SELF-RESONANT ELECTRICALLY SMALL ANTENNA

DESCRIPTION

OBJECT OF THE INVENTION

The present invention is applicable to the antenna miniaturization design, for example, in the technical field of Radiofrequency Identification

(RFID) by a micro-antenna coupled to a chip conforming an electronic label, commonly termed RFID tag, and attached to an object, animal or a person for its/his/her automatic identification.

More particularly, the invention that is disclosed herein relates to an antenna that achieves self-resonance without needing any external matching network between the antenna and the source (for example an RFID chip) and can be reduced in size arbitrarily, just adjusting different parameters of the resonant structure (at the expense of a reduced read range). This tiny antenna is especially suitable for RFID applications because it can be fabricated in a single layer substrate, with small dimensions as the antennas used in RFID tags require.

BACKGROUND OF THE INVENTION

The size reduction of antennas is a fundamental issue for different communications applications. Antennas should be integrated in different electronic products as mobile phones, laptops, personal digital assistant (PDA), etc., and they require a small antenna capable of being integrated with different products.

Another common application for small antennas is Radio

Frequency Identification (RIFD). This technology allows the identification of any object with the aid of an electronic tag attached to it. This electronic tag

is composed by a small antenna and a micro-chip. In the technological development of Radiofrequency Identification, the tiny antennae of the RFID electronic tag can operate in a low-frequency band (LF), around 125 kHz, others in the high-frequency band (HF) at 13.56 MHz and some last ones are developed to work in the 900 MHz range, in the ultra-high-frequency (UHF) band. Different implementations of the RFID tags carrying in the interior thereof the microchip connected to the printed circuit antenna are known, for example, implemented in self-adhesive labels, capsules, coins, cards, badges, etc.

Normally, the size of a given antenna is in the order of the wavelength. This restriction means that antennas for low frequencies will be larger than antennas for high frequencies. In contrast, small antennas herein are commonly defined as antennas that fit in a sphere of radius λ/(2ττ), being λ the wavelength.

One of the most usual antennas is the resonant dipole as known in literature. A resonant dipole is a balanced antenna formed by a wire with length slightly shorter than half a wavelength fed at the centre.

A self-resonant antenna, as the resonant dipole, is an antenna whose input impedance is purely real. The maximum power transfer theorem states that, for a linear network with fixed source impedance, the maximum power is delivered from the source (antenna) to the load (chip) when the load impedance is the complex conjugate of the source impedance.

For a self-resonant antenna, as the impedance is real, the maximum power will be delivered when the antenna and source impedance are equal.

Based on the maximum power transfer theorem, if the antenna is not self-resonant, usually a matching network is needed in order to achieve

the maximum power transfer between antenna and load.

As the resonant dipole, the self-resonant antennas known so far have a size in the order of the wavelength, which for some applications is very large. If the size of the antenna is required to be reduced, the input impedance becomes reactive (inductive or capacitive, depending of the structure of the antenna).

Therefore, the common solution for small antenna design and in order to achieve resonance is the introduction of a matching network, inevitably increasing the overall size and the cost.

Among the well-known self-resonant structures, besides the aforementioned resonant dipole, the Split Ring Resonator (SRR), introduced by Pendry (see "Magnetism from conductors and enhanced non linear phenomena" by J. B. Pendry et al., IEEE Transactions on Microwave Theory and Techniques, vol. 47, pp. 2075-2084, November 1988) is a great contribution to the field of metamaterials since it is the first particle able to achieve negative values of effective magnetic permeability. The structure of such resonator consists of two concentric metallic rings. Both rings have a certain thickness (c) and small gaps etched on opposite sides, as shown in Figure 1 A. The SRR has a mean radius (r ₀ ) measured just in between the two concentric rings. Also, Figure 1 B shows the equivalent circuit of a SRR (proposed in "Comparative analysis of edge and broadside coupled split ring resonators for metamaterial design. Theory and experiments" by R. Marques et al., IEEE Transactions on Antennas and Propagation, vol. 51 , pp. 2572- 2581 , October 2003), where the total capacity (C ₀ ) between the rings is Co=2πroC _Pu i, where C _pu ι is the capacity between rings per unit length. The resonant frequency of the SRR is given by fo=(L _s C _s ) ^'V2 /2π, where C _s is the series connexion of the capacities corresponding to the upper and lower parts, i.e. C _s =C ₀ IA. The induction (L ₅ ) can be approximated by the induction of a single ring with a radius equal to the mean radius (r ₀ ) of the SRR and

width (c) of each concentric ring.

The behaviour of the SRR in its first resonance can be approximated by a resonant dipole (stated in "Magnetism from conductors and enhanced non linear phenomena" by J. B. Pendry et al., IEEE Transactions on Microwave Theory and Techniques, vol. 47, pp. 2075-2084, November 1988) and then its magnetic polarization is expressed by:

wherein B ₂ is the axial magnetic component of the electromagnetic field, Qo is a geometric factor and ω ₀ is the resonant frequency of the SRR.

According to the previous expression, the polarizability will have extreme values near the resonant frequency. Since the current in the SRR is uniform, it can be approximated by a plane loop and so the following expression applies: m _z = IS wherein / is the current through the SRR and S is the total area. Hence, the current / through the SRR is:

From this expression it can be seen that the current in the SRR (I) is very large near the resonant frequency, even for a small structures. Figure 2 shows the current density distribution in a SRR at the resonant frequency.

Due to the resonant behaviour of the SRRs, a periodic array of these resonators, such as the one shown in Figure 3, illuminated by a properly polarized incoming field does not allow the propagation of

electromagnetic waves for a specific frequency range. Thanks to such an effect due to the effective medium theory, a periodic array of SRRs can be used as a filter for millimetre waves and microwaves. An example of this use is EP 1675212 A1 , wherein a planar transmission element, such as a microstrip line or a central metallic plane with dielectric substrate on both sides and a conducting strip formed on it, is mounted in magnetic coupling with an in-series insertion of several SRRs. Besides, EP 1675212 A1 provides an antenna or a battery of antennae which incorporates the described filter comprising said array of SRRs for emission and reception of electromagnetic waves, because the behaviour of the array of SRRs as an effective medium allows the propagation of fast waves for a given frequency, and then it behaves as a leaky wave antenna.

Other variations of SRRs are depicted in Figures 4-7 (see "Equivalent-circuit models for split-ring resonators and complementary split- ring resonators coupled to planar transmission lines" by J. D. Baena et al., IEEE Trans, on Microwave Theory and Techniques, vol. 53 (4), pp. 1451- 1461 , April 2005), showing structures and equivalent circuits respectively of:

Non-bianisotropic SRR (NBSRR), shown in Figure 4: it presents a

180° rotation symmetry in the plane of the SRR; as a consequence of this symmetry the NBSRR avoids cross-polarization effects while keeping the single-plane geometry.

Double-Slit SRR (D-SRR) or Distorted/Dual Split Ring Resonator, shown in Figure 5: it also presents the aforementioned symmetry, thus avoiding cross polarization; however, the D-SSR equivalent circuit differs from that of the SRR, being the frequency of resonance twice than that of a SRR of identical size.

Spiral resonator (SR), shown in Figure 6, and Double spiral resonator (DSR), shown in Figure 7: The SR presents a structure composed by a spiral element with two radii. The DSR has two coupled spiral elements

In both cases, the resonant frequency does not only depend on the overall size. As can be seen from their equivalent circuits, the SR as well as the DSR allow for a reduction of the resonant frequency with respect to the SRR.

Following the Babinet principle, the SRR has a dual counterpart which is so-called Complementary SRR (CSRR). Metal parts of the SRR are changed by slots in a conducting plane in the CSRR. In this way, electric currents in the rings are changed by magnetic currents in the slots and electric and magnetic fields surrounding the SRR are swapped by each other in the CSRR. Magnetic currents in the slots do no physically exist; actually they are a mathematical model for modelling the electric currents on the conducting plane. The currents are not confined to the edges of the slot but rather spread out over the conducting plane. In the SRR, the currents are more confined, and a higher current density flows through the rings. Because of this, power loss in SRR due to metal losses can be higher (lower efficiency) than in CSRR.

Returning to resonant simple structures like the dipole, when it is used in antennas, a solution to overcome the reduction of the radiation resistance due to the miniaturization of the antenna is using a folded structure, which allows a x4 increment of the radiation resistance. At the resonant frequency using a folded dipole allows to increase the real component of the input impedance (radiation resistance and loss resistance) without varying the resonant frequency. A dipole antenna and a single folded- dipole antenna are shown in Figure 8A and 8B respectively.

DESCRIPTION OF THE INVENTION

The present invention is intended to resolve the problem outlined above on miniaturized antenna design without needing to introduce a matching network in the antenna and satisfying both of two antenna design requirements: small size and matching to the source. Thus, one aspect of

this invention deals with an antenna which comprises a self-resonant radiating structure that is perfectly adaptable to manufacture of micro- antennas for Radiofrequency Identification (RFID). And hence, another aspect of the invention refers to an RFID tag which comprises an antenna configured with this self-resonant radiating structure as described as follows.

The antenna proposed in this invention comprises at least a radiant element consisting of a resonant structure, built in a planar substrate and excited at a feed point, which produces an electric current through the feed point when said resonant structure is excited by a magnetic field (or an electric field in case the complementary resonant structure, applying the Babinet principle, is used) pointed in a direction transversal to the planar substrate. The resonant structure can be modelled by an equivalent electric circuit with inductance and capacitance that determine its resonant frequency.

More over, such self- resonant structure can be used as a near field UHF tag antenna, because it can be excited by the magnetic near (or evanescent) field from a reader antenna.

Contrary to the radiated fields, which decouple from the antenna and travel at the speed of light in waveforms, near fields exist only coupled to the antenna, and confined to a region in its vicinity. This property can be used in RFID to gain control and resolution over the space in which tags will be detected.

Preferably, an antenna comprising a radiant element that is a self- resonant structure as defined above is one based on the possible split ring resonator configurations (SRR, CSRR, DSRR, etc.).

If a variable magnetic field pointed towards the axis of both rings (internal and external rings) conforming a split ring resonator structure is

applied, due to the gaps built in these rings, the generated currents only can flow by means of the displacement current, because of the high capacitive values originated between the internal and external rings. The conductors introduce an inductive behaviour to the circuit and combined to the capacity between the rings, the SRR has a resonant behaviour when excited by an axial magnetic flux, showing a high diamagnetism over the first resonance.

Since the split ring resonator structure can resonate at a frequency not only dependent on its overall size, this means that the size of the resonator can be reduced arbitrarily for a given frequency and so, when the structure is fed to produce electromagnetic radiation, the SRR is a self- resonating and radiating element which becomes an antenna as small as required.

In order to feed the antenna, a small slit or gap can be done in the middle of the SRR, without modifying significantly the resonance frequency, because the equivalent circuit of this SRR behaves as a RLC series circuit at the resonant frequency and said resonant frequency is not affected by introducing a series resistor in the feeding point or feeding port etched in the external or internal ring.

An advantage of the antenna based on the SRR configuration is that the resonant antenna overall size can be reduced as much as needed just by increasing the overall inductance and capacitance between rings of the SRR.

A main difference of the present invention from the antennae described in EP 1675212 A1 lies in the electromagnetic radiation originated by the rings of the SRR. The radiation pattern of the SRR antenna described here is almost omni-directional with maximum gain in the plane containing the rings. If these rings have a radius much smaller than the wavelength, the SRR can be modelled, at the resonant frequency, as a loop antenna with an

equivalent radius equal to the mean radius (r ₀ ) of the SRR and an equivalent width equal to the width (c) of the rings. Thus, the radiation pattern of the SRR is similar to the one generated by a loop antenna. However, the SRR radiating structure is self-resonant, whilst the loop is purely inductive and requires a matching network to maximize transferring of power to the load of the antenna. For a loop antenna, the load must be the complex conjugated of the antenna impedance and the inductive component must be cancelled. On the contrary, the SRR does not need any matching network to the load and, at the same time, the resonant frequency can be kept independent from the SRR size, being an optimal configuration to be applied in miniature antennae.

That is not applicable in EP 1675212 A1 , wherein the radiant element of the antenna is a transmission line, not the SRR, but the SRR array structure behaves as a metamaterial or effective medium allowing the propagation of fast waves through the transmission line and then radiating power as a leaky wave antenna, constituted by the combination of all rings, and where each individual ring does not radiate by itself.

As it has been explained before, a magnetic field through the SRR-based antenna induces a current around the rings. Based in this principle, another way to feed the antenna proposed here is exciting the SRR by means of a metallic loop which can be etched inside or outside the SRR. This feeding method is especially suitable when the inductance of the SRR is not high enough to cancel out the capacitive component of the antenna load, for example, the capacitance of an RFID chip.

One way to increase the capacitance between rings (in order to decrease the resonant frequency) is by decreasing the separation between them, and to do it so without increasing the resolution needed in the fabrication of the SRR structure, an option for implementation of the invention is to put each ring on a different layer of a common substrate as if it where a capacitor.

When the physical dimension of the SRR is reduced keeping the resonant frequency constant, i.e., not dependent on the ring size (because of the reduction in size is compensated by changing other parameters of the structure), one of the consequences is decreasing of the radiation resistance, and in turn, the reduction of the radiation efficiency of the antenna. Similarly as the increment of radiation resistance is achieved in a resonant dipole by the technique of the folded structure, a folded SRR antenna can be used to increase more than four times the radiation resistance for a given (constant) resonant frequency with respect to the SRR antenna for matching purposes.

Another way to increase the radiation resistance is to shift the feed port along the ring. Because of the current density in each ring decreases as it gets close to the gap of the ring, the feed point displacement along the external or internal ring achieves higher radiation resistance without modifying the resonant frequency. Moving the feed port results in an unbalanced antenna, so it is not suitable for applications which require a balanced transmission line, but it is perfectly valid for RFID applications.

Most RFID tags have their maximum radiation direction perpendicular to the plane containing the tag itself, but with the antenna based on the SRR in any of the proposed configurations the maximum direction of radiation is situated in the plane containing the antenna. This is advantageous for diverse applications, for example, an RFID tag with an

SRR-based antenna can be placed inside a cap on a bottle so that the RFID reader can interrogate the SRR-based antenna when the reader antenna reaches the cap, being the optimum read direction the natural one defined by the major surface of the cap.

Assuming the SRR antenna is placed in 3D space with the Z direction parallel to the ring axis, its polarization is almost linear with the electric field contained in the XY plane. Nevertheless, there can be a small cross-polarization due to the bianisotropy of the SRR particle. Different

modifications can be done in order to improve the axial ratio, as for example the utilization of the Non-bianisotropic SRR (NB-SRR).

Other preferable structures that have a resonant frequency not only dependent of their overall size, as in the SRR, are the Double-slit SRR

(D-SRR) the spiral resonator (SR) and the Double-spiral resonator (DSR).

In addition to the self-resonant structures cited above, another possible configuration is the counterpart of the SRR following the Babinet principle, that is, the Complementary SRR (CSRR). There are different ways of feeding an antenna based on the CSRR. In this case, the resonant (CSRR) structure is excited by an electric field perpendicular to the plane containing the CSRR structure, according to the Babinet principle. Because of the swapping between magnetic and electric fields in the complementary SRR, the antenna can be fed through capacitive coupling. For RFID applications, the CSRR antenna can have an RFID chip just soldered across the gap (i.e., in the radial direction).

Further alternatives to increase the inductance and capacitance of the SRR are either by meandering or interdigitating its perimeter. Basically, an interdigitated split ring resonator increases the capacitance of the equivalent circuit due to a longer gap and wider surface of the interdigitated rings, resulting in a reduction of the resonant frequency. However, the thickness of the rings in the interdigitated split ring resonator leads to decreasing the inductance of the equivalent circuit. In order to avoid this reduction of the equivalent inductance but go on further decreasing the resonant frequency, a meandered split ring resonator may be used. The capacitance of the meandered split ring resonator equivalent circuit is increased with respect to the SRR, though the equivalent capacitance of the meandered split ring resonator is lower than the equivalent capacitance of the interdigitated split ring resonator, but the resonant frequency is reduced with respect to both previous cases (SRR and interdigitated split ring

resonator) because of the increase of the equivalent inductance.

Applying the Babinet principle, any of the different options presented in this invention has the slot counterpart, i.e. can be realized just swapping metal parts by slots on a metal plane.

A main benefit of the present invention, in any of the diverse implementation ways disclosed here, is that the antenna can be fabricated very easily using a planar, rigid or flexible, substrate. This means that the fabrication process involves lower costs and also the fabricated antenna can be easily integrated for numerous applications that demand strictly reduced dimensions.

DESCRIPTION OF THE DRAWINGS

To complete the description being made and to assist in a better understanding of the characteristics of the invention, in accordance with a preferred example of practical embodiment, this description is accompanied, as an integral part of the same, with a set of drawings which illustrates but does not restrict, in which the following has been represented:

Figure 1. - It shows the structure (A) with relevant dimensions and the equivalent circuit model (B) of a split ring resonator, according to prior art.

Figure 2. - It shows the uniform and high current density distribution in a SRR at the resonant frequency, according to the behaviour at magnetic polarization of the SRR studied in prior art.

Figure 3. - It shows an effective medium composed by a plurality of split ring resonators, according to the normal behaviour studied in prior art of the effective magnetic permeability with negative values near the resonant frequency.

Figure 4. - It shows the structure (A) and the equivalent circuit model (B) of a non-bianisotropic split ring resonator, according to prior art.

Figure 5. - It shows the structure (A) and the equivalent circuit model

(B) of a double-slit split ring resonator, according to prior art.

Figure 6. - It shows the structure (A) and the equivalent circuit model (B) of a spiral resonator, according to prior art.

Figure 7. - It shows the structure (A) and the equivalent circuit model (B) of a double spiral resonator, according to prior art.

Figure 8. - It shows a dipole (A) and a folded-dipole (B) antennae, according to prior art.

Figure 9. - It shows a structure (A) and an equivalent circuit model (B) of an antenna based on the normal SRR configuration with a feed point, according to a possible embodiment of this invention.

Figure 10. - It shows a three-dimensional representation of the radiation pattern from the antenna shown in Figure 9(A), being the SRR rings placed in the XY plane with their centre at the origin.

Figure 11. - It shows an antenna based on a non-bianisotropic SRR structure, according to another possible embodiment of this invention.

Figure 12. - It shows the optimum directions pointed by arrows for reading a conventional RFID tag, according to prior art, and a SRR-based RFID tag according to a possible embodiment of the invention.

Figure 13. - It shows the SRR-based RFID tag depicted in Figure 12

put inside a cap of a bottle to be read by an RFID reader antenna.

Figure 14. - It shows an antenna based on a loop feeding SRR structure, with a smaller metallic loop inside the SRR to feed the antenna, according to another alternate possible embodiment of this invention, and a detail (C) of an RFID chip connected to the antenna in the loop.

Figure 15. - It shows an antenna based on a loop feeding SRR structure built in slots, with a smaller loop etched inside the SRR to feed the antenna, according to yet another alternate possible embodiment of this invention, and a detail (C) of an RFID chip connected to the antenna in the loop.

Figure 16. - It shows an equivalent circuit model of the antenna based on the loop feeding SRR structure depicted in Figure 14.

Figure 17. - It shows an antenna based on a broad side coupled SRR structure with each one of the two rings is built in a different layer of the planar dielectric substrate, according to another alternate embodiment of this invention.

Figure 18. - It shows an antenna based on a folded SRR structure, configured with two arms, according to yet another alternate embodiment of this invention.

Figure 19. - It shows an antenna based on a feed port shifted SRR structure, according to another example for embodiment of this invention.

Figure 20. - It shows an antenna based on an interdigitated SRR structure, according to another possible example for embodiment of this invention.

Figure 21. - It shows an antenna based on a meandered SRR structure, according to yet another possible example for embodiment of this invention.

Figure 22. - It shows an antenna based on a complementary SRR structure fed by two electrodes creating an electric field, according to a last example for embodiment of this invention.

Figure 23. - It shows an antenna based on the complementary SRR structure with an RFID chip soldered directly across the gap of the slot-ring

(radial direction).

Figure 24. - It shows an antenna based on a single loop resonant structure.

Figure 25. - It shows an antenna based on a resonant structure consisting of a single split ring.

Figure 26. - It shows an antenna based on a folded SRR structure configured with three arms, according to another option for embodiment of this invention.

Figure 27. - It shows an antenna based on a meandered SRR structure configured by defining spirals with inclined lines, according to yet another possible example for embodiment of this invention.

PREFERRED EMBODIMENT OF THE INVENTION

In the light of Figures 9A and 9B, it is possible to describe one of the preferred embodiments of the invention as an antenna comprising a radiant element which is a split ring resonator (2) composed by an internal ring (R1 )

and an external ring (R2) with respective gaps etched in diametrical opposition. The two rings (R1 , R2) are concentric, and can be made of metal, built in a common planar substrate. The SRR antenna structure, drawn in Figure 9A, can be modelled by an equivalent electric circuit, depicted in Figure 9B, including the feeding source for the antenna. The resonant frequency is achieved by properly selecting the dimensions of the SRR: width and separations between the rings (R1 , R2) and overall size. The antenna input impedance is generally composed by real and imaginary components. If the source impedance is not purely real, as usual in an RFID chip, the SRR antenna still resonates but at another frequency. The inductive and capacitive values of the equivalent circuit model determine the value of the resonant frequency. In Figure 9B, the radiation and loss resistances (R _rad , Ri _oss ) of the antenna are included in determining the real component of the antenna input impedance in the equivalent circuit, in which there is a resistance from the source (R _SO ur _ce )- The inductance (Lsrr) and capacitance

(Csrr) values of the SRR determines the imaginary component of the antenna input impedance..

By the Babinet principle, the SRR structure can be applied in fabricating a slot antenna wherein the two concentric rings (R1 , R2) are configured as slots in the common planar substrate, and carry magnetic current instead of electric current. This configuration can be useful, for example, to build an RFID tag out of a metal sheet, such as those covering the pills in a blister packaged pharmaceutical product.

The SRR antenna is excited at a feed point (1 ) producing an electric current through said feed point (1 ) when the resonant structure is excited by a magnetic field pointed in a direction transversal to the planar substrate containing the SRR structure There are alternative implementations of feeding said antenna: either just exciting one of the rings of the SRR structure at the feed point (1 ) so that the antenna is fed directly through said ring as a dipole, either through a loop built in said substrate that generates

the magnetic field pointed in a direction transversal to the said common substrate.. The radiation pattern of the SRR antenna is almost omnidirectional with maximum gain in the plane defined by the common substrate, as shown in Figure 10, where the SRR antenna is placed with the ring axis parallel to the Z direction.

The polarization is almost linear with the electric field contained in the XY plane. However, there can be a small cross-polarization due to the bianisotropy of the SRR. Different modifications can be done in order to improve the axial ratio, as for example the utilization of a NB SRR or Non- bianisotropic SRR (3), whose structure is depicted in Figure 11 and showing the feed point (1 ) for the NB SRR antenna. This alternative is very suitable for building RFID tags because it allows an optimum reading direction just in the same plane of the label or the RFID tag.

Figure 12 shows the reading direction of a conventional RFID tag (4), wherein the maximum direction of radiation is perpendicular to axis of the dipole-like antenna, i.e. there is a null radiation direction in the axis, versus the reading direction of a SRR-based RFID tag (5). For the conventional RFID tag (4) in Figure 12 the optimum reading direction is in the XZ plane, whilst the SRR-based RFID tag (5) has its optimum reading direction in the plane of the antenna itself, i.e. XY plane in Figure 12. This property derived by the SRR and that can be improved by an NB SRR allows to insert either the NB SRR-based RFID tag or SRR-based RFID tag (5) inside, for example, a cap of a bottle (7) so that a conventional RFID reader antenna (6) can read such label when going up to the neck of the bottle (7), as shown in Figure 13.

In case the inductance of the SRR is not enough to cancel out the capacitance of an RFID chip (9) integrated in the label, an approach is that the RFID antenna of this label is based on a loop feeding SRR structure, as the example given in Figure 14. The SRR is excited with a small loop (8) configured inside the internal ring (R1 ) of the SRR. Another alternative is to

feed the SRR with a larger loop outside the external ring (R2) of the SRR. According to the Babinet principle, a complementary design can be realized just swapping metallic rings and feeding loop by slot rings and slot loop in a metal plane, and magnetic and electric fields by electric and magnetic fields, respectively. Figure 15 shows the loop feeding SRR in slot, complementary to that of Figure 14, wherein the RFID chip (9) can be soldered, within the internal loop, in the radial direction.

The loop feeding SRR structure shown in Figure 14 can be modelled by the equivalent electric circuit drawn in Figure 16, wherein the antenna impedance (Za) at the SRR resonant frequency is given by:

„ „ O) ² M ² . CO ² M ^{2 Z a = Z loon + — = R I loooopp + JVL ₁ lOoOop _P +}

- ¹ SRR ^R rad + ^R loss

^K Ra ^~ - ^K Rhop ₊ + ^ω * ^M *

^R rad ^{+ R} loos being Z _srr and Z| _0O p the SRR and loop impedances respectively, and R and X stand for the real and imaginary parts of the corresponding impedance. The impedances Z _srr and Z| _OOP have corresponding SRR and loop inductances (L _srr , L| _Oop ) and the SRR introduces a capacitance (C _3n -)- Notice that using this loop feeding SRR structure, for a resonant SRR, the antenna's real and imaginary parts of the input impedance can be adjusted separately by changing the inductance of the loop (L| _Oop ) and the mutual inductance between the loop and the SRR. However, these two parameters are related by:

M = k _y JL _hop L _SRR where, k is known as the coupling factor.

This equivalent circuit model helps to match the antenna input impedance to the input impedance of an RFID chip. RFID chips usually have capacitive input impedance that can be well matched by the loop feeding SRR structure.

The loop feeding SRR structure can work also at frequencies

below or above resonance in order to achieve a better matching. For example, for frequencies just below resonance, the inductive behaviour of the antenna input impedance is increased. This can be used to compensate the capacitive behaviour of an RFID chip with a smaller overall size.

Another possible embodiment of the invention refers to print one of the rings of the SRR in a top layer of the substrate and the other ring is printed in the opposite layer of said substrate, as depicted in Figure 17, defining a broad side coupled SRR. In this way the capacitance between the rings (R1 , R2) of the broad side coupled SRR can be controlled with the thickness of the substrate and the width of the metal strips. RFID label substrates usually have a thickness of about 40 microns, so the capacitance between the rings (R1 , R2) printed in different layers can be very high.

Yet another possible embodiment of this invention deals with folding one or both rings of the SRR in order to achieve a larger radiation resistance. An example of a folded split ring resonator (11 ) structure is drawn in Figure 18.

For comparison, Table 1 shows the self-resonant frequency and real part of the input impedance of different resonant structures. All the structures have been simulated with a full wave MoM [Method of Moments] simulator assuming they are in free space, made of copper and have the same size with a maximum value about 20 millimetres.

Table 1.- Characteristics of different radiating structures.

The single split ring resonates at 2.36 GHz. At this frequency the length of the ring is approximately half a wavelength. This means that it is equivalent to the resonant frequency of a dipole of the same length (however, a dipole would have a larger overall size because it is straight).

Looking at Table 1 , it can be seen that the higher input resistance is for a single loop antenna; however the resonant frequency is 5.5 GHz. The input impedance of the single loop at 1.72 GHz is 15.2 + J979 ω, which is highly inductive. If we cancel out the reactive part by means of a series capacitor, the input resistance would be 15.2 ω, which is very close to the folded split ring resonator, but the folded SRR does not need any matching network or external lumped components.

Moreover, the folded structure used in the folded split ring resonator has two arms. In order to increase more the input resistance, more arms can be used. As instance, a three-arms folded SRR, drawn in Figure 26, with identical overall size, would have a resonant frequency of 1.72 GHz and input impedance of 27 ω.. The input resistance is about N ² times the input resistance of the non-folded structure, where N is the number of arms.

Another option to increase the radiation resistance is to shift the feed point (1 ) along the ring, as shown in Figure 19, because the current in

the ring decrease as you get closer to the gap. The antenna becomes unbalanced, but for RFID applications, since the small RFID chip (9) is placed directly on the antenna, this is no disadvantage. For instance, for a 20 mm diameter SRR, shifting the feed port 30 degrees results in an increase of the radiation resistance of about 17%.

Further possible embodiments of the invention, in order to get an increased capacitance of the SRR, are an antenna configured with an interdigitated split ring resonator (12) shown in Figure 20, or an antenna based on a meandered split ring resonator (13) that is shown in Figure 21 and additionally allows to increase the inductance of the normal SRR structure. There can be many different patterns to implement these interdigitated split ring resonator (12) and meandered split ring resonator (13), either by configuring the interdigitated/meandered rings by straight lines, as drawn in Figures 20/21 , or defining spirals with inclined lines, as depicted in Figure 27, etc. In the interdigitated split ring resonator (12), the equivalent capacitance is higher than the capacitance of the simple SRR structure since a wider surface and longer gap is defined between the interdigitated rings. On the other hand, since.the equivalent inductance of the rings can be increased by either increasing the ring lenth or reducing the ring thickness, in meandered split ring resonator (13) the equivalent inductance is also higher than in the simple SRR structure..

There is a last example for implementation of the invention that relates to the Babinet principle and is the complementary of the SRR, being another possible preferred embodiment of this invention an antenna based on a complementary split ring resonator (14) as shown in Figures 22 and 23.

In Figure 22, two metallic layers (15a, 15b) of a substrate (15) are shown, depicted in black and grey respectively, in which the antenna based on the CSRR or complementary split ring resonator (14) is built, being fed through capacitive coupling. At one layer (15a) there are the two concentric rings defined as slots conforming the CSRR, that is, the part without metal in the

layer (15a) is the CSRR. At the other layer (15b) of the metal substrate (15), there are two electrodes connected to the feed point (1 ), so that an electric field is generated between the two electrodes and crosses through the slots/rings in the former layer (15a). While in a conventional SRR, the antenna is excited by a magnetic field crossing the rings, in the complementary SSR, i.e., the CSRR, since the magnetic and electric fields are swapped, the excitation of the antenna is given by the electric field produced between the electrodes. The RFID chip (10) can be soldered at the same metal layer (15b) with the electrodes of the metal substrate (15). Figure 23 shows another way to feed the CSRR antenna by soldering the RFID chip

(10) in the gap of any of the two rings, in the radial direction.

Note that by the Babinet principle, any of the different options of implementation presented for this invention, included double-slit SRR, spiral resonator and double spiral resonator structures, has the slot counterpart, i.e. can be realized just swapping metal rings by slots.

Some preferred embodiments of the invention are described in the dependent claims which are included next.