Thesis Overview

This thesis is organized as below. Chapter 2 presents the formulation to calculate the near-field coupling coefficient. It is based mainly on the coupling quotient expressed in terms of the antenna far fields [15]. However, the associated numerical complexity due to the usage of the fast Fourier transform (FFT) and the tedious truncation methods has been greatly reduced.

For verification, the formula is used to calculate the coupling coefficients of several near-field setups. In Chapter 3, three commonly-seen scenarios are simulated using Ansoft HFSS. The results are compared with those computed via the proposed method, and they agree well.

In Chapter 4, a near-field UHF RFID system is chosen as an example. All the results obtained through measurement, HFSS simulation, and the formulation are demonstrated and compared. Some factors are found and discussed for enhancing the coupling level. Additionally, several practical applications in near-field UHF RFID systems are performed, and the proposed formulation may be helpful for determining the near-field read range and read reliability.

Finally, some observations and design guidelines are summarized in Chapter 5.

Three Appendices are attached at the end of this thesis. The derivation of coupling quotient in terms of far-field patterns is shown in Appendix 1. The general solution of the scalar Helmholtz equation in spherical coordinates is derived in Appendix 2.

Moreover, in Appendix 3, it derives the orthogonality relationships of tesseral harmonics.

Chapter 2

Near-Field Coupling Coefficient

2.1 Introduction

In wireless communication, it’s crucial to determine the coupling coefficient, that is, the amount of power accepted by the receiving antenna when a given amount of power comes from the transmitting antenna. When the receiving antenna is located in the far field of the transmitting antenna, the coupling coefficient can be determined by the Friis equation:

2 t r

4

C G G p

d λ π

⎛ ⎞

= ⎜ ⎝ ⎟ ⎠

(2.1)

where Gt, Gr are the gains of transmitting and receiving antennas, respectively, d is the antenna spacing, and p is the polarization mismatch loss between the two antennas. As for the near-field case, in order to determine the coupling coefficient between the transmitting and receiving antennas, we require other approaches described in this chapter. We have organized this part into following sections. In Section 2.2, we categorize the exterior fields of the transmitting antenna, and clarify the near-field region considered in this thesis. Section 2.3 presents the theory for computing the coupling coefficient versus longitudinal displacement of two antennas separated along axis, which is considered as the prototype of the three-dimensional formulation. Since

the transmitting and receiving antennas are often randomly oriented, we merge the orientation obstacle into the formulation described in subsection 2.3.3. Furthermore, the coupling coefficient versus relative displacement of two antennas in a transverse plane normal to the separation axis is also discussed in Section 2.4. Finally, the capability of the formulation is summarized in Section 2.5.

2.2 Antenna Field Regions

The exterior fields of a transmitting antenna can be divided into near-field and far-field regions as shown in Fig. 2.1 [14], [19]. The near-field region is further divided into two sub-regions, the reactive and radiating near field. In the reactive near field, energy is stored in the electric and magnetic fields very close to the transmitting antenna instead of radiating from the source. The near-field region is commonly taken to extend about λ π2 from the surface of the antenna. However, with the experience of

near-field measurement, it indicates that a distance of one wavelength ( λ ) determines a more reasonable outer boundary to the reactive near field. Once the distance from the

transmitting antenna is more than one wavelength, the electric and magnetic fields tend

to propagate predominantly in phase, but do not exhibit a plane-wave characteristic

(exp ikr r ) until they reach the far-field region. This propagation region between the

( )

reactive near field and the far field is called the radiating near field.

D

Fig. 2.1 Antenna near and far field regions.

The far-field region extends to infinity and the direction of electric field, magnetic

field and propagation are perpendicular among one another in this region. The inner

radius of the far field can be estimated from the general free-space integral for the

vector potential and is typically set at2D² λ λ+ . Notice that the added λ covers the possibility of the maximum dimension D of the antenna being smaller than a

wavelength. In other words, the so-called Rayleigh distance 2D² λ is measured from

the outer boundary of the reactive near field of the antenna.

2.3 Antenna Coupling versus Longitudinal Displacement

Consider a receiving antenna placed in the near field of a transmitting antenna as

depicted in Fig. 2.2. The incident and emergent waveguide mode coefficients for the

transmitting (receiving) antenna are aT and bT (aR and bR) respectively. Referring to [15],

the coupling quotient between the transmitting and receiving antennas is defined as

bR/aT. It can be interpreted as the signal coupled into the receiving antenna when a unit

signal is fed into the transmitting antenna, which is identical to the definition of the

forward transmission coefficient of the scattering parameters S21, when the transmitting

and receiving antennas and the region in between are considered as a two-port network.

Since we are more interested in the coupled power level, |bR/aT|² is used instead. It

means the amount of power accepted by the receiving antenna when a unit power comes

from the transmitting antenna. Mostly, |bR/aT|² is expressed in decibels and is referred to

as the power coupling level or the coupling coefficient C here in this thesis.

Transmitting

Fig. 2.2 Arbitrarily oriented receiving antenna in the near field of a transmitting antenna.

2.3.1 Spherical Wave Expansions for the Coupling Coefficient

The coupling quotient between the transmitting and receiving antennas can be

written as [15]

t to the transmitting antenna.

alized vector

far-is the position vector of the

rece and

transmitting antennas, respectively. CR is a mismatch constant defined as iving antenna with respec

field patterns for the receiving and

T θ where η is the intrinsic impedance of free space, ZRFeed is the characteristic impedance of the feed waveguide of the receiving antenna, and ΓR, ΓL are the reflection coefficients of the feed waveguide when looking into the receiving antenna and its passive load,

respectively. The derivation of (2.2) is done by Yaghjian [15] and shown in Appendix 1.

Note from (2.2) that the coupling quotient is a function of the position vector r.

The double integral in (2.2) is taken over the transverse components of propagation

vector dkx and dky, and the inner product of the two vector far-field patterns in the

integrand represents the interaction between the transmitting and receiving antennas.

The integral interval K < k means that only the propagating waves are integrated, which

corresponds to the real part of the complex power.

Applying the Laplacian operator ∇² to (2.2) yields

( ) ( )

Recasting (2.4) and we have

(

^{2 2}

)

^R

⁰

T

k b

∇ + a =

(2.5) which means that the coupling quotient satisfies the scalar Helmholtz equation. As a

result, the coupling quotient can be expanded by linear combination of the elementary

wave functions, and the most general form is a summation over all possible values of m

and n [16], written as (see Appendix 2)

( )¹

( ) (

0

)

⁰ and are the spherical Hankel functions of the first kind and the associated

Legendre polynomials, respectively. Bnm are the spherical wave coefficients. Here, the

coupling quotient is expanded by a set of known basis which can be determined by

forward recurrence relations or obtained in Matlab and Mathematica databases, and

leaving only the spherical wave coefficients Bnm unknown.

( )1

hn P_n^m

Transmitting

Fig. 2.3 Rotated (primed) coordinate system with receiving antenna on the z’-axis.

Through the above series expansion method, the singularity that occurs when γ

approaches zero can be avoided, and the integration variables dkx and dky are changed to

be dθ0 and dφ0, resulting in a simpler double integral. To further simplify (2.6) and facilitate evaluation of Bnm, the coordinate system in Fig. 2.2 is rotated around the origin,

namely the phase center of the transmitting antenna, such that the phase center of the

receiving antenna lies on the z-axis of the rotated coordinate system as depicted in Fig.

2.3.

Therefore, in this new coordinate system

r = ˆzd

and θ0 = 0°. The relative orientation between the transmitting and receiving antennas can then be accounted for

simply by rotating the far-field patterns accordingly. In addition, it is known that the

associated Legendre polynomial P_n^m

(

cosθ₀

)

, for its argument being unity, is nonzero

where DT and DR are the largest dimensions of the transmitting and receiving antennas,

respectively. The coupling quotient in (7) is now a function of the antenna spacing d

rather than the position vector r. The remaining work is to evaluate the unknown

spherical wave coefficients Bnm and Bn.

2.3.2 Evaluation of the Spherical Wave Coefficients

To evaluate Bnm and acquire Bn in (2.7), first we begin with (2.2), and let the

separation distance r approach to infinite. According to the Sommerfeld radiation

condition, (2.2) can be written as

( ) ² ( ) ( )

On the other hand, as r the spherical Hankel function in (2.6) has an

approximation of large argume

( ) ( ) ( )

Clearly ,e^ikr kr can be canceled out. In a further step, we multiply both side of

(2.10) by P_n^m

(

cosθ0

)

e^-imφ0, and exploit the orthogonality relationships of those basis

functions as shown by Appendix 3, we have

( ) ( )

Given the 3D vector far-field patterns for both transmitting and receiving antennas

and the relative orientation, the associated inner product in the integrand of (2.12) could

readily be calculated. Please note that to evaluate Bn Yaghjian exploited an FFT

algorithm in [14] to convert the double integral into summations. In this work, a simple

numerical integration is adopted to calculate Bn directly from (2.12). Substituting Bn

thus obtained into (2.7) yields the desired coupling quotient. Although an infinite series

is needed based on (2.7) to compute the coupling quotient, it has been observed that the

series would converge with merely less than ten terms.

Furthermore, in the far-field Friis equation (2.1) p= ⋅e eˆ ˆ_{t R} ² indicates the polarization mismatch loss between two antennas, where and are unit vectors

representing the polarization of the electric field of the transmitting and receiving

antennas, respectively. In the proposed near-field formulation, the polarization

mismatch loss has also been consulted by the pattern inner product ˆ_t

e eˆ_R

R T

f ⋅ f since we

can always express f_R as θˆf_Rθ +ϕˆf_Rϕ and f_T as θˆf_Tθ +ϕˆf_Tϕ . Consequently, the

proposed formulation, in a sense, can be regarded as a near-field counterpart of the Friis

transmission formula.

2.3.3 Relative Orientations

To evaluate the inner product f_R⋅ f_T, the normalized far-field vector patterns( fR

and fT ) are transferred from the spherical coordinate system to the rectangular

coordinate system. Since there is often a relative orientation between transmitting and

receiving antennas, consider each antenna rotates about Z-axis as illustrated in Fig. 2.4.

We convert f f_φ, _θ from spherical coordinates into f f f_x, ,_{y z} in rectangular

x

y z

k

θ

A

φ

A

k

z

K

x

y z

k

θ

A

φ

A

k

z

K

Fig. 2.4 A relative orientation of the receiving antenna in terms of spherical coordinate system

(

θ φA^, A

)

.

f , ,

After obtaining _x f f_{y z}, we can substitute it into (2.12) to compute the pattern

inner product, and further attain (2.7).

2.4 Antenna Coupling versus Transverse Displacement

In the preceding work, we evaluate the coupling coefficient versus the longitudinal

axis between the transmitting and receiving antenna. Mostly, in this situation the

coupling coefficient is larger than the scenario that the receiving antenna has an offset

(Δx, Δy) on a transverse plane and is separated from the transmitting antenna by d.

Typically this scenario is often our concern for application purpose.

The coupling coefficients are also obtained for this scenario. Consider the

transmitting antenna is located at the coordinate origin, while the receiving antenna

“scans” on a transverse plane with a constant antenna orientation. Fig. 2.5 shows the

receiving antenna located at an off-axis point A’ with transverse offsets (Δx, Δy) from

the on-axis point A. The transverse offsets can then be converted into the relative

orientation for the antennas.

1

Given the tag antenna position A’(Δx, Δy, d) and the 3D patterns of the reader and

tag antennas, the associated coupling coefficient can be computed by rotating the 3D

patterns in accordance with the relative antenna orientation. Also, note that the antenna

spacing in the formula should be d’ instead of d.

x

Fig. 2.5 The receiving antenna has an offset (Δx, Δy) on the transverse plane normal to the separation axis.

2.5 Summary

In this chapter, we specify the near-field region discussed in this thesis. A simple

formulation has been presented for computing the coupling coefficients between two

antennas that are placed in the near field of each other and are arbitrarily oriented.

Although the formula is complicated to some extent, it could be regarded as a near-field

counterpart of the Friis transmission formula. Based on the proposed formula and

program, all the information we need to compute the near-field coupling coefficient are

the 3D radiation patterns of each antenna and their relative orientation.

Chapter 3

Comparisons between the Formulation and HFSS Simulation

3.1 Introduction

In order to verify the proposed formulation, three classic scenarios in the UHF band are considered in this chapter. The design frequencies of all the antennas are at 915 MHz. The associated coupling coefficients between the transmitting and receiving antennas are computed and compared to those simulated using Ansoft HFSS. Please note that, in the HFSS simulation, the quantity |S21|² is used for comparison, which is obtained by assuming port 2, namely the receiving antenna in our cases, being perfectly

matched to its load impedance. For consistency, this condition can be included in our formulation merely by setting ΓRL = 0. Also, it must be mentioned that according to the

condition in (2.7) the coupling coefficients can be computed only when the antenna

separation is larger than the mean value of the largest dimensions for the transmitting and receiving antennas. Therefore, d ≥ 85 mm is chosen in the following examples.

3.2 Side-by-Side, Parallel Half-Wave Dipoles

Consider two identical, y-directed half-wavelength dipole antennas, one of which is placed at the origin and the other on the z-axis with a separation d. The former is

chosen as the transmitting antenna, while the latter is the receiving antenna. Since it is not difficult to derive the normalized vector far-field pattern of an ideal y-directed half-wavelength dipole based on its well-known z-directed counterpart, they are given as

Substituting (3.1) and (3.2) into (2.12) yields the desired spherical wave coefficients Bn. The computed coefficients Bn diminishes significantly for higher order terms when n > 7 leading to fast convergence of (2.7). In the HFSS simulation, the configuration of the dipole is shown in Fig 3.1, and the corresponding patterns at 915 MHz are shown in Fig 3.2.

Fig. 3.1 Geometry of the HFSS simulated dipole.

(a) (b)

Fig. 3.2 Simulated radiation patterns of the dipole at 915MHz.

(a) x-z plane and (b) y-z plane.

calculated coupling coefficient (by close-form pattern expression)

simulated S21 (by HFSS)

Fig. 3.3 Coupling coefficient versus antenna separation for polarization-matched dipoles.

The near-field coupling coefficient as a function of antenna spacing d computed by the proposed method and those obtained via HFSS are depicted in Fig. 3.3. Excellent agreement can be observed verifying the proposed formulation.

3.3 Side-by-Side, Polarization-Mismatched Half-Wave Dipoles

In the preceding subsection, the two dipoles are polarization matched corresponding to the best case in a two-dipole system. However, in most cases, they are arbitrarily oriented. Besides, to demonstrate the capability of our method, a scenario

having polarization-mismatched dipoles is also considered. In the current case, the receiving dipole lying on the y-z plane is rotated by 20° around its phase center. This

can be accounted for in our formulation simply by transforming the coordinate system of the vector far-field pattern of the receiving dipole accordingly. Using (2.13),

θA andφ_A defined in Fig. 2.3 are 20° and 90°, respectively. Accordingly the corresponding rectangular components of the receiving antenna are

cos 20 sin 20

xR R

yR R

zR R

f f

f f

f f

φ

θ

θ

⎧ = −

⎪ = ° ⋅

⎨ ⎪ = − ° ⋅

⎩

(3.3)

Likewise, Bn thus obtained diminishes significantly for n > 9 leading to fast convergence of (2.7). The coupling coefficients thus obtained are plotted in Fig. 3.4.

One can see that the coupling coefficients are smaller here than in the preceding case because of the polarization mismatch between the two dipoles.

50 100 150 200 250 300 350 400

calculated coupling coefficient (by close-form pattern expression)

simulated S21 (by HFSS)

20°

Fig. 3.4 Coupling coefficient versus antenna separation for polarization-mismatched dipoles.

3.4 Polarization-Matched Square Loop and Half-Wave Dipole

Here, a square loop antenna having its perimeter equal to a wavelength is used to replace the transmitting dipole in Section 3.2. The loop antenna is centered at the origin with the loop lying on the x-y plane and oriented in such a way that the resultant polarization is aligned with the y-directed receiving dipole. In the HFSS simulation, the structure of the square loop antenna and the patterns are shown in Fig 3.5 and Fig 3.6, respectively.

x y

Fig. 3.5 Geometry of the HFSS simulated square loop.

(a) (b)

Fig. 3.6 Simulated radiation patterns of the square loop antenna at 915MHz.

(a) x-z plane and (b) y-z plane.

We observe that the simulated pattern in the y-z plane is doughnut-shaped, while the x-z plane pattern is omni-directional with a slightly shaking at ±90°. This circumstance indicates that its normalized co-polarized component of the far-field pattern can be represented as an array composed of two parallel dipoles a quarter wavelength apart. Consequently, the radiation patterns of the square loop can be approximated using the principle of pattern multiplication with the element factor

2 2

while the array factor can be derived as

sin sin

1

^j2

AF e

π θ φ

= +

(3.6) The coupling coefficient for this setup can thus be computed as a function of the antenna spacing. The results are compared with those simulated and shown in Fig. 3.7.

In this example, the error is larger than previous two cases due to the far-field pattern of square loop is an approximation, which is not a exact solution used in previous cases.

50 100 150 200 250 300 350 400

calculated coupling coefficient (by close-form pattern expression)

simulated S21 (by HFSS)

Coupling Coefficient (dB)

Antenna Separation d (mm)

Fig. 3.7 Coupling coefficient versus antenna separation for polarization-matched square loop and dipole.

3.5 Summary

In the previous three scenarios, the agreement between the computed results and those simulated by HFSS indicates that the proposed method can be utilized to determine the near-field coupling coefficient as the relative orientation, the antenna spacing, and the far-field patterns of the transmitting and receiving antennas are known.

Chapter 4

Application in Near-Field UHF RFID System

4.1 Introduction

A RFID system is a spontaneous wireless data collection technology with a long history [18]. Depending upon their operating principle, RFID systems are classified into three categories: passive, semi-passive, and active. A passive RFID system is the least complex and cheapest, hence widely used for many applications. Without a power supply of a passive tag its own, the required energy to turn on the tag chip depends upon the electromagnetic field coupling from the reader. Accordingly, two different coupling techniques are further categorized: near-field coupling and far-field coupling.

Low frequency (LF, 125-134 kHz) and high frequency (HF, 13.56 MHz) RFID systems are short-range systems based on near-field coupling. On the other hand, Ultra-high frequency (UHF, 860-960 MHz) and microwave (2.4 GHz and 5.8 GHz) RFID systems are typically long-range systems based on far-field coupling. LF and HF RFID systems have been deployed in the market for many commercial applications.

However, the larger size of the antennas used in the LF/HF band systems confines their further development. Thus, it is straight forward to reduce antenna size by designing the system in a higher frequency band, such as the UHF band. In addition, the near-field

UHF RFID systems have other superiorities, including higher data rate, and lower manufacturing cost, making them suitable for item-level tagging.

The near-field UHF RFID system is composed of a reader and a tag just as in the ordinary RFID systems. The simplified system architecture is depicted in Fig. 4.1. The power generated by the reader circuitry Preader is transferred to the reader antenna, and then acquired by the tag antenna through near-field coupling. The power absorbed by the tag chip Pchip can be expressed as [19]

chip reader reader chip

P = P × τ × × C τ

(4.1) where τreader and τchip are the impedance mismatch coefficients of the reader and tag between the front-end circuitry and the associated antenna, respectively. They can be expressed as

Please note that since both the impedances of tag and chip are complex, we use a

Please note that since both the impedances of tag and chip are complex, we use a

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