistance of Wire
RDC
=
l
------
σS
=
l
-------------
σπa
2
Ω(
)
where:
l = total length of the wire
σ = conductivity of the wire (mho/m)
S = cross-sectional area = π r2
a = radius of wire
For a The resistance must be kept small as possible for
higher Q of antenna circuit. For this reason, a larger
diameter coil as possible must be chosen for the RFID
circuit. Table 5 shows the diameter for bare and
enamel-coated wires, and DC resistance.
AC Resistance of Conductor
At DC, charge carriers are evenly distributed through
the entire cross section of a wire. As the frequency
increases, the magnetic field is increased at the center
of the inductor. Therefore, the reactance near the
center of the wire increases. This results in higher
impedance to the current density in the region. There-
fore, the charge moves away from the center of the
wire and towards the edge of the wire. As a result, the
current density decreases in the center of the wire and
increases near the edge of the wire. This is called a
skin effect. The depth into the conductor at which the
current density falls to 1/e, or 37% (= 0.3679) of its
value along the surface, is known as the skin depth and
is a function of the frequency and the permeability and
conductivity of the medium. The net result of skin effect
is an effective decrease in the cross sectional area of
the conductor. Therefore, a net increase in the AC
resistance of the wire. The skin depth is given by:
δ
=
1
-----------------
πfµσ
where:
f = frequency
µ = permeability (F/m) = µ
µo = Permeability of air = 4 π x 10-7 (h/m)
µr = 1 for Copper, Aluminum, Gold, etc
µr
ο
= 4000 for pure Iron
σ = Conductivity of the material (mho/m)
= 5.8 x 107 (mho/m) for Copper
= 3.82 x 107 (mho/m) for Aluminum
= 4.1 x 107 (mho/m) for Gold
= 6.1 x 107 (mho/m) for Silver
= 1.5 x 107 (mho/m) for Brass
EXAMPLE 4:
The skin depth for a copper wire at 13.56 MHz and
125 kHz can be calculated as:
EQUATION 15:
δ
=
------------------------------------------------------------------------
)
πf 4π 10
) 5.8 10
(
×
(
1
7–
×
7
0.0661
------------------
=
f
m(
)
=
0.018
mm(
)
for 13.56 MHz
=
0.187
mm(
)
for 125 kHz
As shown in Example 4, 63% of the RF current flowing
in a copper wire will flow within a distance of 0.018 mm
of the outer edge of wire for 13.56 MHz and 0.187 mm
for 125 kHz.
The wire resistance increases with frequency, and the
resistance due to the skin depth is called an AC
resistance. An approximated formula for the AC
resistance is given by:
DS00710C-page 6
2003 Microchip Technology Inc.
AN710
Resistance of Conductor with Low
Frequency Approximation
When the skin depth is almost comparable to the radius
of conductor, the resistance can be obtained with a low
frequency approximation[5]:
EQUATION 18:
Rlow freq
≈
l
------------- 1
σπa
2
+
2
1
------ a
δ---
48
Ω(
)
The first term of the above equation is the DC
resistance, and the second term represents the AC
resistance.
EQUATION 16:
=
Rac
=
l
--------------------
σAactive
fµ
l
πσ-------
------
2a
=
(
Rdc
) a
2δ------
≈
l
-----------------
2πaδσ
Ω(
)
Ω(
)
Ω(
)
where the skin depth area on the conductor is,
Aactive 2πaδ
≈
The AC resistance increases with the square root of the
operating frequency.
For the conductor etched on dielectric, substrate is
given by:
EQUATION 17:
=
Rac
l
------------------------
σ w t+(
)δ
=
l
----------------
w t+(
)
πfµ
σ---------
Ω(
)
where w is the width and t is the thickness of the
conductor.
2003 Microchip Technology Inc.
DS00710C-page 7
AN710
TABLE 5:
AWG WIRE CHART
Wire
Size
(AWG)
Dia. in
Dia. in
Mils
(bare)
Mils
(coated)
Ohms/
1000 ft.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
289.3
287.6
229.4
204.3
181.9
162.0
166.3
128.5
114.4
101.9
90.7
80.8
72.0
64.1
57.1
50.8
45.3
40.3
35.9
32.0
28.5
25.3
22.6
20.1
17.9
—
—
—
—
—
—
—
131.6
116.3
106.2
93.5
83.3
74.1
66.7
59.5
52.9
47.2
42.4
37.9
34.0
30.2
28.0
24.2
21.6
19.3
0.126
0.156
0.197
0.249
0.313
0.395
0.498
0.628
0.793
0.999
1.26
1.59
2.00
2.52
3.18
4.02
5.05
6.39
8.05
10.1
12.8
16.2
20.3
25.7
32.4
Wire
Size
(AWG)
Dia. in
Dia. in
Mils
(bare)
Mils
(coated)
Ohms/
1000 ft.
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
15.9
14.2
12.6
11.3
10.0
8.9
8.0
7.1
6.3
5.6
5.0
4.5
4.0
3.5
3.1
2.8
2.5
2.2
2.0
1.76
1.57
1.40
1.24
1.11
17.2
15.4
13.8
12.3
11.0
9.9
8.8
7.9
7.0
6.3
5.7
5.1
4.5
4.0
3.5
3.1
2.8
2.5
2.3
1.9
1.7
1.6
1.4
1.3
50
1.1
Note: mil = 2.54 x 10-3 cm
0.99
41.0
51.4
65.3
81.2
106.0
131
162
206
261
331
415
512
648
847
1080
1320
1660
2140
2590
3350
4210
5290
6750
8420
10600
DS00710C-page 8
2003 Microchip Technology Inc.
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