**4. Coplanar-waveguide structures**

where Pr is the power received by RFID tag, Pt

134 Radio Frequency Identification from System to Applications

tenna on the RFID tag with a maximized gain Gr.

**3. Introduction to left-handed propagation**

**Figure 3.** Reconfigurable CRLH-TL

the gain of tag antenna, Gt

is power transmitted by RFID reader, Gr is

(2)

(3)

is the gain of reader, λ is free space wavelength of the operating

frequency of reader, R is distance between reader and tag and q is impedance mismatch fac‐ tor (0 ≤ q ≤ 1) between impedance of the antenna on the tag and the input impedance of the ASIC on the tag. Equation (1) assumes a perfect polarization match between the antenna on the reader and the antenna on the RFID tag. Reorganizing (1) and solving for R, the follow‐

> *qGtGr Pt Pr*

> > *qGtGr Pt Pth*

Equation (3) is useful for designers to determine the maximum operating range of the tag. Typically the approach by a designer is to maximize the Rmax. One way of achieving this is to minimize the mismatch between tag antenna and ASIC impedances or design a receive an‐

To help illustrate the use of ZOR properties to improve the gain and matching of a compact antenna on a passive UHF RFID tag, several properties of left-handed (LH) propagation will be introduced and summarized here. It is well known that the equivalent circuit of a tradi‐ tional printed microstrip TL consists of a series inductance and a shunt capacitance. The ser‐ ies inductance is caused by the current travelling down the printed TL and the shunt

If the minimum power required for tag operation is Pth then Equation (2) can be written as

ing equation for determining the read rang of a tag can be derived [17,18] as:

*<sup>R</sup>* <sup>=</sup> *<sup>λ</sup>* 4*π*

*Rmax* <sup>=</sup> *<sup>λ</sup>* 4*π*

> The term "Coplanar" means sharing the same plane and this is the type of transmission line where the reference conductors are in the same plane as of signal carrying conductor. The signal carrying conductor is placed in the middle with a reference plane conductor on either side as shown in Fig. 4. The advantage of having both conductors in the same plane lies in the fact that it is easier to mount lumped components between the two planes and it is easier to realize shunt and series configurations. The CPW was first proposed by Wen [19] and since then have been used extensively in wireless communications [20,21].

> The disadvantage of CPW is that it can be difficult to maintain the same potential between the reference and signal conductors throughout the signal trace. Nevertheless many advan‐ ces have been made by using CPW such as novel filters [22] and right/left handed propaga‐ tion on CPW lines [23].

**Figure 4.** CPW transmission line on ungrounded dielectric

Several properties of the CPW-TL in Fig. 4 are derived next. These expression will be used later to describe the ZOR-RFID antenna. The attenuation and phase constants can be derived by performing a quasi-static analysis of a CPW [24]. The phase velocity and characteristic impedance equations can be written as [24]:

$$
\omega \upsilon\_{cp} = \left(\frac{2}{\varepsilon\_r + 1}\right)^{1/2} \mathcal{C} \tag{4}
$$

*εre*

<sup>2</sup> *tanh* {1.785log (*h* / *G*) + 1.75} +

kind and the ratio K(k)/K(k') has been reported in [24,25] as:

*<sup>π</sup> ln* <sup>2</sup> <sup>1</sup> <sup>+</sup> *<sup>k</sup>*

*K* (*k* ' ) *<sup>K</sup>* (*<sup>k</sup>* ) <sup>=</sup> <sup>1</sup>

> *K* (*k '*) *<sup>K</sup>* (*<sup>k</sup>* ) <sup>=</sup> *<sup>π</sup> ln* 2 1 + *k '* 1 - *k '*

> > *P ' <sup>π</sup><sup>G</sup>* (1 +

*<sup>P</sup>* ={ *<sup>k</sup>*

The attenuation constant due to dielectric losses is [24]:

1 (1 - *k* ) *k* *W <sup>G</sup>* ){ 1.25

*P '* =( *<sup>K</sup> <sup>K</sup> '* )<sup>2</sup>

( *K*

*RsεreZ*0*cp*

and

and

[24]:

where

and

*αc*

*cw* =4.88*\**10-4

*<sup>ε</sup>re* <sup>=</sup> *<sup>ε</sup><sup>r</sup>* <sup>+</sup> <sup>1</sup>

*<sup>t</sup>* <sup>=</sup>*εre* - 0.7(*εre* - 1)*<sup>t</sup>* / *<sup>G</sup> K* (*k* ) *<sup>K</sup>* (*<sup>k</sup> '*) <sup>+</sup> 0.7*<sup>t</sup> G*

Design of a Zeroth Order Resonator UHF RFID Passive Tag Antenna with Capacitive Loaded Coplanar…

*kG*

Here W is the width of the center conductor, G is the spacing between the center conductor and the reference conductor, εr is the relative permittivity of the dielectric, c is the speed of light and t is the thickness of the conductor. K(k) is the complete elliptic integral of the first

Using equations (4)-(13) the attenuation constant due to ohmic losses can be calculated as

*<sup>π</sup> ln* <sup>4</sup>*π<sup>W</sup>*

<sup>2</sup> <sup>+</sup> *<sup>W</sup> <sup>G</sup>* - 1.25*<sup>t</sup>*

(1 - <sup>1</sup> - *<sup>k</sup>* 2)(1 - *<sup>k</sup>* 2)3/4 *for* 0.0≤*<sup>k</sup>* <sup>≤</sup>0.707

*<sup>K</sup> '* )<sup>2</sup> *for* 0.707≤*<sup>k</sup>* <sup>≤</sup>1.0

*<sup>t</sup>* <sup>+</sup> <sup>1</sup> <sup>+</sup> 1.25*<sup>t</sup> πW*

*<sup>π</sup><sup>G</sup>* (1 <sup>+</sup> *ln* <sup>4</sup>*π<sup>W</sup>*

*<sup>h</sup>* {0.04 - 0.7*k* + 0.01(1 - 0.1*εr*)(0.25 + *k*)} (11)

<sup>1</sup> - *<sup>k</sup> for* 0.707≤*<sup>k</sup>* <sup>≤</sup><sup>1</sup> (12)

*for* <sup>0</sup>≤*<sup>k</sup>* <sup>≤</sup>0.707 (13)

*P* (15)

*Rs* = *ρπfμ* (17)

*<sup>t</sup>* ) <sup>2</sup> }*dB* / *unit length* (14)

(16)

(10)

137

http://dx.doi.org/10.5772/53284

and

$$Z\_{0cp} = \frac{\text{30\pi}}{\sqrt{\varepsilon\_{re}}} \frac{\text{K}\{\mathbf{k}\_e\}}{\text{K}\{\mathbf{k}\_e\}}\tag{5}$$

where

$$k\_e = \frac{W\_e}{\left(W\_e + 2G\_e\right)} \cong k + \frac{\left(1 \cdot k^2\right)\Delta}{2G} \tag{6}$$

$$k = \frac{W}{W + 2G} \tag{7}$$

$$
\Delta = \left(1.25t \,/\,\pi\right) \mathbf{\tilde{1}} + \ln\left(4\pi W \,/\, t\right) \mathbf{\tilde{1}} \tag{8}
$$

$$\mathbf{k}^{\prime} = \begin{pmatrix} 1 \ -k^{\prime} \end{pmatrix}^{\prime} \tag{9}$$

Design of a Zeroth Order Resonator UHF RFID Passive Tag Antenna with Capacitive Loaded Coplanar… http://dx.doi.org/10.5772/53284 137

$$\varepsilon\_{re} \triangleq \varepsilon\_{re} - \frac{0.7(\varepsilon\_{re} - 1)t / G}{\left[\frac{K(k)}{K(k)}\right] + \frac{0.7r}{G}} \tag{10}$$

and

Reference plane

136 Radio Frequency Identification from System to Applications

**Figure 4.** CPW transmission line on ungrounded dielectric

impedance equations can be written as [24]:

h

and

where

εr

G W G

Reference plane

εr

*c* (4)

*<sup>K</sup>* (*ke*) (5)

<sup>2</sup>*<sup>G</sup>* (6)

<sup>2</sup> (9)

*<sup>W</sup>* <sup>+</sup> <sup>2</sup>*<sup>G</sup>* (7)

∆ =(1.25*t* / *π*) 1 + ln (4*πW* / *t*) (8)

t

Ungrounded

dielectric

Signal plane

Several properties of the CPW-TL in Fig. 4 are derived next. These expression will be used later to describe the ZOR-RFID antenna. The attenuation and phase constants can be derived by performing a quasi-static analysis of a CPW [24]. The phase velocity and characteristic

*<sup>ε</sup><sup>r</sup>* <sup>+</sup> <sup>1</sup> )1/2

)

(1 - *k* 2) ∆

*vcp* =( <sup>2</sup>

*<sup>Z</sup>*0*cp* <sup>=</sup> <sup>30</sup>*<sup>π</sup> εre t K* (*ke '*

(*We* <sup>+</sup> <sup>2</sup>*Ge*) ≅*k* +

*<sup>k</sup>* <sup>=</sup> *<sup>W</sup>*

=(1 - *k* 2)

1

*k '*

*ke* <sup>=</sup> *We*

$$\varepsilon\_{re} = \frac{\varepsilon\_r + 1}{2} \left[ \tanh\left\{ 1.785 \log \left< h \, \, / \, G \right> + 1.75 \right\} + \frac{kG}{h} \left[ 0.04 \cdot 0.7k + 0.01 \{ 1 \cdot 0.1 \varepsilon\_r \} (0.25 + k) \right] \right] \tag{11}$$

Here W is the width of the center conductor, G is the spacing between the center conductor and the reference conductor, εr is the relative permittivity of the dielectric, c is the speed of light and t is the thickness of the conductor. K(k) is the complete elliptic integral of the first kind and the ratio K(k)/K(k') has been reported in [24,25] as:

$$\frac{\mathbb{V}\_{K}(k\,\prime)}{\mathbb{V}\_{K}(k)} = \frac{1}{\pi} \ln \left[ 2 \frac{1 + \sqrt{k}}{1 + \sqrt{k}} \right] \\
\text{for } 0.707 \le k \le 1 \tag{12}$$

and

$$\frac{\chi\_{\{k^{\prime}\}}}{\chi\_{\{k^{\prime}\}}} = \frac{\pi}{\ln\left[2\frac{1+\sqrt{k^{\prime}}}{1+\sqrt{k^{\prime}}}\right]} \text{ for } 0 \le k \le 0.707 \tag{13}$$

Using equations (4)-(13) the attenuation constant due to ohmic losses can be calculated as [24]:

$$\alpha\_c^{cv} = 4.88^\* 10^{-4} R\_s \varepsilon\_{re} Z\_{0cp} \frac{p^\*}{\pi G} \left( 1 + \frac{W}{G} \right) \left| \frac{\frac{1.25}{\pi} \ln \frac{4\pi W}{t} + 1 + \frac{1.25}{\pi W}}{\left[ 2 + \frac{W}{G} - \frac{1.25t}{\pi G} \left( 1 + \ln \frac{4\pi W}{t} \right) \right]^2} \right| dB \right| \text{ unit length} \tag{14}$$

where

$$P^{'} = \left(\frac{K}{K^{'}}\right)^{2} P^{'} \tag{15}$$

$$P = \begin{cases} \frac{k}{(1 - \sqrt{1 - k^2})(1 - k^{-2})^{3/4}} \text{ for } 0.0 \le k \le 0.707\\ \frac{1}{\left(1 - k\right)\sqrt{k}} \left(\frac{K}{K}\right)^2 \text{ for } 0.707 \le k \le 1.0 \end{cases} \tag{16}$$

and

$$R\_s = \sqrt{\rho \pi f \mu} \tag{17}$$

The attenuation constant due to dielectric losses is [24]:

$$\alpha\_d = 27.3 \frac{e\_r}{\sqrt{e\_m}} \frac{e\_r \cdot 1}{e\_r + 1} \frac{\tan \delta}{\lambda\_0} \text{ dB} \left| \text{ unit length} \right. \tag{18}$$

Here tan(δ) is the loss tangent of the dielectric and the total attenuation can be written as:

$$
\alpha\_{cwp} = \alpha\_c + \alpha\_d \tag{19}
$$

Thus, the phase constant can be calculated as [20]:

$$
\mathcal{B}\_{cpw} = \frac{2\pi f}{v\_{cp}}\tag{20}
$$

**Figure 6.** Interdigital capacitor loaded CPW unit cell

terms of an ABCD matrix as [20]:

from (19) and (20), respectively.

*A B C D CPW*

and

and

Since the unit cell will be repeated periodically and will be symmetric about the port of the antenna, it will resemble the TL in Fig. 5. Therefore, the propagation constant γ (where γ = α + jβ) and characteristic impedance (also known as block impedance) Z<sup>B</sup> can be expressed in

Design of a Zeroth Order Resonator UHF RFID Passive Tag Antenna with Capacitive Loaded Coplanar…

http://dx.doi.org/10.5772/53284

139

*ZB* <sup>=</sup> *BZ*<sup>0</sup>

Next, the ABCD matrix of the circuit shown in Fig. 5 can be determined as [20]:

cosh *<sup>γ</sup>CPW <sup>L</sup>*

*<sup>Y</sup>*0sinh *<sup>γ</sup>CPW <sup>L</sup>*

*C D inter*-*digital capacitor*

=

*A B*

Here L is the length of the unit cell and Z0 is the characteristic impedance of the CPW. The propagation constant of the TL is γCPW = αCPW + βCPW where αCPW and βCPW can be calculated

<sup>2</sup> *<sup>Z</sup>*0sinh *<sup>γ</sup>CPW <sup>L</sup>*

<sup>2</sup> cosh *<sup>γ</sup>CPW <sup>L</sup>*

<sup>=</sup> <sup>1</sup> <sup>1</sup> *jωC* 0 1

2

2

cosh *γL* = *A* (21)

*<sup>A</sup>* <sup>2</sup> - <sup>1</sup> (22)

(23)

(24)

Next, these expressions will be used to introduce the interdigital capacitor loaded CPW which will then be used to design a ZOR-RFID antenna.

#### **5. Interdigital capacitor loaded CPW**

An Interdigital capacitor loaded transmission line provides a series resonance. The Zeroth Order Resonance (ZOR) of an interdigital capacitor loaded CPW has been investigated and reported in [26]. The equivalent transmission line model of an interdigital capacitor loaded transmission line is shown in Fig. 5 and consists of two symmetric transmission lines inter‐ connected with a series capacitance. The host transmission line has been shown equally div‐ ided into two parts. Since the size of the unit cell is much smaller than the guided wavelength, the transmission line can be modeled with an equivalent circuit with a series inductance and shunt capacitance (as discussed in Section 3).

**Figure 5.** Equivalent circuit model of interdigital capacitor loaded

The geometry (layout) of the interdigital capacitor based unit cell is shown in Fig. 6. The ca‐ pacitance between the interdigital capacitor and bilateral ground plane is fairly small as compared to the series capacitance of the interdigital capacitor so it can be neglected. This unit cell can be repeated periodically to design the ZOR antenna.

**Figure 6.** Interdigital capacitor loaded CPW unit cell

Since the unit cell will be repeated periodically and will be symmetric about the port of the antenna, it will resemble the TL in Fig. 5. Therefore, the propagation constant γ (where γ = α + jβ) and characteristic impedance (also known as block impedance) Z<sup>B</sup> can be expressed in terms of an ABCD matrix as [20]:

$$\text{a}\cosh\gamma L = A\tag{21}$$

and

*<sup>α</sup><sup>d</sup>* =27.3 *<sup>ε</sup><sup>r</sup>*

138 Radio Frequency Identification from System to Applications

Thus, the phase constant can be calculated as [20]:

which will then be used to design a ZOR-RFID antenna.

inductance and shunt capacitance (as discussed in Section 3).

TL

**Figure 5.** Equivalent circuit model of interdigital capacitor loaded

unit cell can be repeated periodically to design the ZOR antenna.

**5. Interdigital capacitor loaded CPW**

*εre*

*εre* - 1 *ε<sup>r</sup>* + 1 tan *δ*

Here tan(δ) is the loss tangent of the dielectric and the total attenuation can be written as:

*<sup>β</sup>cpw* <sup>=</sup> <sup>2</sup>*π<sup>f</sup> vcp*

Next, these expressions will be used to introduce the interdigital capacitor loaded CPW

An Interdigital capacitor loaded transmission line provides a series resonance. The Zeroth Order Resonance (ZOR) of an interdigital capacitor loaded CPW has been investigated and reported in [26]. The equivalent transmission line model of an interdigital capacitor loaded transmission line is shown in Fig. 5 and consists of two symmetric transmission lines inter‐ connected with a series capacitance. The host transmission line has been shown equally div‐ ided into two parts. Since the size of the unit cell is much smaller than the guided wavelength, the transmission line can be modeled with an equivalent circuit with a series

TL TL

The geometry (layout) of the interdigital capacitor based unit cell is shown in Fig. 6. The ca‐ pacitance between the interdigital capacitor and bilateral ground plane is fairly small as compared to the series capacitance of the interdigital capacitor so it can be neglected. This

Cs

*<sup>λ</sup>*<sup>0</sup> *dB* / *unit length* (18)

(20)

*αcwp* =*α<sup>c</sup>* + *α<sup>d</sup>* (19)

TL

$$Z\_B = \frac{BZ\_0}{\sqrt{A^2 \cdot 1}}\tag{22}$$

Here L is the length of the unit cell and Z0 is the characteristic impedance of the CPW. The propagation constant of the TL is γCPW = αCPW + βCPW where αCPW and βCPW can be calculated from (19) and (20), respectively.

Next, the ABCD matrix of the circuit shown in Fig. 5 can be determined as [20]:

$$
\begin{bmatrix} A & B \\ C & D \end{bmatrix}\_{CPW} = \begin{bmatrix} \cosh\frac{\gamma\_{CPW}L}{2} & Z\_0 \sinh\frac{\gamma\_{CPW}L}{2} \\\\ Y\_0 \sinh\frac{\gamma\_{CPW}L}{2} & \cosh\frac{\gamma\_{CPW}L}{2} \end{bmatrix} \tag{23}
$$

and

$$
\begin{bmatrix} A & B \\ C & D \end{bmatrix}\_{inter-\text{-}light\ capacitor} = \begin{bmatrix} 1 & \frac{1}{j\omega C} \\ 0 & 1 \end{bmatrix} \tag{24}
$$

Here L/2 represents half of the CPW length. The ABCD matrix of the whole unit cell can be calculated from (23) and (24) as:

$$
\begin{bmatrix} A & B \\ C & D \end{bmatrix} = \begin{bmatrix} A & B \\ C & D \end{bmatrix}\_{CPW} \ast \begin{bmatrix} A & B \\ C & D \end{bmatrix}\_{inter-\text{-diagonal capacitor}} \ast \begin{bmatrix} A & B \\ C & D \end{bmatrix}\_{CPW} \tag{25}
$$

From (25), parameter A can be calculated and (21) can be written as:

$$\left\{ \cosh \alpha L \, \cos \beta L \, \right. \left. + \left[ j \sinh \alpha L \, \sin \beta L \, \right. \right. \left. = M + jN + \frac{1}{j2 \, \omega \, \omega \, \text{C}} \left( O + jP \right) \right. \tag{26}$$

where

$$M \text{ =} \cosh \alpha\_{\text{CPW}} L \text{ } \cos \beta\_{\text{CPW}} L \tag{27}$$

*<sup>β</sup>* <sup>=</sup> <sup>1</sup>

**Figure 7.** Layout of proposed ZOR RFID antenna with capacitor loaded CPW [30]

**5.1. Zeroth order resonance**

on the antenna.

design frequency as:

*<sup>L</sup> cos*-1( *<sup>Q</sup>* <sup>2</sup> <sup>+</sup> (*<sup>R</sup>* + 1)2 - *<sup>Q</sup>* <sup>2</sup> <sup>+</sup> (*<sup>R</sup>* - 1)2

where Q and R are the right hand sides of (31) and (32), respectively. The key idea when designing a ZOR antenna is to determine the frequency at which equation (34) is equal to zero. Since the propagation constant is inversely proportional to the wavelength, when equation (34) is zero, the wavelength at that frequency is equal to infinity. At this frequency, the antenna looks infinitely long electrically. In the next section, the expressions derived here for the interdigital capacitor loaded CPW will be used to design a ZOR-RFID antenna.

Design of a Zeroth Order Resonator UHF RFID Passive Tag Antenna with Capacitive Loaded Coplanar…

The layout of the proposed ZOR RFID antenna is shown in Fig. 7 [30]. The port of the an‐ tenna is located in the middle of the antenna with series capacitance down each arm. The operating principle of this antenna is based on the capacitive input impedance of the pas‐ sive RFID ASIC. At resonance, the interdigital capacitors are supporting a wave propagat‐ ing along the antenna. Since the input impedance of the ASIC is also capacitive the ASIC also supports wave propagation along the antenna in a manner similar to the interdigital capacitors [30]. During this process, the ASIC harvests the required power to perform the desired tasks and communicate while simultaneously supporting the wave propagating

The first step in the design process is to determine what capacitance is required to equate β to zero at the desired operating frequency such that the antenna looks infinitely long. For discussion, the non-zero frequency at which β becomes zero is known as the zeroth order resonance (ZOR) frequency [26], [30]. For simplicity a lossless (α = 0) CPW line is assumed and then from (31) the required capacitance can be calculated to achieve ZOR at a particular

<sup>2</sup> ) (34)

http://dx.doi.org/10.5772/53284

141

$$N \text{ =} \sinh \alpha\_{CPW} L \text{ } \sin \beta\_{CPW} L \tag{28}$$

$$O \text{=} \sinh \alpha\_{CPW} L \,\cos \beta\_{CPW} L \tag{29}$$

and

$$P \text{ = } \cosh \alpha\_{CPW} L \text{ } \sin \beta\_{CPW} L \tag{30}$$

In (26) α represents the attenuation constant and β represents the phase constant of the Bloch wave propagating on the unit cell whereas αCPW and βCPW are attenuation and phase constants, re‐ spectively, of the host CPW. From (26) the real and imaginary parts can be separated which gives:

$$
\cosh aL \, \cos \beta L \, \text{ =} \cosh a\_{CPW} L \, \cos \beta\_{CPW} L \, \text{ +} \frac{\cosh a\_{CPW} L \, \sin \beta\_{CPW} L}{2Z\_0 \omega \mathbb{C}} \tag{31}
$$

and

$$
\sinh\alpha L \,\sin\beta L \,\text{ =} \sinh\alpha\_{\text{CPW}} L \,\sin\beta\_{\text{CPW}} L \,\text{ --} \frac{\sinh\alpha\_{\text{CPW}} L \,\cos\beta\_{\text{CPW}} L}{2Z\_{\text{CP}}\text{C}}\tag{32}
$$

The unknowns in (31) and (32) are α and β of the Bloch wave. Solving for α and β gives:

$$\alpha = \frac{1}{L} \cosh^{-1} \left( \frac{\sqrt{Q^2 + (R + 1)^2} + \sqrt{Q^2 + (R - 1)^2}}{2} \right) \tag{33}$$

and

Design of a Zeroth Order Resonator UHF RFID Passive Tag Antenna with Capacitive Loaded Coplanar… http://dx.doi.org/10.5772/53284 141

$$\beta = \frac{1}{L} \cos^{-1} \left( \frac{\sqrt{Q^2 + (R+1)^2} - \sqrt{Q^2 + (R-1)^2}}{2} \right) \tag{34}$$

where Q and R are the right hand sides of (31) and (32), respectively. The key idea when designing a ZOR antenna is to determine the frequency at which equation (34) is equal to zero. Since the propagation constant is inversely proportional to the wavelength, when equation (34) is zero, the wavelength at that frequency is equal to infinity. At this frequency, the antenna looks infinitely long electrically. In the next section, the expressions derived here for the interdigital capacitor loaded CPW will be used to design a ZOR-RFID antenna.

**Figure 7.** Layout of proposed ZOR RFID antenna with capacitor loaded CPW [30]

#### **5.1. Zeroth order resonance**

Here L/2 represents half of the CPW length. The ABCD matrix of the whole unit cell can be

*C D inter*-*digital capacitor*

In (26) α represents the attenuation constant and β represents the phase constant of the Bloch wave propagating on the unit cell whereas αCPW and βCPW are attenuation and phase constants, re‐ spectively, of the host CPW. From (26) the real and imaginary parts can be separated which gives:

The unknowns in (31) and (32) are α and β of the Bloch wave. Solving for α and β gives:

*<sup>L</sup> cosh* -1( *<sup>Q</sup>* <sup>2</sup> <sup>+</sup> (*<sup>R</sup>* <sup>+</sup> 1)2 <sup>+</sup> *<sup>Q</sup>* <sup>2</sup> <sup>+</sup> (*<sup>R</sup>* - 1)2

*\* A B C D CPW*

1

*M* =cosh *αCPW L* cos *βCPW L* (27)

*N* =sinh *αCPW L* sin *βCPW L* (28)

*O* =sinh *αCPW L* cos *βCPW L* (29)

*P* =cosh *αCPW L* sin *βCPW L* (30)

cosh *αCPW L* sin *βCPW L*

sinh *αCPW L* cos *βCPW L*

<sup>2</sup>*Z*0*ω<sup>C</sup>* (31)

<sup>2</sup>*Z*0*ω<sup>C</sup>* (32)

<sup>2</sup> ) (33)

*<sup>j</sup>*2*<sup>Z</sup>* <sup>0</sup>*ω<sup>C</sup>* (*<sup>O</sup>* <sup>+</sup> *jP*) (26)

(25)

calculated from (23) and (24) as:

where

and

and

and

*A B <sup>C</sup> <sup>D</sup>* <sup>=</sup> *<sup>A</sup> <sup>B</sup>*

140 Radio Frequency Identification from System to Applications

*C D CPW*

*\* A B*

From (25), parameter A can be calculated and (21) can be written as:

cosh *αL* cos *βL* + *j*sinh *αL* sin *βL* =*M* + *jN* +

cosh *αL* cos *βL* =cosh *αCPW L* cos *βCPW L* +

sinh *αL* sin *βL* =sinh *αCPW L* sin *βCPW L* -

*<sup>α</sup>* <sup>=</sup> <sup>1</sup>

The layout of the proposed ZOR RFID antenna is shown in Fig. 7 [30]. The port of the an‐ tenna is located in the middle of the antenna with series capacitance down each arm. The operating principle of this antenna is based on the capacitive input impedance of the pas‐ sive RFID ASIC. At resonance, the interdigital capacitors are supporting a wave propagat‐ ing along the antenna. Since the input impedance of the ASIC is also capacitive the ASIC also supports wave propagation along the antenna in a manner similar to the interdigital capacitors [30]. During this process, the ASIC harvests the required power to perform the desired tasks and communicate while simultaneously supporting the wave propagating on the antenna.

The first step in the design process is to determine what capacitance is required to equate β to zero at the desired operating frequency such that the antenna looks infinitely long. For discussion, the non-zero frequency at which β becomes zero is known as the zeroth order resonance (ZOR) frequency [26], [30]. For simplicity a lossless (α = 0) CPW line is assumed and then from (31) the required capacitance can be calculated to achieve ZOR at a particular design frequency as:

$$\mathbf{C} = \frac{\cosh \alpha\_{\text{CPW}} \ L \ \sin \beta\_{\text{CPW}} \ L}{2\omega\_r Z\_0 \{1 \ - \cosh \alpha\_{\text{CPW}} \ L \ \cos \beta\_{\text{CPW}} \ L\ \}} \tag{35}$$

**5.2. Zeroth order resonator RFID antenna measurements**

antennas are given in Table 1 and [30].

**Table 1.** Design parameters of proposed ZOR RFID antenna

following equations were used to predict the maximum read range:

Again, the proposed ZOR RFID antenna with the capacitor loaded CPW is shown in Fig. 7. The antenna is composed of four series connected unit cells, where each unit cell has a lay‐ out similar to the image in Fig. 6. The proposed antenna has a 50 ohm CPW at one end and a high characteristic impedance short circuit line on the other end similar to [26] and [30]. The Higgs-2 by Alien Techonologies [29] RFID ASIC was used and attached at the port of the antenna (at the center). The Higgs-2 has an input impedance of Zin = 13.73 + j142.8 Ω at 915 MHz. The antenna was designed on a Rogers TMM4 substrate with εr = 4.5, tan δ = 0.002 and a substrate thickness of H = 1.524 mm. The design parameters of the proposed ZOR RFID

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A wider central strip was used to obtain the required series capacitance as shown in Fig. 7 and the gap between the central conductor and reference conductors on either side was made as large as possible so that the parasitic shunt capacitance could be made as small as possible. This ensured a dominant series capacitance created by the interdigital capacitance and the input impedance of the passive UHF RFID ASIC connected to the antenna port. Fur‐

The ZOR RFID antenna shown in Fig. 7 was simulated in Ansoft HFSS v.13. The simulated input resistance, reactance and reflection coefficient are shown in Fig. 9, Fig. 10 and Fig. 11,

> C 2.4 pF w3 0.66 mm W 8.82 mm S1 12.17 mm L 17.56 mm S2 0.35 mm S 7.96 mm L1 5 mm w1 0.4 mm *l* 16.2 mm W2 3 mm g 0.36 mm

Next, to measure the read range of the prototype tag, an Alien Technologies ALR-9900 RFID reader was used [29] (with maximum output power of 1W). It was connected to a circularly polarized antenna with a gain of 6dBi and the RFID Tag was placed in an anechoic chamber. A read range of 3.4 m was determined with the RFID reader; however the *max read range* was not determined because the overall dimensions of the anechoic chamber were too small. An alternate method has been provided in [30] and [31] to predict the maximum achievable read range based on system power levels and measurements. This method uses the Friis transmission equation and the fact that a certain minimum power is required to activate the tag. Using this information the output power of the RFID reader was reduced until the read‐ er could no longer detected the tag at 3.4 m. The required attenuation was 7 dB. Then the

thermore, this will simplify the ABCD matrix representation of each unit cell.

respectively. The fabricated prototoype ZOR RFID antenna is shown in Fig. 12 [30].

Since we are interested in designing a ZOR antenna for the passive UHF RFID band, 915 MHz is taken as the operating frequency and from (35) the required capacitance can be cal‐ culated as C = 2.64 pF.

The unit cell shown in Fig. 7 was simulated in ADS 2009 with design parameters L = 17.56 mm, W = 8.82 mm, w3 = 0.36 mm, S = 7.96 mm and H = 1.524 mm. A Rogers TMM4 (εr = 4.5 and tan δ = 0.002) was used as a substrate. For the lossless case the attenuation constant of the CPW and loss tangent of the substrate was assumed to be zero and a perfect conductor was considered. The capacitance of the unit cell was extracted [10] to be Cextracted = 2.4 pF which is close to the required capacitance for ZOR at 915 MHz. The dispersion characteris‐ tics are plotted in Fig. 8. It can be noted that the attenuation constant decreases monotonical‐ ly and becomes zero after 944 MHz. Similarly the propagation constant remains zero and after 944 MHz it increases monotonically. Thus 944 MHz can be taken as ZOR frequency for the given unit cell which comes within 3.2% of the required resonance frequency of 915 MHz. More discussion on this is reported in [30].

For the lossy case the attenuation constant of the CPW was calculated using (19) and the loss tangent was taken as tan δ = 0.002. The conductivity was defined as σ = 5.8 x 107 S/m with a conductor thickness of 35 µm. The dispersion characteristics for the lossy case were also pre‐ sented in Fig. 8. A similar response for both the lossy and lossless case is shown except for the fact that the phase constant is non-zero below the ZOR point and similarly the attenua‐ tion constant is non-zero after the ZOR point. Here the ZOR point is taken as the point at which α = β and it coincides with the lossless ZOR point [26],[30].

**Figure 8.** Dispersion diagram of lossless and lossy interdigital capacitor loaded CPW

#### **5.2. Zeroth order resonator RFID antenna measurements**

*<sup>C</sup>* <sup>=</sup> cosh *<sup>α</sup>CPW <sup>L</sup>* sin *<sup>β</sup>CPW <sup>L</sup>*

culated as C = 2.64 pF.

142 Radio Frequency Identification from System to Applications

MHz. More discussion on this is reported in [30].

which α = β and it coincides with the lossless ZOR point [26],[30].

**Figure 8.** Dispersion diagram of lossless and lossy interdigital capacitor loaded CPW

Since we are interested in designing a ZOR antenna for the passive UHF RFID band, 915 MHz is taken as the operating frequency and from (35) the required capacitance can be cal‐

The unit cell shown in Fig. 7 was simulated in ADS 2009 with design parameters L = 17.56 mm, W = 8.82 mm, w3 = 0.36 mm, S = 7.96 mm and H = 1.524 mm. A Rogers TMM4 (εr = 4.5 and tan δ = 0.002) was used as a substrate. For the lossless case the attenuation constant of the CPW and loss tangent of the substrate was assumed to be zero and a perfect conductor was considered. The capacitance of the unit cell was extracted [10] to be Cextracted = 2.4 pF which is close to the required capacitance for ZOR at 915 MHz. The dispersion characteris‐ tics are plotted in Fig. 8. It can be noted that the attenuation constant decreases monotonical‐ ly and becomes zero after 944 MHz. Similarly the propagation constant remains zero and after 944 MHz it increases monotonically. Thus 944 MHz can be taken as ZOR frequency for the given unit cell which comes within 3.2% of the required resonance frequency of 915

For the lossy case the attenuation constant of the CPW was calculated using (19) and the loss tangent was taken as tan δ = 0.002. The conductivity was defined as σ = 5.8 x 107 S/m with a conductor thickness of 35 µm. The dispersion characteristics for the lossy case were also pre‐ sented in Fig. 8. A similar response for both the lossy and lossless case is shown except for the fact that the phase constant is non-zero below the ZOR point and similarly the attenua‐ tion constant is non-zero after the ZOR point. Here the ZOR point is taken as the point at

<sup>2</sup>*ωrZ*0(1 - cosh *<sup>α</sup>CPW <sup>L</sup>* cos *<sup>β</sup>CPW <sup>L</sup>* ) (35)

Again, the proposed ZOR RFID antenna with the capacitor loaded CPW is shown in Fig. 7. The antenna is composed of four series connected unit cells, where each unit cell has a lay‐ out similar to the image in Fig. 6. The proposed antenna has a 50 ohm CPW at one end and a high characteristic impedance short circuit line on the other end similar to [26] and [30]. The Higgs-2 by Alien Techonologies [29] RFID ASIC was used and attached at the port of the antenna (at the center). The Higgs-2 has an input impedance of Zin = 13.73 + j142.8 Ω at 915 MHz. The antenna was designed on a Rogers TMM4 substrate with εr = 4.5, tan δ = 0.002 and a substrate thickness of H = 1.524 mm. The design parameters of the proposed ZOR RFID antennas are given in Table 1 and [30].

A wider central strip was used to obtain the required series capacitance as shown in Fig. 7 and the gap between the central conductor and reference conductors on either side was made as large as possible so that the parasitic shunt capacitance could be made as small as possible. This ensured a dominant series capacitance created by the interdigital capacitance and the input impedance of the passive UHF RFID ASIC connected to the antenna port. Fur‐ thermore, this will simplify the ABCD matrix representation of each unit cell.

The ZOR RFID antenna shown in Fig. 7 was simulated in Ansoft HFSS v.13. The simulated input resistance, reactance and reflection coefficient are shown in Fig. 9, Fig. 10 and Fig. 11, respectively. The fabricated prototoype ZOR RFID antenna is shown in Fig. 12 [30].


**Table 1.** Design parameters of proposed ZOR RFID antenna

Next, to measure the read range of the prototype tag, an Alien Technologies ALR-9900 RFID reader was used [29] (with maximum output power of 1W). It was connected to a circularly polarized antenna with a gain of 6dBi and the RFID Tag was placed in an anechoic chamber. A read range of 3.4 m was determined with the RFID reader; however the *max read range* was not determined because the overall dimensions of the anechoic chamber were too small. An alternate method has been provided in [30] and [31] to predict the maximum achievable read range based on system power levels and measurements. This method uses the Friis transmission equation and the fact that a certain minimum power is required to activate the tag. Using this information the output power of the RFID reader was reduced until the read‐ er could no longer detected the tag at 3.4 m. The required attenuation was 7 dB. Then the following equations were used to predict the maximum read range:

**Figure 9.** Proposed ZOR RFID antenna input resistance

**Figure 10.** Proposed ZOR RFID antenna input reactance

$$P\_{r\_{min}} = \frac{P\_{t\_{max}} G\_t G\_r \lambda^2}{(4\pi R\_{max})^2} \tag{36}$$

Putting α = 7 dB and Rmeasured = 3.4 m in (38) gives a predicted max read range of 7.6 m which meets or exceeds the performance of similar and large passive UHF RFID tags available on

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The expanding use of passive UHF RFID systems has increased the performance demands on readers, tags, software and manufacturing costs. Because of these new constraints, the desire for more compact and better performing tags is beginning to grow. In this chapter, a summary of passive UHF RFID systems has been presented with several of the key antenna design requirements mentioned. Following this introduction, background on left-handed

the market today.

**Figure 11.** Input reflection coefficient of proposed ZOR RFID antenna

**Figure 12.** Fabricated ZOR RFID antenna [30]

**6. Conclusion**

and

$$P\_{r\_{min}} = \frac{P\_{t\_{max}}}{\alpha} \frac{G\_l G\_r \lambda^2}{(4\pi R\_{measured})^2} \tag{37}$$

Since (36) and (37) both use minimum received power, they can be equated to produce

$$R\_{\text{max}} = 10^{\alpha\_{d8}/20} R\_{\text{measured}} \tag{38}$$

Putting α = 7 dB and Rmeasured = 3.4 m in (38) gives a predicted max read range of 7.6 m which meets or exceeds the performance of similar and large passive UHF RFID tags available on the market today.

**Figure 11.** Input reflection coefficient of proposed ZOR RFID antenna

**Figure 12.** Fabricated ZOR RFID antenna [30]

#### **6. Conclusion**

**Figure 9.** Proposed ZOR RFID antenna input resistance

144 Radio Frequency Identification from System to Applications

**Figure 10.** Proposed ZOR RFID antenna input reactance

and

*Prmin* =

*Pt max α*

Since (36) and (37) both use minimum received power, they can be equated to produce

*GtGr<sup>λ</sup>* <sup>2</sup>

*Prmin* =

*Pt maxGtGr<sup>λ</sup>* <sup>2</sup>

(4*πRmax*)2 (36)

(4*πRmeasured* )2 (37)

*Rmax* =10*αdB*/20*Rmeasured* (38)

The expanding use of passive UHF RFID systems has increased the performance demands on readers, tags, software and manufacturing costs. Because of these new constraints, the desire for more compact and better performing tags is beginning to grow. In this chapter, a summary of passive UHF RFID systems has been presented with several of the key antenna design requirements mentioned. Following this introduction, background on left-handed propagation, co-planar waveguides and interdigital capacitor loaded co-planar waveguides have been introduced and summarized. From these sections, the ZOR-RFID antenna for pas‐ sive UHF RFID tags is presented. The operating principle behind the ZOR-RFID antenna is the use of interdigital capacitors along the length of the antenna to support wave propaga‐ tion. Furthermore, the capacitive input impedance of the passive RFID ASIC attached to the port of the antenna supports propagation in a manner similar to the interdigital capacitors. This allows the ASIC to still harvest power and communicate while supporting wave propa‐ gation. Measurements show that a predicted 7.6 m read range is possible with this new an‐ tenna design. This read range is comparable to existing commercially available passive UHF RFID tags with similar overall sizes.

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