Antenna Circuit Design For Rfid Applications-Microchip.pdf
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AN710
Antenna Circuit Design for RFID Applications
REVIEW OF A BASIC THEORY FOR
RFID ANTENNA DESIGN
Author:
Youbok Lee, Ph.D.
Microchip Technology Inc.
Current and Magnetic Fields
INTRODUCTION
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:
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.
EQUATION 1:
µ
o
I
4πr
Weber m
2
B
=
---------
(
cos
α
2
–
cos
α
1
)
(
⁄
)
φ
where:
I
=
current
r
=
distance from the center of wire
µ
0
=
permeability of free space and given
as 4
x 10
-7
(Henry/meter)
π
In a special case with an infinitely long wire where:
α
1
=
-180°
α
2
=0°
Equation 1 can be rewritten as:
EQUATION 2:
µ
o
I
2πr
Weber m
2
B
=
---------
(
⁄
)
φ
FIGURE 1:
CALCULATION OF MAGNETIC
FIELD B AT LOCATION P DUE TO
CURRENT
I
ON A STRAIGHT
CONDUCTING WIRE
Ζ
Wire
α
2
dL
R
α
I
α
1
P
0
X
B (into the page)
r
2003 Microchip Technology Inc.
DS00710C-page 1
AN710
FIGURE 2:
CALCULATION OF MAGNETIC
FIELD B AT LOCATION P DUE TO
CURRENT
I
ON THE LOOP
The magnetic field produced by a circular loop antenna
is given by:
EQUATION 3:
µ
o
INa
2
2 a
2
B
z
=
----------------------------------
X
32
⁄
r
2
(
+
)
I
coil
µ
o
INa
2
2
α
1
r
3
r
2
>>a
2
=
------------------
-----
for
a
R
where
r
y
P
I
=
current
radius of loop
distance from the center of loop
B
z
z
a
=
V
o
=
sin
ωt
r
=
µ
0
=
permeability of free space and given as
4 π x 10
-7
(Henry/meter)
FIGURE 3:
DECAYING OF THE MAGNETIC
FIELD B VS. DISTANCE
r
The above equation indicates that the magnetic field
strength decays with 1/r
3
. 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.
B
r
-3
r
DS00710C-page 2
2003 Microchip Technology Inc.
AN710
INDUCED VOLTAGE IN AN ANTENNA
COIL
EQUATION 5:
B
·
S
ψ
=
∫
d
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.
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.
EQUATION 4:
d
dt
V
=
–
N
-------
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:
FIGURE 4:
A BASIC CONFIGURATION OF READER AND TAG ANTENNAS IN RFID APPLICATIONS
Tag Coil
V = V
0
sin(ωt)
Ta g
B = B
0
sin(ωt)
I = I
0
sin(ωt)
Reader
Electronics
Tuning Circuit
Reader Coil
2003 Microchip Technology Inc.
DS00710C-page 3
AN710
EQUATION 8:
Using Equations 3 and 5, Equation 4 can be rewritten
as:
V
0
=
2πfNSQB
o
cos
α
EQUATION 6:
where:
N
2
dΨ
21
N
2
d
S
V
=
–
-------------
=
–
-----
(
B
⋅
d
)
∫
dt
dt
f
=
frequency of the arrival signal
µ
o
i
1
N
1
a
2
2 a
2
N
=
number of turns of coil in the loop
N
2
d
----------------------------------
·
S
–
=
-----
∫
d
area of the loop in square meters (m
2
)
S
=
dt
32
⁄
r
2
(
+
)
Q
=
quality factor of circuit
µ
o
N
1
N
2
a
2
πb
2
Β
o
=
strength of the arrival signal
(
)
di
1
dt
=
–
-----------------------------------------
-------
α
=
angle of arrival of the signal
32
⁄
2 a
2
r
2
(
+
)
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.
M
di
1
dt
=
–
-------
FIGURE 5:
ORIENTATION DEPENDENCY OF
THE TAG ANTENNA
where:
V
=
voltage in the tag coil
i
1
=
current on the reader coil
a
=
radius of the reader coil
B-field
b
=
radius of tag coil
r
=
distance between the two coils
M
=
mutual inductance between the tag
and reader coils, and given by:
a
Ta g
EQUATION 7:
2
µ
o
π
N
1
N
2
()
ab
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.
M
=
--------------------------------------
32
⁄
2 a
2
r
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 V
o
in a tuned loop coil is given by:
DS00710C-page 4
2003 Microchip Technology Inc.
AN710
EXAMPLE 1:
CALCULATION OF B-FIELD IN
A TAG COIL
EXAMPLE 3:
OPTIMUM COIL DIAMETER
OF THE READER COIL
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:
The MCRF355 device turns on when the antenna
coil develops 4 V
PP
across it. This voltage is rectified
and the device starts to operate when it reaches 2.4
V
DC
. The B-field to induce a 4 V
PP
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 11:
EQUATION 9:
3
---
a
2
r
2
(
+
)
NI
=
K
-------------------------
V
o
=
2πfNSQB
o
cos
α
=
4
a
2
and
2B
z
µ
o
K
=
---------
where:
⁄
2πfNSQ
42
(
)
–
2
B
o
=
-----------------------------------
=
0.0449
(
µwbm
)
cos
α
By taking derivative with respect to the radius a,
where the following parameters are used in the
above calculation:
12
⁄
3 2
⁄
a
2
r
2
2a
3
2aa
2
r
2
d N()
da
K
32
⁄
(
+
)
(
)
–
(
+
)
(85.6 x 54) mm
2
(ISO card
size) = 0.0046224 m
2
Tag coil size
=
--------------
=
---------------------------------------------------------------------------------------------------
a
4
Frequency
=
13.56 MHz
12
⁄
a
2
2r
2
) a
2
r
2
(
–
(
+
)
Number of turns =
4
=
K
--------------------------------------------------------
a
3
Q of tag antenna
coil
= 0
The above equation becomes minimized when:
AC coil voltage to
turn on the tag
=4 V
PP
The above result shows a relationship between the
read range versus optimum coil diameter. The optimum
coil diameter is found as:
cosα
=
1 (normal direction, α = 0).
EQUATION 12:
EXAMPLE 2:
NUMBER OF TURNS AND
CURRENT (AMPERE-TURNS)
a
=
2
r
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:
where:
a
=
radius of coil
r
=
read range.
EQUATION 10:
The result indicates that the optimum loop radius, a, is
1.414 times the demanded read range r.
a
2
r
2
32
⁄
2B
z
(
+
)
N(
rms
=
-------------------------------
µa
2
–
6
) 0.1
2
2
32
⁄
2 0.0449
(
×
10
(
+
(
0.38
)
)
=
---------------------------------------------------------------------------------------
–
7
) 0.1
2
(
4π
×
10
(
)
=
0.43 ampere - turns
(
)
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
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