# Power Transmission of UHF Passive Embedded RFID in Tires

Authors: Shengbo Hu; Bing Si; Heng Shu; Jinrong Mo
Journal: International Journal of Antennas and Propagation
 (2014)

---

## Abstract

UHF passive RFID tags embedded in tires have a deep impact on tire life cycle management and tire monitoring. In this work, we present the power transmission of UHF passive embedded RFID in tires. In UHF passive embedded RFID systems in tires, the bidirectional radio link between reader and tags goes through air and tires. The total path loss contains reflection loss at tire-air boundaries and attenuation loss in the tires. The power transmission is based on the permittivity of tires and tire-air boundary conditions. We give an OCP method for measuring the permittivity of tires. By analyzing the radio link for UHF passive RFID, we establish a model of wave propagation of UHF embedded RFID in tires and make numerical analyses. Numerical analyses show that the error of the OCP methods for measuring the permittivity of tires is small, the parallel polarization and normal incidence of wave are chosen for improving the performance of the UHF embedded RFID in tires, and distance is chosen to keep power transmission function from locating valley.


---

## Body

## 1. Introduction

Acting as sensors, passive RFID tags can avoid sensor nodes bulky and battery powered. For that reason, UHF passive tags embedded in tires have been used widely for tire life cycle management in the USA and the European Union [1, 2]. To meet the Automotive Industry Action Group’s B-11 standard for North American, Michelin began offering automakers the option of purchasing tires with embedded tags [3]. Besides, the combinations of UHF passive tags embedded in tire and tire pressure monitoring are paid attention highly to improve the reliability of tire and tire control systems [4].However, range has been one of the hardest challenges in UHF passive RFID embedded in tires, because the rubber makes it harder to read the tag. When Michelin took off-the-shelf, UHF passive tags and embedded them in tires, the read distance dropped to less than three inches [3]. The main difference between the common RFID and RFID embedded in tires is communication medium, which attenuates RF power from the reader in RFID embedded in tires. To improve the range and reliability of RFID embedded in tires, it is of great concern to study power transmission of wave propagation for UHF passive embedded RFID in tires, because the tags do not contain any battery and rely on the electromagnetic field for both power and communication. In this paper, we present the power transmission of wave propagation for UHF passive embedded RFID in tires and lay out the foundations for reliable communication in this environment.In UHF passive RFID systems, a bidirectional radio link is established between reader and tags, which can be classified a forward link from the reader to tags and a backward link from the tags to reader [5]. Depending on the characteristics of reader and tags, the propagation channel properties like path loss and fading, the power transmission coefficient and the channel transmissions are investigated in [5–7]. In UHF passive embedded RFID systems in tires, the bidirectional radio link between reader and tags goes through air and tires. The total path loss contains several factors: reflection loss due to reflected power at tire-air boundaries, attenuation loss in the tires, and spreading loss which is simply due to the radiation properties of antenna. Each of these factors can be analyzed using the permittivity of tires and tire-air boundary conditions.So, this paper focuses on wave propagation for UHF passive embedded RFID in tires based on the permittivity of tires and tire-air boundary conditions. Hence, Section2 presents how to measure the permittivity of tires. Section 3 describes the radio link for UHF RFID systems. Section 4 gives a propagation model of UHF passive embedded RFID systems in car tires. Section 5 describes numerical calculation and discussion. Section 6 concludes this paper.


## 2. Measuring the Permittivity of Tires

### 2.1. Measuring the Permittivity

Several techniques have been developed for measuring the permittivity [8–10]. However, some, such as resonant cavity or wave-guide transmission line cells, require test hardware machining and destructive processing. And open ended coaxial probe (OCP) technique is currently one of the most popular techniques for measuring the permittivity. OCP technique can perform nondestructive, broadband (RF and microwave bands), and high temperature measurement. Its well-developed theory makes it possible to obtain sufficiently accurate results.A schematic for a coaxial open ended probe is shown in Figure1. To reduce significantly measuring error, the material being tested is placed in close contact with the probe’s flat end. The reflection coefficient, measured with a vector network analyzer (VNA), is used as inverse calculation of the permittivity of the material.Measuring reflection coefficients with open ended coaxial probe.
(a)
Measuring system
(b)
Geometry modelAn equivalent circuit of admittance model for a coaxial open ended probe is shown in Figure2. In Figure 2, Y
c is the probe characteristic admittance, and Y
(
ω
,
ε
*
) is the load admittance, including the inner admittance Y
i
(
ω
)
=
j
ω
C
i of the capacitance C
i between outer conductor and inner conductor and the outer admittance Y
o
(
ω
,
ε
*
), obtained by solving the following equation [11]:
(1)
Y
o
(
ω
,
ε
*
)
=
j
2
ω
ε
0
ε
*
[
ln
⁡
⁡
(
b
/
a
)
]
2
∬
a
b
∫
0
π
cos
⁡
φ
e
-
j
k
r
r
d
φ
d
ρ
′
d
ρ
,
where k
=
ω
μ
ε
′, μ is the permeability, ω is the operating frequency, (
ρ
,
ρ
′
,
φ
) are cylindrical coordinates, r
=
[
ρ
2
+
ρ
′
2
-
2
ρ
ρ
′
cos
⁡
φ
]
1
/
2, and a and b are, respectively, the interior and the external radius of the probe. And (1) can be the series expansion form of (2):
(2)
Y
o
(
ω
,
ε
*
)
=
∑
n
=
0
∞
(
-
1
)
(
-
j
ω
)
n
+
1
C
n
ε
*
(
n
+
2
)
/
2
,
where
(3)
C
n
=
2
(
μ
0
ε
0
)
(
n
+
2
)
/
2
n
!
μ
0
[
ln
⁡
(
b
/
a
)
]
2
∬
a
b
∫
0
π
r
n
-
1
cos
⁡
φ
d
φ
d
ρ
′
d
ρ
.Equation (3) shows that C
n is constant. For convenience, (2) can be truncated to 3 terms with the C
0, C
1, and C
2. So, Y
(
ω
,
ε
*
) can be given as below:
(4)
Y
(
ω
,
ε
*
)
=
j
ω
C
i
+
j
ω
ε
*
C
0
+
ω
2
(
ε
*
)
1.5
C
1
+
j
ω
3
(
ε
*
)
2
C
2
,
where ε
*
C
0 is the fringing capacitance of the probe, ω
2
(
ε
*
)
2
C
2 is the fringing capacitance generated from a test material, and ω
2
(
ε
*
)
1.5
C
1 is the equivalent conductance radiated from the probe.Figure 2
The equivalent circuit of admittance model for a coaxial open ended probe.The load admittanceY
(
ω
,
ε
*
) can be obtained from the EM wave reflection coefficient Γ
(
ω
,
ε
*
) using the following relation:
(5)
Y
(
ω
,
ε
*
)
=
Y
c
1
-
Γ
(
ω
,
ε
*
)
1
+
Γ
(
ω
,
ε
*
)
.Hence, measuring the permittivity can be performed using the following steps.Step 1.
Using VNA, we measure the four different reflection coefficientsΓ
1, Γ
2, Γ
3, and Γ
4 associated with the four different frequencies using a standard material with the known permittivity. Using (4) and (5), the four unknown parameters C
i, C
0, C
1, and C
2 can be solved.Step 2.
Using VNA, we measure the reflection coefficientsΓ associated with some frequencies using the test material. Using (4) and (5), the permittivity of the test material can be calculated by a suitable iterative method.


### 2.2. Measurement Setup for Tires

The tire sidewall and the position of the RFID tag embedded in tire are displayed in Figure3. The tag is embedded parallel to the outer steel mesh at a distance that depends on the tire size and ranges from 4 to 8 cm above the inner steel mesh [1].Figure 3
The RFID tag embedded in tires.To reduce significantly measuring error using OCP technique, the tire sidewall specimen has to meet the following conditions.(i)
The surface of the tire sidewall specimen has to be flat. A piece of the tire sidewall is cut out, and the cross section is polished to obtain a flat surface.
(ii)
The specimen has to have semi-infinite thickness so that the penetration of the field must be much smaller than the specimen’s thickness.
(iii)
There must not be air gaps between probe and the tire sidewall specimen.Figure4 illustrates an OCP measurement system. The system consists of a VNA, a thermometer, a coaxial probe, and a manipulator with screw for fixing the tire sidewall specimen. Tightening the screw, the probe is pressed against the specimen until no more variation of the measurement results is observed.Figure 4
The OCP measurement system.


### 2.3. Simulation Verifying Using HFSS

Simulation verifying using HFSS to verify the measurement accuracy using OCP technique, an OCP model using HFSS (high frequency structure simulator) is set up to compare. Given the measured permittivity of tire specimen using the measuring methods presented in Section2.1, the reflection coefficient is solved using the OCP model. And the simulation and measurement reflection coefficients are compared.The OCP model based on HFSS is shown in Figure5. In Figure 5, the inner and outer conductors of the probe are made of gilded brass, and the space between the inner and outer conductor is filled in Teflon dielectric material. The tire specimen is modeled as a cylinder. To avoid perfectly conducting boundaries around the tire sidewall material, an air box is implemented that surrounds the whole simulation setup.Figure 5
OCP model based on HFSS.


## 2.1. Measuring the Permittivity

Several techniques have been developed for measuring the permittivity [8–10]. However, some, such as resonant cavity or wave-guide transmission line cells, require test hardware machining and destructive processing. And open ended coaxial probe (OCP) technique is currently one of the most popular techniques for measuring the permittivity. OCP technique can perform nondestructive, broadband (RF and microwave bands), and high temperature measurement. Its well-developed theory makes it possible to obtain sufficiently accurate results.A schematic for a coaxial open ended probe is shown in Figure1. To reduce significantly measuring error, the material being tested is placed in close contact with the probe’s flat end. The reflection coefficient, measured with a vector network analyzer (VNA), is used as inverse calculation of the permittivity of the material.Measuring reflection coefficients with open ended coaxial probe.
(a)
Measuring system
(b)
Geometry modelAn equivalent circuit of admittance model for a coaxial open ended probe is shown in Figure2. In Figure 2, Y
c is the probe characteristic admittance, and Y
(
ω
,
ε
*
) is the load admittance, including the inner admittance Y
i
(
ω
)
=
j
ω
C
i of the capacitance C
i between outer conductor and inner conductor and the outer admittance Y
o
(
ω
,
ε
*
), obtained by solving the following equation [11]:
(1)
Y
o
(
ω
,
ε
*
)
=
j
2
ω
ε
0
ε
*
[
ln
⁡
⁡
(
b
/
a
)
]
2
∬
a
b
∫
0
π
cos
⁡
φ
e
-
j
k
r
r
d
φ
d
ρ
′
d
ρ
,
where k
=
ω
μ
ε
′, μ is the permeability, ω is the operating frequency, (
ρ
,
ρ
′
,
φ
) are cylindrical coordinates, r
=
[
ρ
2
+
ρ
′
2
-
2
ρ
ρ
′
cos
⁡
φ
]
1
/
2, and a and b are, respectively, the interior and the external radius of the probe. And (1) can be the series expansion form of (2):
(2)
Y
o
(
ω
,
ε
*
)
=
∑
n
=
0
∞
(
-
1
)
(
-
j
ω
)
n
+
1
C
n
ε
*
(
n
+
2
)
/
2
,
where
(3)
C
n
=
2
(
μ
0
ε
0
)
(
n
+
2
)
/
2
n
!
μ
0
[
ln
⁡
(
b
/
a
)
]
2
∬
a
b
∫
0
π
r
n
-
1
cos
⁡
φ
d
φ
d
ρ
′
d
ρ
.Equation (3) shows that C
n is constant. For convenience, (2) can be truncated to 3 terms with the C
0, C
1, and C
2. So, Y
(
ω
,
ε
*
) can be given as below:
(4)
Y
(
ω
,
ε
*
)
=
j
ω
C
i
+
j
ω
ε
*
C
0
+
ω
2
(
ε
*
)
1.5
C
1
+
j
ω
3
(
ε
*
)
2
C
2
,
where ε
*
C
0 is the fringing capacitance of the probe, ω
2
(
ε
*
)
2
C
2 is the fringing capacitance generated from a test material, and ω
2
(
ε
*
)
1.5
C
1 is the equivalent conductance radiated from the probe.Figure 2
The equivalent circuit of admittance model for a coaxial open ended probe.The load admittanceY
(
ω
,
ε
*
) can be obtained from the EM wave reflection coefficient Γ
(
ω
,
ε
*
) using the following relation:
(5)
Y
(
ω
,
ε
*
)
=
Y
c
1
-
Γ
(
ω
,
ε
*
)
1
+
Γ
(
ω
,
ε
*
)
.Hence, measuring the permittivity can be performed using the following steps.Step 1.
Using VNA, we measure the four different reflection coefficientsΓ
1, Γ
2, Γ
3, and Γ
4 associated with the four different frequencies using a standard material with the known permittivity. Using (4) and (5), the four unknown parameters C
i, C
0, C
1, and C
2 can be solved.Step 2.
Using VNA, we measure the reflection coefficientsΓ associated with some frequencies using the test material. Using (4) and (5), the permittivity of the test material can be calculated by a suitable iterative method.


## 2.2. Measurement Setup for Tires

The tire sidewall and the position of the RFID tag embedded in tire are displayed in Figure3. The tag is embedded parallel to the outer steel mesh at a distance that depends on the tire size and ranges from 4 to 8 cm above the inner steel mesh [1].Figure 3
The RFID tag embedded in tires.To reduce significantly measuring error using OCP technique, the tire sidewall specimen has to meet the following conditions.(i)
The surface of the tire sidewall specimen has to be flat. A piece of the tire sidewall is cut out, and the cross section is polished to obtain a flat surface.
(ii)
The specimen has to have semi-infinite thickness so that the penetration of the field must be much smaller than the specimen’s thickness.
(iii)
There must not be air gaps between probe and the tire sidewall specimen.Figure4 illustrates an OCP measurement system. The system consists of a VNA, a thermometer, a coaxial probe, and a manipulator with screw for fixing the tire sidewall specimen. Tightening the screw, the probe is pressed against the specimen until no more variation of the measurement results is observed.Figure 4
The OCP measurement system.


## 2.3. Simulation Verifying Using HFSS

Simulation verifying using HFSS to verify the measurement accuracy using OCP technique, an OCP model using HFSS (high frequency structure simulator) is set up to compare. Given the measured permittivity of tire specimen using the measuring methods presented in Section2.1, the reflection coefficient is solved using the OCP model. And the simulation and measurement reflection coefficients are compared.The OCP model based on HFSS is shown in Figure5. In Figure 5, the inner and outer conductors of the probe are made of gilded brass, and the space between the inner and outer conductor is filled in Teflon dielectric material. The tire specimen is modeled as a cylinder. To avoid perfectly conducting boundaries around the tire sidewall material, an air box is implemented that surrounds the whole simulation setup.Figure 5
OCP model based on HFSS.


## 3. Radio Link for UHF Passive RFID

In passive UHF RFID systems, a bidirectional radio link is established between reader and tags, including a forward link from the reader to tags and a backward link from the tags to reader. What radio link for UHF passive RFID differs from conventional radio is that the backward link resembles radar link. Besides, the RFID tag’s antenna absorbs waves as a function of its load match and reemits waves as a function of its load mismatch.


### 3.1. Power Absorbing Coefficient

RFID tag consists of an antenna and chip. The impedance matching of tag antenna and chip strongly influences the RF power transmission and the communication performance between reader and tags. Because of IC technological limit, the impedance of a chip cannot be chosen arbitrarily [12]. So, the chip’s input impedance is designed to switch between two values, between the conjugate impedance called as absorbing impedance Z
chip
1 and other impedance called as reflecting impedance Z
chip
2. The quality of the impedance match can be defined by the power absorbing coefficient τ, which is the power accepted by the chip and the available power P
tag at the antenna port [5, 12]:
(6)
τ
=
4
Re
[
Z
ant
]
Re
[
Z
chip
1
]
Re
[
Z
ant
+
Z
chip
1
]
2
+
Im
⁡
[
Z
ant
+
Z
chip
1
]
2
,
where Z
ant is the tag antenna’s input impedance and 0
≤
τ
≤
1. When τ
=
1, all available power is absorbed by the chip. And when  τ
=
0, no available power is absorbed by the chip. So, the range of frequency that τ reaches a demand value is defined as the bandwidth of the tag antenna. This shows that a best designed tag antenna is very important to improve the performance of UHF passive RFID.


### 3.2. Power Transmission Coefficient

In a passive RFID, the power absorbed by the chip in forward link can be expressed as(7)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
,
where P
TX
.
reader is the transmitted power from reader and P
chip must be higher than the tag’s sensitivity for the tag’s normal work. And |
S
21
|
2 is the power transmitted coefficient in the forward link, depending on the antenna power transmission of reader and tag (e.g., antenna gain) and the propagation channel properties like path loss and fading [5].The power received by the reader from the tag can be expressed as in the backward link:(8)
P
RX
.
reader
=
|
S
12
|
2
η
P
tag
=
|
S
12
|
2
η
|
S
21
|
2
P
TX
.
reader
,
where η is the modulation efficiency, which is defined as the ratio of the power scattered by the tag and the power available at the tag antenna output. |
S
12
|
2 is the power transmitted coefficient in the backward link. As real propagation environment is symmetrical, |
S
12
|
2
=
|
S
21
|
2.


## 3.1. Power Absorbing Coefficient

RFID tag consists of an antenna and chip. The impedance matching of tag antenna and chip strongly influences the RF power transmission and the communication performance between reader and tags. Because of IC technological limit, the impedance of a chip cannot be chosen arbitrarily [12]. So, the chip’s input impedance is designed to switch between two values, between the conjugate impedance called as absorbing impedance Z
chip
1 and other impedance called as reflecting impedance Z
chip
2. The quality of the impedance match can be defined by the power absorbing coefficient τ, which is the power accepted by the chip and the available power P
tag at the antenna port [5, 12]:
(6)
τ
=
4
Re
[
Z
ant
]
Re
[
Z
chip
1
]
Re
[
Z
ant
+
Z
chip
1
]
2
+
Im
⁡
[
Z
ant
+
Z
chip
1
]
2
,
where Z
ant is the tag antenna’s input impedance and 0
≤
τ
≤
1. When τ
=
1, all available power is absorbed by the chip. And when  τ
=
0, no available power is absorbed by the chip. So, the range of frequency that τ reaches a demand value is defined as the bandwidth of the tag antenna. This shows that a best designed tag antenna is very important to improve the performance of UHF passive RFID.


## 3.2. Power Transmission Coefficient

In a passive RFID, the power absorbed by the chip in forward link can be expressed as(7)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
,
where P
TX
.
reader is the transmitted power from reader and P
chip must be higher than the tag’s sensitivity for the tag’s normal work. And |
S
21
|
2 is the power transmitted coefficient in the forward link, depending on the antenna power transmission of reader and tag (e.g., antenna gain) and the propagation channel properties like path loss and fading [5].The power received by the reader from the tag can be expressed as in the backward link:(8)
P
RX
.
reader
=
|
S
12
|
2
η
P
tag
=
|
S
12
|
2
η
|
S
21
|
2
P
TX
.
reader
,
where η is the modulation efficiency, which is defined as the ratio of the power scattered by the tag and the power available at the tag antenna output. |
S
12
|
2 is the power transmitted coefficient in the backward link. As real propagation environment is symmetrical, |
S
12
|
2
=
|
S
21
|
2.


## 4. Model of Power Transmission of UHF Passive RFID Embedded in Tires

### 4.1. Harmonic Waves

For time-harmonic fields, when the medium presents a conductivityσ and permeability μ, at the operating frequency ω, a permittivity ε
*, the wave equation can be written as a time-independent wave equation towards +z direction:
(9)
∇
2
E
-
γ
2
E
=
0
,
(10)
∇
2
H
-
γ
2
H
=
0
,
(11)
-
γ
2
=
k
2
(
1
-
j
tan
δ
)
=
ω
2
μ
ε
*
,
where ε
*
=
ε
′
(
1
-
j
tan
δ
) and k
=
ω
μ
ε
′ is the wave number corresponding to an unbounded lossless medium with a real dielectric constant ε
′.For uniform plane waves,∇
2
=
∂
2
/
∂
2
z, so (9) and (10) have solutions of the form E
e
γ
z and H
e
γ
z, and the instantaneous values for the fields are given as follows:
(12)
E
→
=
Re
{
E
e
-
α
z
e
j
(
ω
t
-
β
z
)
}
,
H
→
=
Re
{
H
e
-
α
z
e
j
(
ω
t
-
β
z
)
}
,
where the attenuation constant α and the phase constant β can be expressed respectively as follows [13]:
(13)
α
=
ω
(
μ
ε
′
2
)
1
/
2
[
(
1
+
ta
n
2
δ
)
1
/
2
-
1
]
1
/
2
,
β
=
ω
(
μ
ε
′
2
)
1
/
2
[
(
1
+
ta
n
2
δ
)
1
/
2
+
1
]
1
/
2
.So, the electric strength decreases with distancez are given as:
(14)
E
=
E
0
e
-
α
z
cos
⁡
β
z
.Substituting (14) into power equation, we have
(15)
P
=
P
0
|
cos
⁡
2
β
z
|
e
-
2
α
z
.


### 4.2. Power Transmission for RFID Embedded in Tires

The RFID scenarios in space and embedded in tires are shown in Figure6. In Figure 6, the incident angle of waves is θ
i.RFID scenarios.
(a)
RFID scenarios in free space
(b)
RFID scenarios embedded in tireIn the free space, the absorbing power by the RFID tag is given as(16)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
=
τ
(
λ
4
π
R
)
2
G
T
P
TX
.
reader
,
where λ is the free space wavelength, R is the distance from RFID reader, and G
T is the gain of the tag’s antenna.In the scenarios embedded in tires, (16) can be modified as
(17)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
=
τ
(
λ
4
π
R
1
)
2
|
T
c
|
2
G
T
|
cos
⁡
2
β
l
|
e
-
2
α
l
P
TX
.
reader
=
τ
(
λ
4
π
R
1
)
2
G
t
T
(
f
,
θ
i
,
l
)
P
TX
.
reader
,
where R
1 is the distance between tires and the reader, T
c is electric field transmission coefficient at boundary of tires and free space, and T
(
f
,
θ
i
,
l
)
=
|
T
c
|
2
|
cos
⁡
2
β
l
|
e
-
2
α
l is power transmission function, depending on θ
i and the distance l in tires.When a plane EM wave incident at an oblique angle on tires interface, there are two cases to be considered: incident electric field has polarization parallel to the plane of incidence, and incident electric field has polarization that is perpendicular to the plane of incidence. So, from the boundary conditions, that is, continuity of tangential electric and magnetic fields at the car tire interface, and using the Snell’s laws of reflection and refraction, theT
c can be derived as follows.Case 1.
Parallel polarization:(18)
T
c
=
2
η
1
cos
⁡
θ
i
η
1
cos
⁡
θ
t
+
η
0
cos
⁡
θ
i
.Case 2.
Perpendicular polarization:(19)
T
c
=
2
η
1
cos
⁡
θ
i
η
1
cos
⁡
θ
i
+
η
0
cos
⁡
θ
t
.


## 4.1. Harmonic Waves

For time-harmonic fields, when the medium presents a conductivityσ and permeability μ, at the operating frequency ω, a permittivity ε
*, the wave equation can be written as a time-independent wave equation towards +z direction:
(9)
∇
2
E
-
γ
2
E
=
0
,
(10)
∇
2
H
-
γ
2
H
=
0
,
(11)
-
γ
2
=
k
2
(
1
-
j
tan
δ
)
=
ω
2
μ
ε
*
,
where ε
*
=
ε
′
(
1
-
j
tan
δ
) and k
=
ω
μ
ε
′ is the wave number corresponding to an unbounded lossless medium with a real dielectric constant ε
′.For uniform plane waves,∇
2
=
∂
2
/
∂
2
z, so (9) and (10) have solutions of the form E
e
γ
z and H
e
γ
z, and the instantaneous values for the fields are given as follows:
(12)
E
→
=
Re
{
E
e
-
α
z
e
j
(
ω
t
-
β
z
)
}
,
H
→
=
Re
{
H
e
-
α
z
e
j
(
ω
t
-
β
z
)
}
,
where the attenuation constant α and the phase constant β can be expressed respectively as follows [13]:
(13)
α
=
ω
(
μ
ε
′
2
)
1
/
2
[
(
1
+
ta
n
2
δ
)
1
/
2
-
1
]
1
/
2
,
β
=
ω
(
μ
ε
′
2
)
1
/
2
[
(
1
+
ta
n
2
δ
)
1
/
2
+
1
]
1
/
2
.So, the electric strength decreases with distancez are given as:
(14)
E
=
E
0
e
-
α
z
cos
⁡
β
z
.Substituting (14) into power equation, we have
(15)
P
=
P
0
|
cos
⁡
2
β
z
|
e
-
2
α
z
.


## 4.2. Power Transmission for RFID Embedded in Tires

The RFID scenarios in space and embedded in tires are shown in Figure6. In Figure 6, the incident angle of waves is θ
i.RFID scenarios.
(a)
RFID scenarios in free space
(b)
RFID scenarios embedded in tireIn the free space, the absorbing power by the RFID tag is given as(16)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
=
τ
(
λ
4
π
R
)
2
G
T
P
TX
.
reader
,
where λ is the free space wavelength, R is the distance from RFID reader, and G
T is the gain of the tag’s antenna.In the scenarios embedded in tires, (16) can be modified as
(17)
P
chip
=
τ
P
tag
=
τ
|
S
21
|
2
P
TX
.
reader
=
τ
(
λ
4
π
R
1
)
2
|
T
c
|
2
G
T
|
cos
⁡
2
β
l
|
e
-
2
α
l
P
TX
.
reader
=
τ
(
λ
4
π
R
1
)
2
G
t
T
(
f
,
θ
i
,
l
)
P
TX
.
reader
,
where R
1 is the distance between tires and the reader, T
c is electric field transmission coefficient at boundary of tires and free space, and T
(
f
,
θ
i
,
l
)
=
|
T
c
|
2
|
cos
⁡
2
β
l
|
e
-
2
α
l is power transmission function, depending on θ
i and the distance l in tires.When a plane EM wave incident at an oblique angle on tires interface, there are two cases to be considered: incident electric field has polarization parallel to the plane of incidence, and incident electric field has polarization that is perpendicular to the plane of incidence. So, from the boundary conditions, that is, continuity of tangential electric and magnetic fields at the car tire interface, and using the Snell’s laws of reflection and refraction, theT
c can be derived as follows.Case 1.
Parallel polarization:(18)
T
c
=
2
η
1
cos
⁡
θ
i
η
1
cos
⁡
θ
t
+
η
0
cos
⁡
θ
i
.Case 2.
Perpendicular polarization:(19)
T
c
=
2
η
1
cos
⁡
θ
i
η
1
cos
⁡
θ
i
+
η
0
cos
⁡
θ
t
.


## 5. Numerical Analyses

### 5.1. Measuring the Permittivity of Tires

A standard tire (CPC2205/55 R16 91V) with the known permittivity (the permittivity isε
′
=
3.5 and tan
δ
=
0.03 at frequency 866 MHz) is used to determine the parameters C
i, C
0, C
1, and C
2. Using the measuring methods presented in Section 2.1, C
i, C
0, C
1, and C
2 are 0.00113 pF, 2.324 × 10–14 pF, 1.518 × 10–42 pF, and 1.6345 × 10–50 pF, respectively.The measuring results for reflection coefficients in a Smith chart are shown in Figure7, using a test car tire (GL 274A, made in Guizhou Tire Co., LTD., China) with a vector network analyzer (AV 3629/A) between 100 MHz and 5 GHz at room temperature. Using (4) and (5), the permittivity of the test car tire can be determined to be ε
′
=
3.78 and tan
δ
=
0.038.Figure 7
Measured reflection coefficients of a test car tire.Measuring and simulation results can be compared using the methods presented in Section2.3. In the OCP model, the inner and outer radiuses of the probe are 0.65 mm and 2.35 mm, respectively. The thickness of Teflon with a relative permittivity of ε
′ and tan
δ
=
0.001 is 1.35 mm. The test tire is modeled as a cylinder with a radius of 10 mm and a height of 10 mm. The absolute error of the real part of simulation and measuring coefficients and the absolute error of the imaginary part of these versus frequency are shown in Figure 8. And the absolute error of the simulation and measuring coefficients is shown in Figure 9. Figures 8 and 9 show that there is small deviation (<0.004) between simulation and measurement. So, it shows that the numerical simulation has good agreement with physical experiment, and the methods measuring the permittivity of tires are feasible.Figure 8
Absolute error values of real part and imaginary part.Figure 9
Absolute error values.


### 5.2. Effects of Incident Angleθ
i on T
c

The permittivity of the test tire isε
′
=
3.78 and tan
δ
=
0.038 at frequency 866 MHz from Section 5.1. The incident angle θ
i is 0°~90°. A magnitude of T
c for the parallel and perpendicular polarization is shown in Figure 10.Figure 10
Effects ofθ
i on T
c.In Figure10, T
c for the parallel and perpendicular polarization decreases with increasing incident angle θ
i. T
c for the perpendicular polarization decreases faster than T
c for the parallel polarization. This conclusion can be obtained from the experiment in Figure 11. The experiment setup contains a reader XC-RF807 and two liner polarization antennae XC-AF26 (one is a horizontal polarization antenna and the other one is vertical polarization). The carrier frequency of the reader is 866 MHz, and the power o is 30 dBmW. The gain of the antenna is greater than 12 dBi, and the frequency range is from 840 MHz to 868 MHz. The distance between GL274A tire and reader is 1 m, and the depth of the tag embed in the tire is 9 mm. Figure 12 shows the relation between the identification rate and angle of incidence.Figure 11
Experiment setup.Figure 12
Relations between angle of incidenceθ
i and the identification rate.So, the parallel polarization and normal incidence are chosen for improving the performance of UHF RFID embedded in tires.


### 5.3. Effects of Distancel on T
(
f
,
θ
i
,
l
)

For convenience, The incident angleθ
i is 0°, and the permittivity of the test tire is ε
′
=
3.78 and tan
δ
=
0.038 at frequency 866 MHz f. A magnitude of T
(
f
,
θ
i
,
l
) for the distance l is shown in Figure 13.Figure 13
Effects ofl onT
(
f
,
θ
i
,
l
).In Figure13, T
(
f
,
θ
i
,
l
) decreases periodically with increasing the distance l in tires. This conclusion can be obtained from the experiment in Figure 11. In this experiment, 8 GAL274A tires are used from Guizhou tire limited company in China. When the tires are vulcanizing, the depths of the tag embedded in the tire are 0.0 mm (tag is pasted on the surface of the tire), 3.0 mm, 6.0 mm, 9.0 mm, 12 mm, 15 mm, 18 mm, 21 mm, and 24 mm, respectively (because of the limitation of the thickness of the tire, the biggest embedded depth is 24 mm). Figure 14 shows the relation between the recognition rate and the embedded depth l. It means the recognition rate of tire embedded RFID system declines along with l also fluctuates along with l. This means the power transmission of tire embedded RFID system declines along with l also fluctuates along with l.Figure 14
Relationsl and identification rate.So, the distancel is chosen to keep T
(
f
,
θ
i
,
l
) from locating valley.


## 5.1. Measuring the Permittivity of Tires

A standard tire (CPC2205/55 R16 91V) with the known permittivity (the permittivity isε
′
=
3.5 and tan
δ
=
0.03 at frequency 866 MHz) is used to determine the parameters C
i, C
0, C
1, and C
2. Using the measuring methods presented in Section 2.1, C
i, C
0, C
1, and C
2 are 0.00113 pF, 2.324 × 10–14 pF, 1.518 × 10–42 pF, and 1.6345 × 10–50 pF, respectively.The measuring results for reflection coefficients in a Smith chart are shown in Figure7, using a test car tire (GL 274A, made in Guizhou Tire Co., LTD., China) with a vector network analyzer (AV 3629/A) between 100 MHz and 5 GHz at room temperature. Using (4) and (5), the permittivity of the test car tire can be determined to be ε
′
=
3.78 and tan
δ
=
0.038.Figure 7
Measured reflection coefficients of a test car tire.Measuring and simulation results can be compared using the methods presented in Section2.3. In the OCP model, the inner and outer radiuses of the probe are 0.65 mm and 2.35 mm, respectively. The thickness of Teflon with a relative permittivity of ε
′ and tan
δ
=
0.001 is 1.35 mm. The test tire is modeled as a cylinder with a radius of 10 mm and a height of 10 mm. The absolute error of the real part of simulation and measuring coefficients and the absolute error of the imaginary part of these versus frequency are shown in Figure 8. And the absolute error of the simulation and measuring coefficients is shown in Figure 9. Figures 8 and 9 show that there is small deviation (<0.004) between simulation and measurement. So, it shows that the numerical simulation has good agreement with physical experiment, and the methods measuring the permittivity of tires are feasible.Figure 8
Absolute error values of real part and imaginary part.Figure 9
Absolute error values.


## 5.2. Effects of Incident Angleθ
i on T
c

The permittivity of the test tire isε
′
=
3.78 and tan
δ
=
0.038 at frequency 866 MHz from Section 5.1. The incident angle θ
i is 0°~90°. A magnitude of T
c for the parallel and perpendicular polarization is shown in Figure 10.Figure 10
Effects ofθ
i on T
c.In Figure10, T
c for the parallel and perpendicular polarization decreases with increasing incident angle θ
i. T
c for the perpendicular polarization decreases faster than T
c for the parallel polarization. This conclusion can be obtained from the experiment in Figure 11. The experiment setup contains a reader XC-RF807 and two liner polarization antennae XC-AF26 (one is a horizontal polarization antenna and the other one is vertical polarization). The carrier frequency of the reader is 866 MHz, and the power o is 30 dBmW. The gain of the antenna is greater than 12 dBi, and the frequency range is from 840 MHz to 868 MHz. The distance between GL274A tire and reader is 1 m, and the depth of the tag embed in the tire is 9 mm. Figure 12 shows the relation between the identification rate and angle of incidence.Figure 11
Experiment setup.Figure 12
Relations between angle of incidenceθ
i and the identification rate.So, the parallel polarization and normal incidence are chosen for improving the performance of UHF RFID embedded in tires.


## 5.3. Effects of Distancel on T
(
f
,
θ
i
,
l
)

For convenience, The incident angleθ
i is 0°, and the permittivity of the test tire is ε
′
=
3.78 and tan
δ
=
0.038 at frequency 866 MHz f. A magnitude of T
(
f
,
θ
i
,
l
) for the distance l is shown in Figure 13.Figure 13
Effects ofl onT
(
f
,
θ
i
,
l
).In Figure13, T
(
f
,
θ
i
,
l
) decreases periodically with increasing the distance l in tires. This conclusion can be obtained from the experiment in Figure 11. In this experiment, 8 GAL274A tires are used from Guizhou tire limited company in China. When the tires are vulcanizing, the depths of the tag embedded in the tire are 0.0 mm (tag is pasted on the surface of the tire), 3.0 mm, 6.0 mm, 9.0 mm, 12 mm, 15 mm, 18 mm, 21 mm, and 24 mm, respectively (because of the limitation of the thickness of the tire, the biggest embedded depth is 24 mm). Figure 14 shows the relation between the recognition rate and the embedded depth l. It means the recognition rate of tire embedded RFID system declines along with l also fluctuates along with l. This means the power transmission of tire embedded RFID system declines along with l also fluctuates along with l.Figure 14
Relationsl and identification rate.So, the distancel is chosen to keep T
(
f
,
θ
i
,
l
) from locating valley.


## 6. Conclusions

From now on, UHF RFID tags embedded in tires have a deep impact on tire life cycle management and tire monitoring. So, we present the power transmission of wave propagation for UHF embedded RFID in tires.In UHF passive embedded RFID systems in tires, the bidirectional radio link between reader and tags goes through air and tires. The total path loss contains reflection loss at tire-air boundaries. So, we give the OCP method for measuring the permittivity of tires. By analyzing the radio link for UHF passive RFID, we establish a model of wave propagation of UHF embedded RFID in tires and make numerical analyses. Finally, we make the conclusion as follows.(i)
The error of the OCP methods for measuring the permittivity of tires is small. And the methods can be used in measuring the permittivity of tires for designing the UHF embedded RFID in tires.
(ii)
It is necessary to optimize and design the antenna of tag for the impedance matching of tag antenna and chip. This can improve the performance of the UHF embedded RFID in tires.
(iii)
The parallel polarization and normal incidence are chosen for improving the performance of the UHF embedded RFID in tires. Finally, the distancel is chosen to keep T
(
f
,
θ
i
,
l
) from locating valley.



---

*Source: 897041-2014-02-17.xml*