CA2344327A1

CA2344327A1 - Superconducting resonator and filter devices and methods for manufacturing same

Info

Publication number: CA2344327A1
Application number: CA002344327A
Authority: CA
Inventors: Qi Yuan Ma; Shapur Sahba; Erzhen Gao; Hui Xu
Original assignee: Individual
Current assignee: Columbia University in the City of New York
Priority date: 1998-09-14
Filing date: 1999-09-14
Publication date: 2000-04-13
Also published as: WO2000021195A3; WO2000021195A9; MXPA01002713A; CN1325561A; WO2000021195A2; AU2342500A; EP1114512A2

Abstract

Electromagnetic resonator and filter devices are formed on a substrate havin g opposing sides. A superconductor layer on a first side is patterned in the form of at least one self resonant spiral. Input and output coupling structures, such as inductive loops or spirals, are formed on the opposing side of the substrate. Multi-pole filter devices are formed with several, commonly supported resonator elements disposed in a cooperative relationship on the first side of a substrate. Plural resonator elements can also be used to form multiple-output, channelizing filters.

Description

SUPERCONDUCTING RESONATOR AND FILTER DEVICES AND
METHODS FOR MANUFACTURING SAME
Field of the Invention This invention relates to radio-frequency resonator and filter devices and, more particularly, to such devices formed with a superconducting material.
Background of the Invention Ever since their discovery, high-temperature superconducting (HTS) materials have been considered for use as thin-film resonators and fzlters, such as micro-strip or cavity structures in the GHz-frequency range in microwave I0 communication applications. Use of HTS materials for such devices promises high Q-values due to low electrical loss. This advantage would apply also at Lower frequencies, but conventional quarter-wavelength parallel-coupled designs commonly used at microwave frequencies result in prohibitively large device dimensions in the MHZ-range.
15 One way to realize MHZ-range resonators and filters of practicable dimension is the lumped-element approach, using discrete inductor and capacitor elements. One such structure consists of a two-turn spiral with an inter-digital capacitor between the turns. Another has two spirals and two capacitively coupled rings separated by a dielectric layer. A third includes self resonant spirals.
However.
20 at Low MHZ frequencies, the length of the conductor used to form spirals is generally long which results in a high resistance and Low circuit Q.
Filters can be designed to operate at a single frequency of interest or at multiple frequencies. For example, a channeiizer f lter receive plural frequency signals on a single input port and selectively provides an output signal to one or more 25 output ports. Of interest with respect to channelizer filters is G.
Matthaei et al., "Microwave Filters, Impedance-Matching Network, and Coupling Structures", Chapter 16, Artech House, Dedham, MA, 1980.

SUMMARY OF THE INVENTION
It is an object of the present invention to provide a compact, high Q, low loss resonator structure, suitable for use at frequencies in the MHZ
range.
It is a further object of the present invention to provide a filter employing plural superconducting resonator elements, suitable for use at all radio frequencies, including those in the MHZ range In accordance with one embodiment, an electromagnetic resonator includes a substrate having a f rst face and a second face opposite to the first face. A
superconducting spiral resonator structure is disposed on the first face of said substrate. An input coupling structure and an output coupling structure are disposed on the second face of the substrate and are arranged to effect coupling to spiral resonator.
Preferably, the superconducting spiral resonator structure consists of a high temperature superconducting material, such as yttrium-barium-copper oxide and thallium-barium-calcium-copper oxide. Similarly, the input coupling structure and output coupling structure can also be formed from a similar high temperature superconducting material.
In another embodiment, an electromagnetic filter includes a substrate having a first face and a second face opposite to the first face. A plurality of superconductor spiral resonator structures are disposed on the first face of the substrate. An input coupling structure and an output coupling structure are disposed on the second face of the substrate, and are operatively coupled to at least one of the plurality of superconductor resonator structures.
In a preferred embodiment, the plurality of superconductor spiral resonator structures have an elongate geometry with a first end and a second end and the plurality of superconductor spiral resonator structures are arranged in a substantially side-by-side relationship.
In a further embodiment, the input coupling structure is substantially aligned with the first end of one of the plurality of superconductor spiral resonator structures. Similarly, the output coupling structure can be substantially aligned with WO 00/21195 PCTlUS99/2135b the second end of one of the plurality of superconductor spiral resonator structures.
The plurality of superconductor spiral resonator structures can be formed to have substantially equal resonant frequencies and cooperate as a multipole filter. Alternatively, the plurality of superconductor spiral resonator structures can operate at a plurality of resonant frequencies corresponding to a plurality of outputs, thereby forming a channelizer filter.
BRIEF DESCRIPTION OF THE DRAWINGS
Fig. lA is a schematic top view, enlarged, of an exemplary resonator spiral structure.
Fig. 1 B is a schematic diagram illustrating an enlarged section of Figure lA which details a portion of the spiral structure of Fig. lA.
Fig. 1 C is a physical model for the exemplary resonator spiral structure of Fig. 1 A.
Fig. 1 D is an electrical model corresponding to the physical model of Fig. 1 C.
Fig. 2 is a cross sectional view, not to scale, of the resonator structure of Fig. lA.
Fig. 3 is a graphic representation of an experimentally determined relationship of reflectance as a function of frequency for the resonator spiral structure of Fig. 1.
Figs. 4A to 4C are schematic diagrams of preferred three-pole filters in accordance with preferred embodiments of the invention.
Fig. 5 is a graphic representation of experimentally determined relationships of reflectance (S 11 ) and insertion loss (S 12) as a function of frequency for the filter according to Fig. 4C.
Fig. 6 is a schematic diagram of an alternative resonator structure in accordance with a further embodiment of the invention, including an inductor loop portion and an inter-digital capacitor portion.
Fig. 7 is a schematic diagram of an arrangement of resonator spirals on one side of a substrate, for an exemplary RF channelizing filter with three outputs.

Fig. 8 is a schematic diagram of a resonator spiral included in the filter of Fig. 7.
Fig. 9 is a schematic diagram of an exemplary coupling circuit for the filter of Figure 7 having one input and three output loops formed on the opposite side of the substrate from the filter.
Fig. 10 is an equivalent circuit diagram for the filter of Figs. 7-9.
Figs. 1 I-L3 are graphic representations of reflectance and transmittance far each of the three output loops of the filter of Figs. 7-9:
Throughout the figures, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the subject invention will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments. It is intended that changes and modifications can be made to the described embodiments without departing from the true scope and spirit of the subject invention as defined by the appended claims.
DETAILED DESCRIPTION
Fig. 1 A illustrates the geometry of an exemplary spiral resonator structure and associated dimensions for an embodiment of the resonator which exhibits a resonant frequency of about 24.5 MHZ. Fig. 1 B is an enlargement of a portion of Fig. I A which further shows the exemplary spiral resonator structure being formed with twenty evenly spaced turns composed of a superconductor material, preferably a high temperature superconductor (HTS).. The spiral resonator structure is generally configured for self resonance at a frequency of interest. The inductance, which is provided by the spiral superconductor structure is at resonance with the inherent interturn capacitance of the structure. Such a spiral resonator structure exhibits as unloaded Q-value which exceeds 40,000 when formed from a superconductor material. The equivalent physical and electrical models of the resonator structure of Fig, lA are illustrated in Figs. 1C and 1D, respectively. In the simple circular spiral inductor of Fig. 1 C the inductance can be calculated as 5 PCT/t3S99/21356 L(nH) =0.03937 a2n2 (1) 8a+11c where a-_ Do+Di c= Do_Di ~2) 4 ' 2 5 and n is the number of turns in the spiral, Do is the outer diameter of the spiral structure and D; is the inner diameter of the spiral structure in microns. The resistance of the spiral can be determined by the equation KnanR
R (S2) = S (3) W
where K is a constant (which is assumed to be 1 for a structure with no ground plane), RS is the surface resistance of the material forming the spiral and W is the width of the trace forming the spiral. In the case of a superconductor material, the value of RS is on the order of micro-ohms, which allows large inductances to be formed with low resistance. The inherent capacitance of the spiral resonator structure is C(pf) =3.5x10-SD°+0.06 ( ) Equations 1-4 can be generalized for various geometries by expressing the terms Do and D; in terms of area, as 4a 4a.
D°= ° and D . = 1 (5) n 1 n where ao is the outside area of the resonator structure and a; is the interior area of the resonator structure.

Fig. 2 is a cross sectional view of the resonator of Figure lA. The resonator is formed on a substrate 200 and includes a superconductor spiral structure 202 formed on one side 210 of the substrate 200, as well as an input structure 204 and an output structure 206 formed on an opposing side 208 of the substrate 200.
The input and output structures can be formed using a coiwentional conductor material, such as copper or aluminum. However, forming the input and/or output structures from a superconductor material, such as the material used to form the superconductor spiral structure 202, offers advantages in maintaining high circuit Q and low insertion Loss. In one embodiment, the superconductor spiral structure 202 is the spiral resonator structure of Fig. lA. In another embodiment, the superconductor layer structure 202 can take the form illustrated in Fig. 8. In both Fig. IA and Fig 8, the spiral structures are elongate, rather than circular. This feature of the spiral structure 202 allows for more condensed packaging when multiple spiral structures are placed in a side-to-side relationship, such as in embodiments of multi-pole filters to be discussed below. In an exemplary embodiment of a spiral resonator in accordance with Fig. 1 A, the substrate 200 is a two-inch lanthanum aluminate (LAO) wafer substrate having a thickness of about 20 mils. A suitable material for the superconductor spiral structure 202 is yttrium-barium-copper oxide (YBCO) which is deposited as a Layer with a thickness of 200 nm on the substrate 200. The YBCO
film can be deposited on the substrate at a temperature in the range of 700-800°C using laser ablation or a sputtering deposition method. The LAO substrate and YBCO
material are available from several commercial vendors; including Dupont. The YBCO material is superconducting at temperatures up to approximately 77 degrees K.
LAO is a preferred substrate material when YBCO is used to form the superconductor layer structure 202 because of high compatibility in lattice matching between these materials respective crystalline structures. Other suitable substrate materials include magnesium oxide {Mg0) and strontium titanate (STO).
In general, the thickness of the material forming the superconductor spiral structure 202 should exceed the penetration depth of that material. In the case of YBCO; which has a penetration depth of approximately 270 nanometers, films having a thickness in the range from 270 to 450 nanometers may be preferred.

Among other suitable superconductor materials are thallium barium calcium copper oxide (TBCCO) which has a penetration depth of approximately 450 nanometers.
In this case, the TBCGO films may be preferred having a thickness in the range from 450 to 750 nanometers.
An exemplary resonator, such as illustrated in Fig. 1 A, can be formed using a YBCO film on a clean LAO substrate, by a photo-lithographic patterning process according to the following procedure. First, a photo resist, such as Microposit S 1813, manufactured by Shepley of Marlborough, Massachusetts, is applied to one side 208 of the substrate 200 which is then spun at 1500 rpm for 40 seconds to establish a substantially uniform film. The substrate is then heated at about 120°C for 3 minutes to dry the film. Any photo resist on the back side 210 of the substrate 200 is then removed, such as by use of a cotton swab with acetone.
Without exposure, the substrate is placed in a developer solution, such as MF319 manufactured by manufactured by Shepley of Marlborough, Massachusetts, for 1 minute. This establishes a protective film on side 208.
Photo resist is applied to side 210 and is then spun at 4500 rpm for 40 seconds to establish a substantially uniform film. The substrate 200 is heated at about 120° C for 2 minutes. After the substrate is allowed to cool, a positive photo mask of the resonator structure is applied to the substrate 200. The photo mask is then subjected to exposure, such as 25 seconds with UV-light at a power of 5.6 mW/cm2.
The substrate is again placed in a developer solution, such as Microposit MF319 , for 1 minute. Once developed, the structure can be realized by etching away the areas under the exposed photo resist in dilute phosphoric acid solution {such as an 85% (2 micron filter) solution available from Olin Microelectronic Material, Inc. of Norwalk, Connecticut) for 40 seconds for a 200-nanometer layer of YBCO. For a 300 nm layer of YBCO, the approximate etching time is about 80 seconds, as thicker films require longer etching times.
The substrate should then be cleaned to remove any remaining photo resist. This can be accomplished by placing the substrate 200 in a solvent, such as acetone, for approximately 2 minutes.

To protect the superconductor spiral structure established on side 210 from subsequent etching while forming the input and output structures on side 208, a protective layer of photo resist is applied, dried, exposed and developed, as described above.
S The following steps are employed for forming contact pads on the back side 208 of the substrate. The substrate side 208 is cleaned to remove dirt and any photo resist. Next, photo resist is applied, spun, dried, and exposed, in a manner substantially the same as described above, except that a negative mask is used for the contact pads. The substrate is then submerged in chlorobenzene for S minutes and is then developed, as described above. A metallic coating is formed on the contact areas which were cleared by developing the exposed photo resist by depositing 50 nanometers Ag / 100 nanometers Au / 1SO nanometers AG, or SO nanometers Ag I
SO
nanometers Au / 200 nanometers Ag. A lift off process can then be employed to remove the unexposed superconductor, such as by using acetone. if post-annealing is 1 S desired, the resulting structure can be annealed in a pure oxygen, O,, environment at SSO°C atmospheric pressure for 10-20 minutes.
Fig. 3 shows experimentally determined reflectance characteristics of the resonator of Fig. 1 A, with the resonator at a temperature of 77 degrees K. As illustrated in Fig. 3, the exemplary resonator exhibits a resonant frequency of 24.S4SS
MHZ with an unloaded Q-value greater than 40,000. The input structure 204 to the resonator was formed with a single copper coupling loop formed on the back side 208 of the substrate 200, with the coupling loop substantially aligned with one of the circular portions i 02, 104 of the resonator structure 200. A second copper coupling loop, also on the hack side 208 of the substrate 210, is substantially aligned with the 2S other circular portion 102, 104 of the pattern forming the output structure 206. it will be appreciated that instead of single-loop patterns, alternate coupling structures can be employed for the input and output coupling structures, such as mufti-turn spiral structures and the like.
Figs. 4A to 4C illustrate alternate embodiments of a three-pole filter employing a resonator structure in accordance with Fig. lA. The filter configurations, which are merely exemplary, each include three spiral resonator structures 402, 404, 406 as described above, operating at a substantially equal resonant frequency and arranged in a substantially adjacent manner on a first side of substrate 200.
While the resonators are illustrated using the geometry illustrated in Figure I A, other spiral geometries can also be employed. By utilizing an elongate geometry, such as illustrated in Fig. I A or Fig. 7, rather than a circular geometry, the size of f lter employing several spiral resonators is reduced. The difference between the respective embodiments of Figs 4A-4C is in the arrangement of the input structure 204 and output structure 206.
For example, in Fig. 4A, the input structure 204 takes the form of a large loop 408 which couples with an input side of each of the spiral resonator structures 402, 404, 406. Similarly, the output structure in Fig. 4A also employs a large loop which couples with an output side of each of the spiral resonator structures 402, 404, 406. In Fig. 4B, a first small loop, approximately the diameter of an input section of spiral resonator structures 404, 406, 408 is placed opposite the input section I S of the central resonator 404. A similar small loop 414 is placed opposite an output section of resonator 404. Figure 4C employs similar input and output structures to that of Fig. 4B except that the input loop 416 is placed opposite an input section of resonator 406 whereas the output loop 418 is placed opposite an output section of resonator 402, thus maximizing the separation between the input and output coupling structures.
Exemplary 3-pole filter embodiments in accordance with Figs. 4A-4C
were tested at 77 degrees K. Reflection loss (S 11 ) and insertion loss (S 12) were measured with an HP-8712B RF Network Analyzer, for each of the three peaks of each filter. Table I shows measured date for each of the configurations illustrated in Figs.4A-4C.

WO 00J2119S PCTlUS99/21356 Table 1.
ep ak #1 e~ak #2 en ak #3 __________________________________________________________:____________________ ____________ (a) f[MHz] 23.65 23.92 24.27 loss[dB] -3.5 -8.0 -3.5 -7.0 21.0 -5.5 (b) f[MHz] 22.55 63.33 88.74 10 loss[dB] -3.03 -29.56 -5.48 -12.88 -2.70 -37.28 (c) f[MHz] 24.07 24.28 24.50 loss[dB] -6.37 -2.02 -4.62 -2.55 -6.56 -2.05 For the filter according to Fig. 4C, the single-peak Q-value after coupling is approximately 600. The maximum insertion loss between peaks Nos. 1 and 3 is -6.91 dB. At frequencies outside the passband, for example, Less than 23.77 MHZ or greater than 25.03 MHZ, insertion loss exceeds 40 dB (dynamic range), as shown in Fig. 5.
While the embodiments of Figure 4 illustrate 3-pole filter configurations, it will be appreciated that n-pole configurations are also possible, where n is the number of resonator structures employed.
Fig. 6 illustrates an alternate configuration suitable for use as the input structure 204 and/or the output structure 206, which includes an inductor portion 602 which is formed with a plurality of turns of conductor or superconductor material and a capacitor portion 604 which is formed by inter-digitally coupled conductor or superconductor segments. As with the resonator sections, the inductance and capacitance values for the coupling structure of Fig. 6 are selected to achieve resonance at the desired operating frequency. Thus, a more frequency selective coupling structure cari be formed on one side of a substrate, having a resonant frequency substantially matching the resonant frequency or frequencies of a multi-pale resonator element on the other side of the substrate, opposite to the respective input/output coupling structures.
Figs. 7-9 illustrate an exemplary multi-output, channelizing RF filter which can be formed using the photo lithographic process described above. The filter can be formed on a single LAO substrate on which 300-nanometer thick YBCO
layers are deposited, patterned and processed, front and back. Three spiral resonators 702, 704, 706 can be formed which are suitably spaced on a first side 210 of the substrate 200. Generally, rather than operate at a common resonant frequency, each resonator in the channelizing filter application operates at a resonant frequency corresponding to a particular channel, or frequency, of interest. In a channeling filter application it is desirable to minimize mutual coupling between adjacent resonators, therefore, the spacing between resonators 702, 704, 706 should be relatively large. However;
as physical space is also at a premium, the coupling can be reduced by providing an end-to-end offset between adjacent resonators, as illustrated in Fig. 7. On the opposite side 208 of the substrate 200, an input coupling structure 902 is disposed opposite a first end of resonator 704 and three coupling structures, 904, 906, 908 are disposed such that each loop is in substantial alignment with an output end of one of the resonators 702, 704, 706. Coupiing structure 902 serves as an R.F input coupling structure, and coupling structures 904, 906, 908 serve as output coupling structures for the channelized outputs such that each output will allow only frequencies in a selected band to appear at its terminals. The coupling structures can be simple loops, mufti turn spirals or more frequency selective structures, such as illustrated in Figure 6.
The equivalent circuit of the filter of Figs. 7-9 is illustrated in Fig. 10.
The filter of Figs. 7-9 can be modeled with a first transformer 1002 which is driven by source 1000 having an ideal voltage source and a series resistance equal to the characteristic impedance of the system {typically 50 ohms). The primary of transformer 1002 represents input structure 902 whereas the secondary of transformer 1002 represents a portion of resonator 704. Transformers 1004, 1006, 1008 represent the mutual coupling between resonators 702, 704, 706 and output structures 906, 906, 908, respectively. Transformers 1010, 1012 represent the mutual coupling between resonators 702, 704 and 704, 706, respectively. The total inductance of resonator 702 is distributed among the secondary of transformer 1002, the primary of transformer 1004 and the primary of transformer 1010. Similarly, the total inductance of resonators 704, 706 are distributed among the series connected transformer components representing each of these structures. Capacitors 1014, 1 O16 and 1 represent the capacitance of resonators 702, 704 and 706 respectively.
Resistors 1020, 1022, 1024 represent the inherent resistance of resonators 702, 704 and 706, respectively. The values of inductance, capacitance and resistance for the circuit model of Figure 10 can be determined using equations 1-5, which are set forth above in connection with Figs. 1 C and 1 D. Resistors RL 1, RL2 and RL3 represent output loads coupled to each of the output coupling structures. Resistors 1026, 1028 and 1030 are high value resistors (i.e., 1 Megohm) are required for the simulation software.
The values of reflection coefficient (S 11 ), transmission coefficient {512, S21), distance between adjacent peaks in each band, separation between the two pass bands, and Q-value of the device can be suitably selected based on particular application requirements. Device applications include single-input, mufti-output RF
and microwave filterslreceivers that can be used for satellite (in the frequency range of a few GHz), cell-phone base stations {a few hundred MHZ), TV, radio and lower-frequency communication systems.
Similar filter structures can be used as pickup coils for magnetic resonance imaging (MRI), with a mufti-resonant structure on one side of a substrate, and output coils on the other. The mufti-resonant structure then also serves for input, which is radiative, and the outputs can serve each for a different frequency to be detected, e.g. each corresponding to a different chemical element in a specimen or organ in medical diagnostics.
Although the present invention has been described in connection with specific exemplary embodiments, it should be understood that various changes, substitutions and alterations can be made to the disclosed embodiments without departing from the spirit and scope of the invention as set forth in the appended claims.

Claims

1. An electromagnetic resonator comprising:
a substrate having a first face and a second face opposite to the first face;

a superconducting spiral resonator structure formed on said first face of said substrate;

at least one input coupling structure disposed on said second face of said substrate;
and at least one output coupling structure disposed on said second face of said substrate.

2. The electromagnetic resonator according to claim 1, wherein the superconducting spiral resonator structure consists of a material selected from the group including yttrium-barium-copper oxide and thallium-barium-calcium-copper oxide.

3. The electromagnetic resonator according to claim 1, wherein said at least one input coupling structure and said at least one output coupling structure are formed from a superconducting material.

4. The electromagnetic resonator according to claim 3, wherein the superconducting material is selected from the group consisting of yttrium-barium-copper oxide and thallium-barium-calcium-copper oxide.

5. The electromagnetic resonator according to claim 1, wherein said at least one input structure and said at least one output structure comprise metallic inductor elements.

6. The electromagnetic resonator according to claim 1, wherein the superconducting spiral resonator structure has an elongate geometry.

7. An electromagnetic filter comprising:

a substrate having a first face and a second face opposite to the first face a plurality of superconductor spiral resonator structures disposed on said first face;
at least one input coupling structure disposed on said second face of said substrate, said at least on input coupling structure being operatively coupled to at least one of said superconductor resonator structures; and at least one output coupling structure disposed on said second face of said substrate, said at least one output coupling structure being operatively coupled to at least one of said superconductor resonator structures.

8. The electromagnetic filter of claim 7, wherein each of said plurality of superconductor spiral resonator structures have an elongate geometry with a corresponding first end and a second end, and said plurality of superconductor spiral resonator structures being arranged in a substantially side-by-side relationship.

9. The electromagnetic filter of claim 8 wherein said at least one input coupling structure is substantially aligned with said first end of at least one of said plurality of superconductor spiral resonator structures.

10. The electromagnetic filter of claim 9 wherein said at least one output coupling structure is substantially aligned with said second end of at least one of said plurality of superconductor spiral resonator structures.

11. The electromagnetic filter of claim 8. wherein at least one of said first ends is offset from the first end of an adjacent superconductor spiral resonator structure.

12. The electromagnetic filter according to claim 7, wherein at least one of said input coupling structures and said at least one of said output coupling structures comprise a distinct inductor portion and capacitor portion.

13. The electromagnetic filter according to claim 8, wherein said plurality of superconductor spiral resonator structures consist of a material selected froth the group including yttrium-barium-copper oxide and thallium-barium-calcium-copper oxide.

14. The electromagnetic filter according to claim 7, wherein the at least one input coupling structure and the at least one output structures comprise metallic inductor elements.

15. The electromagnetic filter according to claim 7, wherein the at least one input coupling structure and the at least one output coupling structure are formed from a superconducting material.

16. The electromagnetic filter according to claim 7, wherein each of said plurality of superconductor spiral resonator structures are resonant at substantially the same frequency.

17. The electromagnetic filter according to claim 7 wherein said plurality of superconductor spiral resonator structures are resonant at a plurality of frequencies, each of said plurality of frequencies corresponding to one of said at leant one output coupling structures.

18. An electromagnetic filter comprising:
a substrate having a first face and a second face opposite to the first face;
a plurality of superconductor spiral resonator structures disposed on said first face, said plurality of superconductor spiral resonator structures having an elongate geometry with a first end and a second end and a length defined therebetween, said plurality of superconductor spiral resonator structures being arranged in a substantially side-by-side relationship with respect to said length with a gap between adjacent resonator structures;
at least one input coupling structure disposed on said second face of said substrate, said at least on input coupling structure being operatively coupled to at least one of said superconductor resonator structures; and at least one output coupling structure disposed on said second face of said substrate, said at least one output coupling structure being operatively coupled to at least one of said superconductor resonator structures.

19. The electromagnetic filter of claim 18, wherein at least one of said first ends is offset from the first end of an adjacent superconductor spiral resonator structure whereby the coupling between adjacent resonators is reduced.