Patent Description:
The present disclosure relates to metamaterial resonators, and to applications of such resonators, for example, in planar microwave transmission structures.

Metamaterials are artificial materials that are engineered to have properties that are not found in nature, and that are not necessarily possessed by their constituent parts alone. In this sense, metamaterials may be assemblies of multiple individual elements, unit cells, or a cell array, on any scale, from nano to bulk.

A metamaterial simultaneously exhibiting a relative effective permeability and a relative effective permittivity below zero over a wide bandwidth, and may include: one of a two- or three-dimensional arrangement of unit cells or a cell array, each of the unit cells having a magnetic dipole moment and an electric dipole moment that are dependent upon one or more of an incident magnetic/electric field, and a coupling mechanism for coupling the incident magnetic field and electric field to one or more devices. Optionally, the coupling mechanism includes one or more of a split ring and a pair of parallel plates coupled by one of a rod and a wire.

Some artificial composite materials exhibit simultaneous negative values of electric permittivity (ε< <NUM>) and magnetic permeability (µ < <NUM>). These materials may exhibit the following properties: an artificial homogenous structure; simultaneous negative permittivity (-ε) and permeability (-µ); the electric field, magnetic field, and wave-vector of an electromagnetic wave therein forming a left-handed triad, and having backward wave propagation, anti-parallel group and phase velocity; reversal of Snell's Law (negative index of refraction); reversal of the Doppler effect; reversal of the Vavilov-Cerenkov effect; and breaking the diffraction-limit.

The characteristics of artificial composite metamaterials can depend on any of the properties of the host material, embedded material, the volume of the fraction, the operating frequency, and/or morphology of the composite material (e.g., dimension, shape of the host structure and/or guest structure). Thus, controlling the dynamics of the morphology of the embedded structure provides one way of control over a change of the properties of the artificial composite metamaterials (e.g., permittivity, permeability, refractive index).

One key to the design of artificial metamaterial resonators is selecting a geometric shape that induces currents that form loops with a relatively uniform distribution, thereby producing a strong magnetic moment. One type of geometry used is a split-ring resonator (SRR). SRRs are sub-wavelength resonators that are able to inhibit signal propagation in a narrow band within the vicinity of their resonant frequency, provided that the magnetic field is polarized along the ring's axis. SRRs can be modeled as LC resonant tanks that can be externally driven by a magnetic field to inhibit signal propagation in a narrow band if properly oriented. The particular resonance frequency or frequencies of a given medium having an SRR may depend on a combination of factors, including (a) width of the split or "break" of the ring, (b) ring width, (c) distance between concentric rings, (d) substrate permittivity, (e) substrate thickness, and (f) orientation of the SRR. Other factors may include the number of rings (e.g., <NUM>, <NUM>, <NUM>, etc.) and the number of splits or breaks in each ring (e.g., <NUM>, <NUM>, <NUM>, etc.) of the SRR. Factors like the width of the split, ring width, distance between concentric rings, and number of splits or breaks in each ring typically have a direct proportion with the resonant frequencies while factors like the substrate permittivity, substrate thickness typically have an inverse proportion to the resonant frequency.

It is known that tunable metamaterial ring resonators may be formed on a thin film. However, such tunable resonators generally act as their own medium and not, e.g., as a complementary circuit on a circuit board having another device (e.g., a voltage controlled oscillator). Moreover, known SRRs are generally configured to resonate at a frequency on the order of THz due to physical limitations in the shape and size of the SRR ring structure. Additionally, it is described in<NPL>, that a voltage controlled oscillator may be designed with an evanescent mode möbius coupled resonator in order to minimize vibration noise and microphonic effects to prevent unwanted modulation. However, the resonator structures provide only a narrow tuning range. The resonator structures further exhibit inferior phase noise performance, and an active device is required to stabilize the operation. Accordingly, and in order to implement an SRR structure as a complementary circuit on a circuit board, it would be desirable to provide an SRR cell and/or SRR array having a structure with physical parameters for improved performance. Additionally, it would be desirable to provide a resonator structure capable of resonating at a wide range of frequencies.

In some examples outside the claimed subject-matter, the metamaterial resonator may include first and second concentric split ring elements forming a substantially planar split ring resonator. Each concentric split ring element may be substantially annular with a break extending radially from a center of the split ring resonator through the annulus, the break of the first split ring element extending in the opposite direction as the break of the second split ring element. The resonator may also include first and second ports coupled to the split ring elements. The ports may be coplanar with and edge-coupled to the first split ring element. Alternatively, the ports may be broadside coupled to the metamaterial resonator, the first port being located along a first plane parallel to the first and second split ring elements, and the second port being located along a second plane parallel to the first and second split ring elements, with the first and second planes extending transversely away from the plane of the split ring elements in opposing directions.

In some examples outside the claimed subject-matter, the resonator may include a first and second pairs of concentric split ring elements, each forming a substantially planar split ring resonator, and each concentric split ring element including a break extending radially outward from a point within the split ring resonator, the break of the first split ring element extending in the opposite direction as the break of the second split ring element, and each pair of elements having line symmetry with one another over an axis bisecting the resonator. The split ring pairs may be respectively coupled to first and second ports.

In some examples outside the claimed subject-matter, the resonator may include a first pair of concentric split ring elements forming a substantially planar split ring resonator, each concentric split ring element being substantially annular with a break extending radially outward from a point within the split ring resonator, a second pair of concentric split ring elements having line symmetry with the first pair of concentric split ring elements over an axis bisecting the resonator, a first connection line coupling the inner split ring elements of the first and second pair, a second connection line coupling the outer split ring elements of the first and second pair, a first port coupled to the first connection line, and a second port coupled to the second connection line. The resonator may further include a ground plane below each of the split ring elements, and an etch-out on the ground plane.

Both the first and second split ring elements may be the same shape (e.g., circle, square, oval and rectangle). The resonator may be adapted to have at least one resonant frequency of about <NUM> or lower, and/or phase noise of the oscillating circuit of the device may be about -135dBc/Hz or greater at an offset of <NUM>.

Another aspect of the disclosure outside the claimed subject-matter provides for a resonant circuit including a möbius strip resonator having a topology in which a closed path formed by the möbius strip resonator maps onto itself and is continuous, and a metamaterial split ring resonator. The metamaterial split ring resonator may be operatively coupled to the möbius strip resonator. In some respects, a conductive strip of the möbius strip resonator may include one or more break, thus making the möbius strip resonator itself also a metamaterial split ring resonator. The resonant circuit may adapted to have at least one resonant frequency of about <NUM> or lower.

In some examples outside the claimed subject-matter, the möbius strip resonator may include a substantially planar conductive strip arranged in a spiral, the conductive strip having an inner end and an outer end, and extending two or more revolutions around a centerpoint of the spiral. The resonator may also include a first via coupled to the first end, a second via coupled to the second end, and an electrically conductive connection between the first and second vias, thereby connecting the first and second ends of the conductive strip to form a möbius strip.

In some examples outside the claimed subject-matter, the möbius strip resonator may include first and second substantially annular conductive elements arranged on parallel first and second planes, respectively, each substantially annular conductive element having a respective first break defining respective first and second ends. The resonator may also include a first via extending transversely between the first and second plane and connecting the first end of the first substantially annular conductive element to the second end of the second substantially annular conductive element, as well as a second via extending transversely between the first and second plane and connecting the second end of the first substantially annular conductive element to the first end of the second substantially annular conductive element, thereby connecting the first and second substantially annular conductive elements to form a möbius strip. The first substantially annular conductive element may edge-coupled to a first port at a location of the first break, and to a second port at a location <NUM> degrees circumferentially from the first break. Or the first substantially annular conductive element may be broadside-coupled to a first port at a location <NUM> degrees circumferentially from the first break, and to a second port at a location -<NUM> degrees circumferentially from the first break.

In some examples outside the claimed subject-matter, each of the first and second substantially annular conductive elements may include a second break, each second break extending radially outward from a center point of the substantially annular conductive element and located approximately <NUM> degrees apart, around the circumference of the substantially annular conductive element, from the first break. The respective second breaks of the first and second substantially annular conductive elements may extend from their respective center points in opposite directions. The first substantially annular conductive element may broadsidee.g., coupled to a first port at the location of the second break, and to a second port at a location <NUM> circumferentially from the first break and <NUM> degrees circumferentially from the second break.

Yet another aspect of the disclosure outside the claimed subject-matter provides for a device including an oscillator circuit adapted to output an electric signal at a given frequency, the given frequency based at least in part on one of an input provided to the device and inherent noise or a nonlinearity in an active part of the oscillator circuit, and any of the above möbius/metamaterial resonant circuits. The resonant circuits may itself include one or more annular resonant elements at least partially overlaying the resonant circuit and adapted to suppress higher order modes generated by the device. Phase noise of the oscillator circuit of the device may be about e.g., 175dBc/Hz or greater at an offset of <NUM>.

Yet a further aspect of the disclosure outside the claimed subject-matter provides for a resonant circuit having a substrate integrated waveguide including a first planar metal layer, a second planar metal layer parallel to the first layer, and a plurality of plated vias extending transversely between the first and second planar metal layers, and connecting the first and second planar metal layers to one another. The resonant circuit may further include a metamaterial resonator operatively coupled to the substrate integrated waveguide. The resonant circuit may be adapted to have at least one resonant frequency of about <NUM> or lower.

In some examples outside the claimed subject-matter, the metamaterial resonator may include first and second concentric split ring elements forming a substantially planar split ring resonator. Each concentric split ring element may have a break extending radially from a center of the split ring resonator. The break of the first split ring element may extend in the opposite direction as the break of the second split ring element. The split ring elements may be coupled to first and second ports. The first and second concentric ring elements may form a substantially planar complementary split ring resonator.

In some examples outside the claimed subject-matter, the metamaterial resonator may be coupled to first and second ports and may include a single substantially circular ring having first and second breaks on opposing sides of the ring. The first and second breaks may be aligned with the first and second ports along a first axis of the resonant circuit, respectively, and each of the breaks defining broken ends of the circular ring. Each broken end of the ring may extend in parallel with the first axis and in the direction towards the first port. In other examples, the metamaterial resonator may be coupled to a single port and each broken end of the ring may extend in the direction towards the single port.

An even further aspect of the disclosure outside the claimed subject-matter provides for a device including an oscillator circuit and one of the above resonant circuits. The device may include one or more varactor diodes coupled to the metamaterial resonator. The phase noise of the oscillator circuit of the device may be about, e.g., <NUM>. 2dBc/Hz or greater at a <NUM> offset.

In some of the above examples, the example metamaterial resonators may implemented as a complementary circuit on a substrate or circuit board (e.g., printed circuit board).

The present disclosure provides for improvements to SRR and other metamaterial resonators, such as combining one or more SRRs into a resonant structure, combining one or more SRRs with a möbius strip resonator, and combining one or more SRRs with a substrate integrated waveguide. Additionally, the present disclosure provides for improvements to operation of other electronic devices, such as voltage controlled oscillators (VCOs) by incorporating one or more of the improved SRR structures into the VCO design.

Metamaterial resonators may be used in many electronic and optoelectronic devices, such as filters and oscillators, in order to reduce noise and compensate for losses by suppressing bands of unwanted frequencies. While other active devices are known to reduce noise and compensate for losses, these devices have their own limitations, such as the noise/losses they themselves introduce into the system(s) or devices that they control. By contrast, the metamaterial resonator introduces comparatively little or no noise to the system or device. The resonator can be set to a resonant state by temporary use of an active device, such as a transistor in, for example, an oscillator circuit. Once the metamaterial resonator is operating at the resonant frequency, the active device may be deactivated, leaving the metamaterial resonator on its own to compensate for losses in the system or device due to its unique properties of simultaneous negative permittivity (-ε) and permeability (-µ) (or negative refractive index). In this respect, the present disclosure provides examples of improved VCO design. However, it is understood that the same or similar improved SRR structures may be applied to other circuits, devices and systems to provide similar improvements (e.g., reduced phase noise, reduced insertion losses, etc.).

<FIG> shows a first example metamaterial resonator <NUM> in accordance with the present disclosure. The resonator <NUM> is made up of a pair of split ring elements <NUM> and <NUM> formed in a substantially planar configuration on a common surface of a substrate <NUM> (e.g., a printed circuit board), and a pair of ports <NUM> and <NUM> (e.g., microstrip arcs) on opposing ends of the substrate <NUM>, edge-coupled to the split ring elements <NUM> and <NUM>. The first and second split ring elements <NUM> and <NUM> are concentric with one another. Each split ring element is annular, with a break <NUM> and <NUM>. The breaks extend through the annulus in a direction radiating from, or otherwise called extending radially outward from, the center of the ring element. In the example of <FIG>, the break <NUM> of the first ring element <NUM> extends from the center of the ring elements toward the first port <NUM>, whereas the break <NUM> of the second ring element <NUM> extends from the center of the ring elements toward the second port <NUM>. In this respect, the break <NUM> of the first ring element <NUM> extends in the opposite direction as the break <NUM> of the second ring element <NUM>. Each of the breaks <NUM> and <NUM> has a uniform width.

In the example of <FIG>, each of the first and second ring elements <NUM> and <NUM> is substantially circular, and each of the ports <NUM> and <NUM> is curved along an outer perimeter of the second ring element <NUM> such that the distance between the second ring element <NUM> and each port (in the direction extending radially from the center of the ring elements) is uniform. However, in other examples, the ring elements may be made in a different shape, such as square, oblong or rectangular. In those other examples, the ports may be appropriately shaped or curved to maintain a uniform distance from the second ring element.

<FIG> shows a second example metamaterial resonator <NUM> having a structure similar to that of the first example resonator <NUM>, except that the first and second ring elements <NUM> and <NUM> are substantially annular rectangles. As in the first example resonator <NUM>, each of the ring elements of the second example resonator <NUM> has a common center, and includes a break <NUM> and <NUM> extending from the common center towards a respective port <NUM> and <NUM>. In the example of <FIG>, the breaks are formed in the longer edge of the rectangular ring elements, but in other examples may be formed in the shorter edge. The edge coupling of each of the ports <NUM> and <NUM> is formed in a substantially straight line to maintain a uniform distance from the second ring element <NUM>. Thus, the ports are each T-shaped.

In each of the first and second example resonators <NUM> and <NUM>, the resonators are edge-coupled to a pair of ports formed on a common surface of the substrate. Also, in each of those examples, the ports are formed on the same surface of the substrate as is the resonator. However, in other examples, a metamaterial resonator may be broadside coupled to ports on a layer above or below the resonator (e.g., a surface of the substrate opposite the resonator). Additionally, or alternatively, each of the ports may be formed on opposing surfaces of the substrate.

<FIG> shows a third example metamaterial resonator <NUM> having a structure similar to that of the second example resonator <NUM>, except that the resonator <NUM> is a complementary of the split ring resonator discussed above and is formed in a metallization layer between two substrates 131a and 131b, and is connected to each of a first port <NUM> on an opposing surface of the first substrate 131a, and to a second port <NUM> on an opposing surface of the second substrate 131b. Each of the ports <NUM> and <NUM> is a substantially planar microstrip formed in a metallization layer on their respective substrate surfaces. The first port <NUM> extends from a first side of the substrate <NUM> (which is made up of substrates 131a and 131b) and the second port extends from an opposing second side of the substrate <NUM>. The breaks <NUM>/<NUM> of the ring elements <NUM>/<NUM> extend radially from the common center of the ring elements in opposing directions. In the example of <FIG>, the breaks extend perpendicular to the directions in which the first and second ports extend, although in other examples (as in <FIG>), the breaks may extend in the same direction as the ports. The metallization layer in which the resonator <NUM> is formed between the substrates 131a and 131b serves as a common ground plane for both of the first and second ports <NUM>/<NUM>.

In each of the first second and third examples resonators <NUM>, <NUM> and <NUM>, the resonator is connected to each of a first and a second port, which may serve as input and output lines (or vice versa) for the resonator. However, in other examples, the resonators may be connected to a single port. For instance, <FIG> shows a fourth example metamaterial resonator <NUM> having a structure (e.g., rings <NUM>/<NUM>, breaks <NUM>/<NUM>) similar to that of the third example resonator <NUM>, except that the resonator <NUM> is formed on a single substrate <NUM> and is connected to a single port <NUM>. In the example of <FIG>, the single port <NUM> is an open ended microstrip line extending in a direction perpendicular to the direction of the breaks <NUM> and <NUM>, although in other examples the breaks may extend in the same direction as the ports.

<FIG> shows a fifth example of a metamaterial resonator <NUM> in accordance with the present disclosure. The metamaterial resonator <NUM> is formed from a first pair of concentric split ring elements <NUM> and <NUM> formed adjacent to a second pair of concentric split ring elements <NUM> and <NUM> on a common surface of a substrate <NUM>. In the example of <FIG>, each of the split ring elements is rectangular. The first pair of split ring elements is connected to a first port <NUM> extending from a first side of the substrate <NUM> along a first axis X, and second pair of split ring elements is connected to a second port <NUM> extending from a second side of the substrate <NUM> opposite the first side, also along the first axis X. The first and second ports <NUM> and <NUM> extend along a line of the first axis X, which in the example of <FIG> is offset from a midpoint of the substrate <NUM>. The first and second pairs of split ring elements have line symmetry to one another along a second axis Y of the substrate perpendicular to the first axis X and, in the present example, bisects the resonator <NUM>.

As with each of the split ring elements in the previous example resonators, each of the split ring elements <NUM>/<NUM>/<NUM>/<NUM> of the fifth example resonator <NUM> includes a break, <NUM>, <NUM>, <NUM> and <NUM>, formed along the long edge of the respective ring element. In the example of <FIG>, for each of the concentric split ring element pairs, the respective breaks of the concentric split ring elements extend, in opposing directions, from a common point that is within the ring or annulus of each split ring element, but offset (e.g., along the long axis of the ring elements) from the center point of the ring elements. Each of the breaks <NUM>, <NUM>, <NUM> and <NUM> is formed along a line extending along the first axis X between the first and second sides of the substrate.

<FIG> shows a sixth example of a metamaterial resonator <NUM> in accordance with the present disclosure. The metamaterial resonator <NUM> is formed from a first pair of concentric split ring elements <NUM> and <NUM> formed adjacent to a second pair of concentric split ring elements <NUM> and <NUM> on a common surface of a substrate <NUM>. In the example of <FIG>, each of the split ring elements is circular. The first pair of split ring elements is connected to a first port <NUM> extending from a first side of the substrate <NUM> along a first axis X, and second pair of split ring elements is connected to a second port <NUM> extending from a second side of the substrate <NUM> opposite the first side also along the first axis X, which in the present example bisects the resonator <NUM>. The first and second ports <NUM> and <NUM> extend along a line of the first axis X, which in the example of <FIG> passes through a midpoint of the substrate <NUM>. The first and second pairs of split ring elements have line symmetry to one another over the first axis X. Each of the inner ring elements <NUM>/<NUM>, and each of the outer ring elements <NUM>/<NUM> is connected by first and second metamaterial connection lines, <NUM> and <NUM> respectively. Each of the metamaterial lines <NUM> and <NUM> extends in parallel to one another parallel a second axis Y of the substrate <NUM> perpendicular to the first axis X.

As with each of the split ring elements in the previous example resonators, each of the split ring elements <NUM>/<NUM>/<NUM>/<NUM> of the sixth example resonator <NUM> includes a break, <NUM>, <NUM>, <NUM> and <NUM>. In the example of <FIG>, for each of the concentric split ring element pairs, the respective breaks of the concentric split ring elements extend along the second axis Y. The breaks <NUM> and <NUM> for each of the inner ring elements <NUM>/<NUM> is formed along a line (e.g., along the second axis Y) offset from a center point of the resonator in the direction of the second port <NUM>. The breaks <NUM> and <NUM> for each of the outer ring elements <NUM>/<NUM> is formed along a line (e.g., along the second axis Y) offset from a center point of the resonator in the direction of the first port <NUM>, with the first metamaterial connection line <NUM> extending through both breaks <NUM>/<NUM>. In some examples, the substrate may include a ground plane (not shown) below each of the split ring elements, in which some of the material of the ground plane is etched out.

<FIG> show loss characteristics for each of the above example resonators <NUM>, <NUM>, <NUM>, <NUM>, <NUM> and <NUM>, respectively. At the resonant frequencies of the respective resonators, transmission of electromagnetic waves is suppressed. This is shown in the plots of 2A-2F as a dip in the transmission characteristic for the respective resonators. As shown in <FIG>, the first example resonator <NUM> exhibits strong resonance at approximately <NUM> and at approximately <NUM>. As shown in <FIG>, the second example resonator <NUM> exhibits strong resonance at approximately <NUM>, at approximately <NUM>, and at approximately <NUM>. As shown in <FIG>, the third example resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the fourth example resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the fifth example resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the sixth example resonator <NUM> exhibits strong resonance at approximately <NUM>.

The above example resonators <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, and <NUM>, or similarly designed resonators, may be incorporated into a voltage controlled oscillator in order to perform improved mode suppression with reduced phase noise, as compared to alternative solutions. The ports of the resonator may be connected to the voltage controlled oscillator. In this respect, each of the resonators may be used as a resonant circuit in another device, as compared to as a resonant negative permittivity/permeability medium (e.g., metamaterial cloaking device).

<FIG> shows a first example voltage controlled oscillator <NUM> including an oscillating circuit and a metamaterial resonator <NUM> having structural and operational properties similar to those of the first example resonator <NUM>. The oscillating circuit outputs an electric signal at a given frequency based at least in part on one or more inputs provided to the VCO and/or inherent noise or a nonlinearity in an active part of the VCO. Like the first example resonator <NUM>, resonator <NUM> is made of concentric circular split ring elements connecting opposing first and second ports. However, unlike the first example resonator <NUM>, which includes only two split ring elements, resonator <NUM> includes four split ring elements, each of the split ring elements having a break that extends along a line, the breaks of each adjacent split ring elements extending from a center point of the resonator <NUM> in opposite directions. Generally, including more split rings in an SRR will increase the quality factor of the SRR, but with greater losses. In designing a voltage controlled oscillator, the number of split rings may be chosen to balance the quality factor and loss needs.

<FIG> shows a second example voltage controlled oscillator <NUM> including an oscillating circuit and a metamaterial resonator <NUM> having structural and operational properties similar to those of the second example resonator <NUM>. Like the second example resonator <NUM>, resonator <NUM> is made of concentric rectangular split ring elements connecting opposing first and second ports. However, unlike the second example resonator <NUM>, which includes only two split ring elements, resonator <NUM> includes four split ring elements, each of the split ring element having a break that extends along a line, the breaks of each adjacent split ring elements extending from a center point of the resonator <NUM> in opposite directions.

<FIG> shows a third example voltage controlled oscillator <NUM> including an oscillating circuit and a metamaterial resonator <NUM> having structural and operational properties similar to those of the fifth example resonator <NUM>. Cascading split rings in an SRR will increase the quality factor of the SRR (e.g., according to the Q-multiplication effect), but again with the effect of increased signal losses. In designing a voltage controlled oscillator, the number of split rings may be chosen to balance the quality factor and loss needs.

<FIG> shows a fourth example voltage controlled oscillator <NUM> including an oscillating circuit and a metamaterial resonator <NUM> having structural and operational properties similar to those of the sixth example resonator <NUM>.

<FIG> show phase noise characteristics for each of the above example voltage controlled oscillators <NUM>, <NUM>, <NUM>, and <NUM>, respectively. In the example of <FIG>, the first example oscillator <NUM> is set to a signal frequency of about <NUM> and exhibits phase noise as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, and as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>. In the example of <FIG>, the second example oscillator <NUM> is set to a signal frequency of about <NUM> and exhibits phase noise as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, and as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>. In the example of <FIG>, the third example oscillator <NUM> is set to a signal frequency of about <NUM> and exhibits phase noise as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, and as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>. In the example of <FIG>, the fourth example oscillator <NUM> is set to a signal frequency of about <NUM> and exhibits phase noise as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, and as low as about <NUM> dBc/Hz at an offset of about <NUM>.

The above metamaterial resonator designs may also be combined with one or more möbius strip resonators to improve operation of a device, such as a VCO. A möbius strip is conformal, continuous, and maps one-to-one onto itself. A signal coupled to a möbius strip does not encounter any obstruction when travelling around the multi-knot loop, in such a way that the loop acts like an infinite transmission line, enabling very high group delay. Thus, möbius coupled planar resonators provide an alternative to the complex circuitry needed to achieve high Q-factor in hybrid coupling techniques. In this respect, the present disclosure is also directed to möbius resonators that may be used in combination with the above and similar metamaterial resonator designs.

<FIG> shows a first example möbius resonator <NUM> in accordance with the present disclosure. The resonator <NUM> is made up of a resonator element <NUM> formed in a substantially planar configuration on a surface of a substrate <NUM>, and a pair of ports <NUM> and <NUM> on opposing ends of the substrate <NUM>. The resonator element <NUM> is wrapped in a substantially planar spiral around the centerpoint of the resonator <NUM>. In the example of <FIG>, the spiral extends for about three revolutions, although in other examples, the spiral may extend for more (e.g., about <NUM>) or fewer (e.g., about <NUM>) revolutions. As used in the present disclosure, the term "spiral" should be understood to include both curves that begin at the centerpoint and wrap around the centerpoint, as well as curves that wrap around the centerpoint beginning at a location radially apart from the centerpoint, thereby leaving a break or opening at the center of the resonator. The ports <NUM> and <NUM> may be curved, as in <FIG>, to maintain a space of uniform width between the port and the resonator element <NUM>.

A first end <NUM> and a second end <NUM> of the resonator element may be connected through a via transition <NUM> over another metallic surface (not shown). In the example of <FIG>, each of the vias connecting the first and second ends <NUM> and <NUM> of the resonator element <NUM> extends transverse to the plane of which the resonator element <NUM> is formed. The via transition may include, for example, a wire bond, or may be formed on a multiplanar printed circuit board (PCB). This connection effectively turns the resonator into a möbius strip, thus raising the quality factor of the resonator.

<FIG> shows a second example möbius resonator <NUM> in accordance with the present disclosure. The second example möbius resonator <NUM> is made up of a pair of split ring elements <NUM> and <NUM> formed on different planes of a multiplanar PCB <NUM>, and a pair of ports <NUM> and <NUM> on opposing ends of the multiplanar printed circuit board (PCB) <NUM>. Each split ring element includes a respective break. In the example of <FIG>, the breaks are radially aligned with one another, and each break defines a first and second end of the respective split ring element. The resonator <NUM> further includes a first via transition <NUM> connecting a first end of the first split ring element <NUM> to a second end of the second split ring element <NUM>, and a second via transition <NUM> connecting a second end of the first split ring element <NUM> to a first end of the second split ring element <NUM>. Each of the vias extends transverse between the respective planes of the multiplanar PCB on which the split ring elements are formed. The result of the via connections between the first and second split ring resonators is that current moving from any point on the resonator elements must traverse both elements before reaching back to the start point. In this respect, the resonator functions as a möbius strip and exhibits a relatively high quality factor, as compared to a resonator of similar structure but without a möbius strip connection.

<FIG> shows a third example möbius resonator <NUM> in accordance with the present disclosure. The structure of the third example möbius resonator <NUM> may be compared to that of the second example möbius resonator <NUM> of <FIG> (e.g., split ring elements <NUM> and <NUM> on different planes of a multiplanar PCB <NUM> and connected to one another through via transitions <NUM> and <NUM> to form a möbius strip), except that each of the split ring elements <NUM> and <NUM> further include an additional split or break <NUM> and <NUM>, respectively. Each of the breaks <NUM> and <NUM> extends radially from a centerpoint of the respective elements <NUM> and <NUM>, and extend radially from their respective centerpoints in opposite directions from one another, and on different planes of the PCB <NUM>. In the example of <FIG>, the breaks are separated from the via transition points by approximately <NUM> and -<NUM> degrees, respectively, around the circumference of the elements <NUM> and <NUM>. Each of the vias extends transversely between the respective planes of the multiplanar PCB on which the split ring elements are formed. It has been found that the breaks of the third example resonator <NUM> cause the resonant frequency of the resonator to move to a lower frequency, as compared to a resonator without such breaks (e.g., the second example resonator <NUM>).

<FIG> shows a fourth example möbius resonator <NUM> in accordance with the present disclosure. The structure of the fourth example möbius resonator <NUM> may be compared to that of the second example möbius resonator <NUM> of <FIG> (e.g., split ring elements <NUM> and <NUM> on different planes of a multiplanar PCB <NUM> and connected to one another through via transitions <NUM> and <NUM> to form a möbius strip), except that the structure is of the fourth example möbius resonator <NUM> is located enturely within the intermediate layers of a multiplanar PCB and the structures of the input and output ports <NUM> and <NUM> have been changed and are on a different plane as compared to the rings of the möbius structure. Specifically, the ports in <FIG> are substantially linear microstrips extending from opposing ends of the PCB <NUM> in a direction perpendicular to the splits in the split ring elements <NUM> and <NUM>. The change in port structure affects the way broadside feeding and collection of the electric signals to and from the resonator <NUM> is performed.

<FIG> shows a fifth example möbius resonator <NUM> in accordance with the present disclosure. The structure of the fifth example möbius resonator <NUM> may be compared to that of the fourth example möbius resonator <NUM> of <FIG> (e.g., split ring elements <NUM> and <NUM> on different planes of a multiplanar PCB <NUM> and connected to one another through via transitions <NUM> and <NUM> to form a möbius strip, and to microstrip ports <NUM> and <NUM>), except that the placement of the ports <NUM> and <NUM> has been changed, and a break <NUM>/<NUM> has been added to each of the split ring elements (like in the example of <FIG>). Specifically, in <FIG>, the break <NUM> of the split ring element on the top plane of the PCB <NUM> is located where the signal is collected, and the break <NUM> of the split ring element on the lower plane is located directly underneath the location at which the electric signal is broadside coupled between the split ring element on the top plane and the input port. In this respect, the ports are radially separated by approximately <NUM> degrees around the circumference of the elements <NUM> and <NUM>.

Advantageously, it has been found that the resonant frequency of möbius strip resonators (e.g., the resonators of <FIG>) is nearly half of that for a standard split ring resonator having the same ring dimensions (e.g., same radius). Thus, introduction of möbius strip structures in the formation of resonators, such as metamaterial resonators, may be beneficial for lowering the resonant frequency of such resonators. This helps to mitigate fabrication issues for devices that are required to work at relatively low frequencies (e.g., kHz, MHz range) without the structures becoming too big to accommodate in miniaturized packages. <FIG> show loss characteristics for each of the above example resonators <NUM>, <NUM>, <NUM>, <NUM> and <NUM>, respectively. As shown in <FIG>, the first example möbius resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the second example möbius resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the third example möbius resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the fourth example möbius resonator <NUM> exhibits strong resonance at approximately <NUM> and at approximately <NUM>.

The möbius resonator examples of <NUM>/<NUM>, by virtue of the presence of both breaks <NUM>/<NUM> and <NUM>/<NUM> and a möbius structure, may be termed metamaterial möbius resonators. As shown in <FIG>, the fifth example möbius resonator <NUM> exhibits strong resonance at even less than about <NUM>, as well as at approximately <NUM>.

<FIG> shows the resonance properties of an example metamaterial möbius resonator, as compared to a metamaterial split-ring resonator and möbius strip resonator having similar resonant frequencies. As shown in <FIG>, each of the example resonators has a resonant frequency of about <NUM>. However, the metamaterial möbius resonator exhibits stronger resonance at the <NUM> frequency than do the other example resonators, resulting in lower losses. Furthermore, the other resonators exhibit relatively strong signals at higher order modes (e.g., at about <NUM> for the möbius strip resonator, at about <NUM> for the metamaterial resonator). By contrast, the metamaterial möbius resonator exhibits high suppression of higher order modes, without sacrificing quality factor and even with an improvement to the total loss characteristics. This is achieved by harnessing the benefits of each of the metamaterial resonators and the möbius strip resonators in a single design. The metamaterial resonator of the design provides the improved suppression of higher order modes, while the möbius strip of the design provides for a superior quality factor (e.g., as compared to a metamaterial resonator of similar ring dimensions).

<FIG> shows a plan view design of a voltage controlled oscillator <NUM> including an oscillating or tuning circuit <NUM> and a resonator <NUM> having both metamaterial and möbius components. The oscillating circuit outputs an electric signal at a given frequency based at least in part on one or more inputs provided to the VCO and/or inherent noise or a nonlinearity in an active part of the VCO. As shown in <FIG>, the resonator <NUM> includes four split ring resonators <NUM>, <NUM>, <NUM> and <NUM> distributed in a four-pole edge-coupled filter array. Split ring resonators <NUM> and <NUM> form a first pair of square resonant elements, and split ring resonators <NUM> and <NUM> form a second pair of square resonant elements disposed adjacent to the first pair of resonant elements. Each resonant element includes a single break (<NUM>, <NUM>, <NUM> and <NUM> respectively). Each of the breaks of the first pair of resonant elements <NUM> and <NUM> extend along a first line (e.g., first axis X) of the voltage controlled oscillator <NUM>, and each of the breaks of the second pair of resonant elements <NUM> and <NUM> extend on a second line parallel to the first line. The breaks of the second pair of resonant elements <NUM> and <NUM> are located on opposing sides of the second pair of resonant elements, and the breaks of the first pair of resonant elements <NUM> and <NUM> are located directly adjacent to one another.

Each split ring resonator further includes a respective möbius strip resonator <NUM>, <NUM>, <NUM> and <NUM> located at about the centerpoint of the respective split ring resonator. The resonator <NUM> of the example of <FIG> also includes a mode suppression ring <NUM> to provide for further improved mode suppression.

<FIG> shows phase noise characteristics for the example voltage controlled oscillator of <FIG>. In the example of <FIG>, the oscillator <NUM> is set to a signal frequency of about <NUM> and exhibits phase noise as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>, and as low as about e.g., <NUM> dBc/Hz at an offset of about <NUM>.

The previously described (or similar) metamaterial resonator designs may also be integrated with a substrate integrated waveguide (SIW) in order to improve operation of a resonator application device, such as a VCO. An SIW is a waveguide-like planar structure that brings together the performance improvements attributable to waveguides with the ease of fabrication attributable to planar structures. Generally, an SIW is formed by adding a top metal layer over a ground plane layer and connecting the layers around their respective perimeters with plated vias. An electromagnetic wave in an SIW structure behaves like it is in a dielectrically-filled rectangular waveguide. The size of the SIW dictates the resonant frequency of the structure. Adding a complementary resonator (e.g., SRR) to the SIW can have the effect of raising or lowering the resonant frequency, depending on the properties of the complementary resonator. In the case of adding a metamaterial resonator, this addition can also increase the quality factor of the resonance. In this respect, the present disclosure is also directed to SIWs that may be used in combination with the above described and similar metamaterial resonator designs.

<FIG> shows a first example SIW resonator <NUM>. The resonator <NUM> is made up of an SIW <NUM> and a complementary split ring metamaterial resonator <NUM> formed on a surface of the SIW <NUM>. The SIW is formed on a substrate <NUM> (e.g., a soft board) by adding a top metal layer <NUM> over the ground plane metal layer (not shown) of the substrate <NUM>. The top and ground layers are connected on each side of the substrate by respective rows of plated vias <NUM>. In the example of <FIG>, the substrate <NUM> includes six or seven vias on each side. The distance between vias, the dimension of the vias, and the dimension of top metal layer and input/output feeding/extraction points may each affect the resonant frequency and loss characteristics of the structure.

In the example of <FIG>, the complementary split ring metamaterial resonator <NUM> substantially resembles the structure of the second example metamaterial resonator <NUM> of <FIG>. For instance, the split ring metamaterial resonator <NUM> of <FIG> includes two concentric square-shaped split ring elements having a common center and breaks extending from the common center in opposite directions. The SIW resonator <NUM> also includes first and second ports <NUM> and <NUM> on opposing ends of the substrate <NUM>. In the example of <FIG>, the ports are microstrip lines extending from a respective opposing ends of the SIW towards the split ring metamaterial resonator <NUM>. The ports <NUM> and <NUM> and breaks in the split ring metamaterial resonator <NUM> are formed along a line on a first axis X of the resonator <NUM>.

<FIG> shows a second example SIW resonator <NUM>. The resonator <NUM> includes an SIW <NUM> and first and second ports <NUM> and <NUM> comparable to the SIW and ports of the first example SIW resonator of <FIG>, and a different variety of a coupled-ring metamaterial resonator <NUM> formed on a surface of the SIW <NUM>. Specifically, the coupled-ring metamaterial resonator <NUM> includes a single circular ring having first and second breaks <NUM> and <NUM> on opposing sides of the ring and aligned with the first and second ports <NUM> and <NUM>. The structure <NUM> is the complementary of a differentially excited coupled-ring resonator and the complement helps in converting the differential excitation to a single ended excitation and hence in incorporating it in the unbalanced SIW resonator. At each of the breaks, the broken ends of the ring extend in the direction of the first axis X towards the first port <NUM>.

<FIG> shows a third example SIW resonator <NUM>. The resonator <NUM> includes an SIW <NUM> and complementary metamaterial resonator <NUM> comparable to the SIW and metamaterial resonator of <FIG>, but includes only one port (e.g., a first port <NUM> towards which the broken ends of the ring extend).

<FIG> show loss characteristics for the example SIW resonators of <FIG>, respectively. As shown in <FIG>, the first example SIW resonator <NUM> exhibits strong resonance at approximately <NUM>. As shown in <FIG>, the second example möbius resonator <NUM> exhibits strong resonance at approximately <NUM>.

<FIG> shows a plan view of a voltage controlled oscillator <NUM>. The voltage controlled oscillator includes an oscillating or tuning circuit <NUM> and an SIW resonator <NUM> similar to the resonator <NUM> of <FIG> (e.g., including an SIW <NUM>, complementary metamaterial resonator <NUM>, and a single port <NUM>, all structurally comparable to that of <FIG>). The port <NUM> is electrically connected to the gate of a transistor <NUM> (e.g., a hetero-junction FET), the transistor in turn being capacitively coupled to an output <NUM> of the VCO <NUM>. The complementary metamaterial resonator <NUM> is connected to a tuning circuit <NUM> through first and second varactor diodes <NUM> and <NUM> located on opposing sides of the complementary metamaterial resonator <NUM>. In the example of FIG. 12A, the oscillator <NUM> shown is adapted to achieve a phase noise of about -<NUM> dBc/Hz at a <NUM> offset from an oscillation frequency of about <NUM>.

<FIG> shows tuning characteristics of the voltage controlled oscillator <NUM> of <FIG> for a range of input voltages. As shown in <FIG>, as the applied voltage to the oscillator increases, the resonant frequency of the oscillator also increases. Furthermore, as the applied voltage increases, the loss characteristics improve and the quality factor of the voltage controlled oscillator also increases. This is further demonstrated in the graph of <FIG>, which plots the unloaded quality factor (Q) for the oscillator over a range of input voltages. Notably, the Q of the oscillator is about <NUM> at 5V, about <NUM> at 10V, about <NUM> at 15V, and about <NUM> at 20V.

<FIG> are photographs of some of the resonant circuits and devices described above. Specifically, <FIG> is a photograph of an array of printed resonant circuits having a structure similar to that of <FIG>. <FIG> is a photograph of an array of printed resonant circuits having a structure similar to that of <FIG>. And <FIG> is a photograph of a VCO having a structure similar to that of <FIG>.

Claim 1:
A device comprising:
a voltage controlled oscillator (<NUM>) adapted to output an electric signal at a given frequency, the voltage controlled oscillator (<NUM>) comprising a tuning circuit (<NUM>) capable of tuning the oscillator to the given frequency based at least in part on an input provided to the device and inherent noise or a nonlinearity in an active part of the voltage controlled oscillator (<NUM>); and
the voltage controlled oscillator (<NUM>) comprising a metamaterial resonator (<NUM>) having both metamaterial and möbius components, the metamaterial resonator adapted to increase the quality factor of the device at the given frequency,
wherein the metamaterial resonator (<NUM>) comprises four split ring resonators (<NUM>, <NUM>, <NUM>, <NUM>) distributed in a four-pole edge-coupled filter array,
wherein two of the split ring resonators (<NUM>, <NUM>) form a first pair of square resonant elements,
wherein the remaining two of the split ring resonators (<NUM>, <NUM>) form a second pair of square resonant elements disposed adjacent to the first pair of resonant elements,
wherein each resonant element comprises a single break (<NUM>, <NUM>, <NUM>, <NUM>),
wherein each of the breaks (<NUM>, <NUM>) of the first pair of resonant elements extend along a first line (X) of the voltage controlled oscillator (<NUM>), and each of the breaks (<NUM>, <NUM>) of the second pair of resonant elements extend on a second line parallel to the first line,
wherein the breaks (<NUM>, <NUM>) of the second pair of resonant elements are located on opposing sides of the second pair of resonant elements, and the breaks (<NUM>, <NUM>) of the first pair of resonant elements are located directly adjacent to one another, and
wherein each split ring resonator (<NUM>, <NUM>, <NUM>, <NUM>) further comprises a respective möbius strip resonator (<NUM>, <NUM>, <NUM>, <NUM>) located at about the centerpoint of the respective split ring resonator (<NUM>, <NUM>, <NUM>, <NUM>).