Using the zeroth order resonance of an inter-digital capacitive unit-cell to design antennas for passive UHF RFID tags

Meander-line and multi-layer antennas have been used extensively to design compact UHF radio-frequency identiﬁcation (RFID) tags; how-evertheoverallsizereductionofmeander-lineantennasislimitedbytheamountofparasiticinductancethatcanbeintroducedbyeachmeander-linesegmentandmulti-layerantennascanbetoocostly.Inthispaper,anewcompactantennatopologyforpassiveUHFRFIDtagsbasedonze-rothorderresonant(ZOR)designtechniquesispresented.Theantennaconsistsoflossycoplanarconductorsandinter-connectedinter-digitalcapacitor(IDC)unit-cellswithaZORfrequencyneartheoperatingfre-quency,whichisakeycomponentinthedesignprocessbecausetheunit-cellschosenforthedesignareinductiveattheoperatingfrequency.Thismakestheunit-cellsveryusefulforantennaminiaturization.Thenewdesigninthisworkhasseveralbeneﬁts;namelythecoplanarlayout can be printed on a single layer, matching inductive loops that reduce antenna efﬁciency are not required and ZOR analysis can be used for the design. Finally, for validation, a prototype antenna was designed with a unit-cell ZOR resonant frequency of 900 MHz, fabricated and characterized. A maximum read-range of 7.6 m was determined.


Introduction:
The demand for more compact antennas on wireless devices is ever increasing. This is especially notable for passive radiofrequency identification (RFID) systems at the UHF band that are being applied in new areas such as medicine [1], textiles [2], vehicle security [3], and musical instruments [4]. Current RFID tags are much more compact than some of the original prototype RFID tags. This is because much research and development have been conducted on novel techniques, such as meander-lines [5] and multi-layer structures [6] to reduce the overall size of the antenna on a passive RFID tag. However, the size reduction of meander-line antennas is limited in part by the amount of parasitic inductance that can be introduced by the meander-line segments [7] and a multi-layer antenna can make an RFID tag very expensive.
Zeroth order resonator (ZOR) antennas [8,9] have shown to be a promising alternative to previously established methods for reducing the overall size of a printed antenna. A different approach is taken in the case of ZOR antennas compared to aforementioned techniques to reduce the overall size. To be specific, ZOR antennas consist of resonant unitcells that each individually behave as an infinite wavelength structure at a particular frequency, denoted as the ZOR frequency (f ZOR ), regardless of size. This then results in a uniform phase and magnitude field distribution across the unit-cell; which in turn improves the radiation of the overall antenna at f ZOR . These resonant unit-cells have an additional feature that can be used in the antenna design process. Depending on layout, when the unit-cell is driven below f ZOR the impedance can be capacitive and when the unit-cell is driven above f ZOR the impedance can be inductive. This work shows that this inductance can be very useful for compact antenna designs and antenna miniaturization.
Techniques for designing and reducing the overall size of an antenna are of great interest to the antenna community and this is particularly true in the RFID area. The objective of this work is to use the ZOR frequency of an inter-digital capacitor (IDC) unit-cell to design a compact single-layer printed antenna on a passive UHF RFID tag. A schematic of the proposed antenna is shown in Figure 1 and the equivalent circuit of the antenna is shown in Figure 2. As the antenna is of dipole nature, the input impedance is capacitive below the resonant frequency and inductive above. Therefore, the resonant frequency can be reduced by introducing inductance along the length of the antenna [7]. For this work, the IDC unit-cell will be used to introduce the inductance by designing the unit-cell to have a ZOR frequency below the operating frequency of the overall antenna. A technique for computing the dimensions of the IDC unit-cell based on the ZOR frequency analysis of a coplanar waveguide (CPW) structure will be shown and further discussion on the design method is presented.
Antenna design methodology using zeroth-order resonant frequency analysis of the IDC unit-cell: The equivalent circuit of the IDC unitcells in Figure 1 is shown in Figure 2b. The IDC series capacitance and inductance are denoted as C IDC and L, respectively. Furthermore, the shunt capacitance between the IDC conductors and the surrounding reference conductor for the CPW structure is denoted as C s . To introduce the required inductance along the length of the RFID antenna, the resonant frequency of the IDC unit-cell in Figure 2b should be below the operating frequency of the overall antenna. One method of determining the frequency in which the IDC unit-cell stops introducing capacitance and starts introducing inductance is to compute the ZOR frequency of the unit-cell, which can be done with ZOR resonant frequency analysis. The ZOR resonant frequency can be determined by analysing the dispersion characteristics of the IDC unit-cell shown in Figure 3a. Particularly, the frequency at which the propagation constant γ = α + jβ = 0 for lossless transmission lines (TLs) is denoted as the ZOR frequency. The distance s between the IDC and reference planes can be assumed to be much smaller than the series IDC, which results in the TL equivalent model in Figure 3b of the IDC unit-cell shown in Figure 3a.
The ABCD matrices of the capacitor loaded CPW unit-cell in Figure 3a are derived next to extract the propagation constant. Generally, the ABCD matrices of the unit-cell can be written as: where the ABCD matrix for the lossy CPW TL can be written as [9]: and the ABCD matrix for a TL with a series loaded IDC can be written as [10]: where the closed-form expressions for the characteristic impedance Z 0 and the propagation constant γ CPW of the lossy CPW TL in Figure 3b can be computed using the expressions in [11]. Next, substituting Equations (2) and (3) into Equation (1), multiplying and equating the real and imaginary parts results in the following where again γ = α + jβ is the propagation constant of the entire IDC unit-cell (this includes the IDC and the TLs on both sides of the IDC). Equations (4a) and (4b) can be simultaneously solved to find the unknowns α and β, which are the attenuation and the phase constants of the Bloch wave on the IDC unit-cell, in the following manner [9] and where F = X 2 + (X + 1) 2 ± Y 2 + (X − 1) 2 , and X and Y are the right-hand sides of Equations (4a) and (4b), respectively. The expressions for α and β obtained from Equations (5) and (6), respectively, can be used to compute the dispersion characteristics of the lossy IDC unitcell. A key point in this antenna design is to implement an IDC unit-cell that has a zero-phase constant (i.e. β = 0) at a frequency in or near the UHF RFID band (depending on the application), or that the right-hand side of Equation (6) becomes zero at the frequency of interest. However, for lossy TLs, α = 0 and β = 0 at the frequency where β may be equal to 0 for the lossless TLs [9]. Therefore, for lossy unit-cells the ZOR frequency is defined as the frequency such that α = β [9]. This condition will be used here as the ZOR frequency for the IDC unit-cells in the antenna design. The first step is to determine the capacitance required to obtain ZOR at the desired frequency (i.e. the frequency where α = β). For this work,

Fig 4 Dispersion and transmission phase of the proposed IDC unit-cell (a) dispersion diagrams of the lossy CPW IDC unit-cell. (b) Simulated S 21 phase of the IDC unit-cell
the operating frequency was chosen to be 900 MHz. Therefore, to introduce the ZOR frequency of the IDC unit-cell is defined to be 900 MHz. The ZOR frequency selection depends on the application. For this work, the antenna is required to be a conjugate match at the operating frequency of 920 MHz to a passive RFID IC attached to the port of the antenna. This then requires the resonant frequency of the antenna and ZOR frequency of the IDC unit-cell to be approximately 900 MHz [7]. Then, when the antenna is driven at higher frequency, the added benefit of the IDC unit-cell inductively loading the antenna will be observed. Next, using the expressions in [11], the required capacitance for a desired ZOR frequency can be calculated as [9] C IDC = cosh α CPW p sinβ CPW p 2ω r (1 − coshα CPW p cosβ CPW p) where ω r = 2π × 900 MHz. Equation (7) can be used in an iterative manner to determine the dimensions of an IDC unit-cell that can be manufactured practically. After several design iterations using Equation (7), the final dimensions of the IDC unit-cell in Figure 3a were determined to be: W = 8.82 mm, finger width f W = 0.66 mm, finger gap f g = 0.36 mm, p = 17.56 mm, s = 7.96 mm, substrate thickness h = 1.524 mm, and conductor thickness t = 35 μm. Rogers TMM4 (ε r = 4.5 and tanδ = 0.002) was used as a substrate. From Equation (7) the computed capacitance to obtain ZOR at 900 MHz was found to be C IDC = 2.64 pF. The dispersion characteristics of the IDC unit-cell are computed using Equations (5) and (6) and are plotted in Figure 4a. The curves that cross at 900 MHz are the dispersion characteristics of the IDC unit-cell computed using Equation (7). It is shown that the phase constant (β) is nonzero below the ZOR frequency and similarly the attenuation constant (α) is non-zero after the ZOR frequency. Here the ZOR frequency is taken as the point at which α = β and it is below the operating band. To validate that inductance will be introduced by the IDC unit-cell, the single cell shown in Figure 3a with dimensions computed above was simulated in Advanced Design Systems (ADS) software. The phase of S 21 was computed and the results are shown in Figure 4b. At 900 MHz, the unit-cell introduced −6.3°of phase on the TL, indicating that it transitions from capacitive to inductive.

Prototype and measurement of the ZOR RFID antenna:
The proposed antenna shown in Figure 1 consists of four series connected IDC unitcells. Each IDC unit-cell has the same layout and dimensions. The final dimensions were determined in HFSS to have a conjugate match at 920 MHz with the passive Higgs-2 [12] RFID IC attached to the antenna port. As with the IDC unit-cell, the antenna was simulated in HFSS on a Rogers TMM4 substrate with ε r = 4.5, tanδ = 0.002 and a substrate thickness h = 1.524 mm. The manufactured prototype tag and the simulated input impedance were shown in Figure 5. Note that the input impedance (Z in = 15 + j145 ) of the antenna is close to conjugate value of the input impedance of the Higgs-2 IC (Z IC = 13.7 + j142.8 ) at 920 MHz. Next, for comparison, the equivalent circuit of the RFID antenna shown in Figure 2 was extracted using ADS and compared to HFSS simulations and the analytical value was computed using Equation (7). The extracted values are shown in the caption of Figure 2 and the IDC capacitance was found to be C extracted = 2.75 pF. This value is within 4.1% of the value computed using Equation (7). The dispersion characteristics of the IDC unit-cell were also computed using Equations (5) and (6) with the extracted capacitance. These results are plotted in Figure 4a for the lossy case. The curves that cross at 885 MHz are the dispersion characteristics of the IDC unit-cell computed using the circuit extraction method. It is shown that the ZOR frequency is f ZOR = 885 MHz and below the operating band of the passive RFID tag.
Furthermore, the input impedance of the prototype antenna was computed using the equivalent circuit. These results are shown to agree with HFSS simulations in Figure 5. Figure 6 shows the input return loss (S 11 ) of the prototype ZOR antenna. The input return loss (S 11 ) also shows that the IDC-integrated proposed antenna has a very narrow bandwidth, which is essential for applications like RFID, GSM 900 satellite downlinks etc. to cancel out wideband unwanted noise.
Next, to measure the read-range of the prototype RFID tag, an Alien technologies ALR-9900 RFID reader having a maximum output power of 1 W was used [12]. The RFID reader was connected to a circularly polarized antenna with a gain of 6 dBi and the prototype RFID tag was placed in an anechoic chamber with the reader antenna. An image of the prototype tag being measured in the anechoic chamber is shown in Figure 5d. The prototype RFID antenna tag was linearly polarized. Because of the limited size of the chamber, a maximum read-range could not be determined by moving the tag away from the reader until it could no longer read. An alternate method has been provided in [13] for such cases where it is not possible to directly measure the maximum read-range due to space limitations. Using the method outlined in [13], the maximum achievable read-range can be predicted based on system power levels and measurements for a known distance between the antenna on a RFID reader and the tag under test. This method uses the Friis transmission equation and the fact that a certain minimum power is required to activate the RFID tag. Using this information the output power if the RFID reader was reduced until the reader initially detected the prototype tag at a distance of 3.4 m. This value is denoted as R measured . The required attenuation to initiate the reading of the tag is denoted as α dB and determined to be 7 dB. Then the following equation was used to predict the maximum read-range: R max = 10 αdB/20 R measured . This then resulted in R max = 7.6 m.
Conclusion: In this paper, an antenna for passive UHF RFID tags with inter-connected IDC unit-cells was proposed and developed. The operating principle behind the RFID antenna depends on the zeroth order resonant (ZOR) frequency of the IDC unit-cells along the length of the antenna to introduce inductance to cancel the input capacitance. Measurements have shown that the methodology presented in this work can be used to design an antenna on a prototype passive RFID tag with a good conjugate match to the passive IC. It was shown that a predicted maximum read-range of 7.6 m was possible with this proposed novel antenna design.