CA2295773A1

CA2295773A1 - High temperature superconducting structures and methods for high q, reduced intermodulation structures

Info

Publication number: CA2295773A1
Application number: CA002295773A
Authority: CA
Inventors: Balam Quitze Andres Willemsen Cortes; Neal O. Fenzi; Roger J. Forse; Albert H. Cardona
Original assignee: Individual
Current assignee: Superconductor Technologies Inc
Priority date: 1997-06-30
Filing date: 1998-06-18
Publication date: 1999-01-07
Also published as: EP1008234A1; WO1999000897A1; US6424846B1; DE69823363T2; US6895262B2; US6026311A; JP2002507359A; DE69823363D1; EP1008234B1; ATE265104T1; US20030087765A1

Abstract

Novel structures and methods for forming useful high temperature superconducting devices, most particularly resonators, are provided.
Structures resulting in reduced peak current densities relative to known structures achieve numerous desirable benefits, especially including the reduced intermodulation effects of earlier resonators. In one aspect of this invention, a spiral in, spiral out resonator is provided, characterized in that it has an odd number of long runs, at least equal to five long runs, where the long runs are connected by turns, and wherein there are at least two sequential turns of the same handedness, followed by at least two turns of the opposite handedness. In yet another aspect of this invention, it has been discovered that reducing the size of the input and output pads of HTS
resonators increases the relative inductance compared to the capacitance. Yet another resonator structure is a spiral snake resonator having a terminal end disposed within the resonator. A wide in the middle structure and wide at peak current density resonator structures utilize enlarged width portions of the resonator in those areas where current density is largest. In yet another aspect of this invention, operation of resonators in high modes, above the fundamental mode, reduce peak current densities. Resonators operated in modes in which current in adjacent long runs are in the same direction further serve to reduce current densities, and intermodulation effects. Symmetric current structures and modes of operation are particularly advantageous where far field effects are compensated for.

Description

DESCRIPTION
High Temperature Superconducting Structures And Methods For High Q, Reduced Intermodulation Structures Field of the Invention This invention relates to structures and methods formed from high temperature superconductors. More particularly, it relates to devices such as resonators having high Q and reduced intermodulation distortion for use as passive microwave devices.
Background of the Invention Electrical components come in various conventional forms, such as inductors, capacitors and resistors. A
lumped electrical element is one whose physical size is substantially less than the wave length of the electro-magnetic field passing through the element. A distributed element is one whose size is larger than that for a lumped element. As an example, a lumped element in the form of an inductor would have a physical size which is a relatively small faction of the wave length used with the circuit, typically less than 1/8 of the wavelength.
Inductors, capacitors and resistors have been grouped together into useful circuits. Useful circuits including those elements include resonant circuits and filters. One particular application has been the formation of filters useful in the microwave range, such as above 500 MHZ.
Considering the case of conventional microwave filters, there have been basically three types. First, lumped element filters have used separately fabricated air wound inductors and parallel plate capacitors, wired together into a filter circuit. These conventional components are relatively small compared to the wave length, and accordingly, make for a fairly compact filters. However, the use of separate elements has proved to be difficult in manufacture, and resulting in large circuit to circuit differences. The second conventional filter structure utilizes mechanical distributed element components. Coupled bars or rods are used to form transmission line networks which are arranged as a filter circuit. Ordinarily, the length of the bars or rods is ~ or '-~ of the wave length at the center frequency of the filter. Accordingly, the bars or rods can become quite sizeable, often being several inches long, resulting in filters over a foot in length.
Third, printed distributed element filters have been used.
Generally they comprise a single layer of metal traces printed on an insulating substrate, with a ground plane on the back of the substrate. The traces are arranged as transmission line networks to make a filter. Again, the size of these filters can become quite large. The structures also suffer from various responses at multiples of the center frequency.
Various thin-filmed lumped element structures have been proposed. Swanson U.S. Patent No. 4,881,050, issued November 14, 1989, discloses a thin-film microwave filter utilizing lumped elements. In particular, a capacitor n network utilizing spiral inductors and capacitors is disclosed. Generally, a multi-layer structure is utilized, a dielectric substrate having a ground plane on one side of the substrate and multiple thin-filmed metal layers and insulators on the other side. Filters are formed by configuring the metal and insulation layers to form capacitive ~-networks and spiral inductors. Swanson U.S.
Patent No. 5175518 entitled "Wide Percentage Band With Microwave Filter Network and Method of Manufacturing Same"

discloses a lumped element thin-film based structure.
Specifically, an alumina substrate has a ground plane on one side and multiple layer plate-like structures on the other side. A silicon nitride dielectric layer is deposited over the first plate on the substrate, and a second and third capacitor plates are deposited on the dielectric over the first plate.
Historically, such lumped element circuits were fabricated using normal, that is, non-superconducting materials. These materials have an inherent loss, and a result, the circuits have various degree of lossiness. For resonant circuits, the loss is particularly critical. The Q
of a device is a measure of its power dissipation or lossiness. Resonant circuits fabricated from normal metals have Q's at best on the order of a few hundred.
With the discovery of high temperature superconduc-tivity in 1986, attempts have been made to fabricate electrical devices from these materials. The microwave properties of the high temperature superconductors has improved substantially since their discovery. Epitaxial superconductive thin films are now routinely formed and commercially available. See, e.g., R. B. Hammond, et al., "Epitaxial T12Ca1BazCuzO$ Thin Films With Low 9.6 GHz Surface Resistance at High Power and Above 77 K", Appl. Phy. Lett., Vol. 57, pp. 825-27, 1990. Various filter structures and resonators have been formed. Other discrete circuits for filters in the microwave region have been described. See, e.g., S. H. Talisa, et al., "Low-and High-Temperature Superconducting Microwave Filters," IEEE Transactions on Microwave Theory and Techniques, Vol. 39, No. 9, September 1991, pp. 1448-1554.
The need for compact, reliable narrow band filters has never been stronger. Applications in the telecommunication fields are of particular importance. As more users desire to use the microwave band, the use of narrow band filters will increase the number of users in the spectrum. The area from 800 to 2,000 MHZ is of particular interest. In the United States, the 800 to 900 MHz range is used for analog cellular communications. The personal communications services are planned for the 1,800 to 2,000 MHZ range.
Many passive microwave devices, for example, resonators, filters, antennas, delay lines and inductors, have been fabricated in planar form utilizing high temperature superconducting thin films. As described, such structures are often smaller than conventional technologies in terms of physical size. However, these devices are also limited in their size given the constraints of fabricating high quality, epitaxial films. As a result, devices fabricated in HTS films are often of a quasi-lumped element nature, that is, where the nominal size the device is smaller than the wavelength of operation. This often results in folding of devices, which leads to significant coupling between lines.
Despite the clear desirability of improved electrical circuits, including the known desirability of converting circuitry to include superconducting elements, efforts to date have been less than satisfactory in all regards. It has proved to be especially difficult in substituting high temperature superconducting materials to form circuits without severely degrading the intrinsic Q of the super-conducting film. These problems include circuit structure, radiative loss and tuning and have remained in spite of the clear desirability of an improved circuit.

Summary of the Invention This patent relates to various novel structures and methods for forming high temperature superconducting devices, most particularly resonators. These devices have 5 high Q, that is, at least in excess of 1,000, more preferably in excess of 25,000, and most preferably in excess of 50,000. Generally, these inventive structures reduce peak current densities relative to known structures.
One significant result of reduced current density in reduced intermodulation effects.
In one aspect of this invention, a spiral in, spiral out snake resonator is provided. The spiral in, spiral out structure is characterized by having an odd number of long runs, at least equal to five, where the long runs are connected by turns, where there are at least two sequential turns of the same handedness, followed by at least two turns of the opposite handedness.
In yet another aspect of this invention, it is has been discovered that by reducing the size of the input and output pads in high temperature superconducting resonators, that the inductance may be increased relative to the capacitance.
Improved useful devices thereby result.
In yet another aspect of this invention, a spiral snake resonator having a terminal end disposed within the resonator is provided. In the preferred mode of this embodiment, multiple long runs are connected by turns, where the turns at one end of the resonator are concentric semicircles, with the center of radius being disposed between long runs. The turns at the second ends of the resonator are also concentric semicircles, though with the center of curvature being disposed at the end of a centrally disposed long run.

In yet another aspect of this invention, a resonator having a relatively larger width of a long run where the current is higher is disclosed. Such a wide in the middle structure may be utilized in conjunction with resonators, especially the spiral in, spiral out resonator. Similarly, resonators may be constructed having varying widths of long runs where the width of the long runs is adapted to reduce the current density in those long runs which, if narrower, would have relatively higher current densities. Other factors, such as impedance matching, may be considered. In the preferred embodiment of this mode, the relative width of adjacent long runs in a zig-zag or snake resonator is 2:3.
In yet another aspect of this invention, resonators are operated in higher modes, that is modes above their fundamental mode. Such operation serves to reduce peak current densities, and also to reduce intermodulation effects.
In yet another aspect of this invention, it has been discovered that operation of a resonator in a symmetric mode provides proved results. Lower current densities are achieved due to currents flowing in substantially the same direction in adjacent legs of the resonator. Devices operated in the symmetric mode are particularly advantageous when for field effects are not significant or are otherwise compensated for.
In yet another aspect of this invention, a hairpin resonator structure operated in a harmonic mode is disclosed. The harmonic hairpin structure and mode results in a symmetric current flow, that is, current flow in the same direction in adjacent long runs within a group.
Superior performance is obtained from such structures, resulting in a 15-20 dB improvement in intermodulation relative to operation of the hairpin at the fundamental frequency.
Accordingly, it is an object of this invention to provide improved high temperature superconducting structures.
It is yet a further object of this invention to provide improved resonators having reduced intermodulation.
It is yet a further object of this invention to provide resonators having reduced peak current densities.
It is yet a further object of this invention to provide high Q, superconducting resonators having reduced intermodulation effects.
Brief Description of the Drawin s Fig. 1 is a plan view of a quasi-lumped element resonator having wide input and output pads in a serpentine or zig-zag inductor structure.
Fig. 2 is a plot of the current and voltage distributions of a '-~ wavelength resonator at its fundamental resonance frequency, plotted above a ~ wavelength resonator structure.
Fig. 3 is a plan view of a zig-zag snake resonator having no significant input and output pad structures.
Fig. 4 is a plan view of a spiral in, spiral out structure having no significant input and output pad structures.
Fig. 5 is a plan view of a spiral in, spiral out structure with input and output pads.
Fig. 6 is a plan view of a spiral snake resonator having no significant input and output pads.
Fig. ? is the spiral snake resonator of Fig. 6 with the end portions shown displaced from the linear portions of the structure.

Fig. 8 is a plan view of a lumped in, spiral in, spiral out resonator with a wide in the middle structure.
Fig. 9 is a graph of the intermodulation product as a function of input power for the lumped element spiral in, spiral out resonator and the wide in the middle spiral in, spiral out resonator.
Fig. 10 is a emulation of a resonator utilizing an electromagnetic simulator.
Fig. 11 is a zig-zag resonator having nonuniform thickness lined widths.
Fig. 12 is a depiction of the electromagnetic simulation.
Fig. 13 is a output of an electromagnetic simulation.
Fig. 14 is a plot of the intermodulation power output as a function of the power input comparing a uniform zig-zag snake resonator with a fat zig-zag snake.
Fig. 15 shows resonate modes for an ideal straight resonator for fixed frequency and stored energy (loaded Q) showing the reduction in peak energy/current density when higher modes are employed.
Fig. 16 shows a graph of the intermodulation product versus input power for the fundamental and first harmonic of a spiral in, spiral out resonator.
Fig. 17a is a plan view of a zig-zag or serpentine resonator at its first harmonic and Fig. 17b is a plan view of a wide at peaks resonator at its first harmonic.
Figs. 18a, b, c and d show outputs of electromagnetic simulations for the magnitude in the fundamental mode (Fig.
18a), the phase in the fundamental mode (Fig. 18b), the langnitude in the ALF mode (Fig. 18c) and the phase in the ALF mode (Fig. 18d).

Fig. 19 shows Sonnet cross-sections for zig-zag, spiral in, spiral out, spiral and ALF spiral in, spiral out resonators.
Fig. 20 shows a plan view of a hairpin resonator.
Fig. 22a shows a graph of the unloaded Q (Q~) as a function of gap spacing.
Fig. 21b shows a graph of the intermodulation as a function of gap width.
Fig. 22 shows a graph of the intermodulation power as a function of input power for a hairpin resonator.
Figs. 23a and 23b show graphs of the current in the hairpin resonator in the fundamental mode (Fig. 23a) and the harmonic mode (Fig. 23b) Detailed Description of the Invention Fig. 1 shows a plan view of a quasi-lumped element resonator having enlarged input and output pads. An input pad 10 (the designation of input and output being arbitrary, and reversible) and an output pad 16 are disposed on opposite sides of a serpentine or zig-zag resonator region 18. Generally parallel long runs 12 are disposed substantially parallel to the longer edge of the input pad 10 and output pad 16. A first long run 12 adjacent to the input pad 10 is connected to a first turn 14 which electrically couples the input pad 10 to the first long run 12. Adjacent long runs 12 are then coupled to their nearest neighbor long runs 12 by corresponding turns 14.
The input pads 10 and output pad 16 serve to increase the equivalent capacitance to ground relative to a structure having no or smaller input and output pads. Preferably, the amount of equivalent capacitance to ground is selected in accordance with the electrical requirements of the circuit.
As shown in Fig. l, the total area occupied by the input pad 10 and output pad 16 exceeds that area occupied by the zig-zag resonator region 18.
The center frequency of such a resonator is j~ oc 1/ LC
5 A condition of resonance is that the energy stored in the magnetic field W1 and the energy stored in the electric field W~ must be equal:
W=W~=W~=2CV1= 2LI~
Then the unloaded Q is much larger than the loaded Q, 10 as is often the case for superconducting filters, then the stored energy at resonance, W, is determined by the loaded Q. Thus, if the frequency and loaded Q are fixed, it is clear that in order to decrease the circulating current we must increase L, while simultaneously decreasing C to preserve the resonant frequency.
Fig. 2 shows the current and voltage distributions of a wavelength resonator at its fundamental resonance frequency. A microstrip format may be utilized to implement a '-~ wavelength transmission line. Such structures generally have inductance and capacitance which form the resonator distributed along the line 20. The current distribution in such a structure at resonance is of the form sin(~x/1) having a maximum in the center of the resonator. The voltage distribution is of the form cos (~tx/1) with maxima at the ends of the resonator.
Fig. 3 shows a plan view of a zig-zag or serpentine snake resonator 30. A first long run 32 is connected to a nearest neighbor long run 34 by a turn 36. In similar fashion, the third long run 38 is connected to the nearest neighbor long run 34 by turn 40. This pattern is repeated until reaching a last long run 42.

Fig. 3 differs from Fig. 1 principally in that the input pad 10 and output pad 16 of Fig. 1 are eliminated or significantly reduced in size. by reducing the size of the capacitor pads 10, 16, the effective inductance of the quasi-lumped resonator is increased in Fig. 3 relative to Fig. 1. For a fixed frequency and loaded Q, this implies that the current density in the resonator can significantly be reduced by removal of the large capacitor pads. This has the effect of making the resonators behave more like folded distributed ('-~ wavelength) resonators. As an added current density reducing benefit, the linewidth of these resonators is usually higher than the linewidth at the highest current point in their QLE counterparts.
To a first approximation, the unloaded Q of an HTS
resonator is Q=wL/RS where w is the resonant frequency and RS. Thus, we see an additional advantage of these resonators over their QLE counterparts in terms of their higher unloaded Qs.
Using these structures, small area resonators can reliably be constructed which have the following desirable properties.
Resonator Area Resonant Frequency Unloaded Q Loaded Q ZMD
(Input Power: -20 dBm) <1 cm2 850 MHZ >50,000 1000 <-80 dBc Fig. 4 shows a plan view of a spiral in, spiral out snake resonator. A first long run 40 is connected to a second long run 48 by a first turn 51. The first turn 51 has a preselected handedness, here taken to be left-handed, though the designation of left and right-handed is arbitrary and therefore reversible. The second long run 48 is then connected by second turn 52, which is of the same handedness as is the first turn 51. The second turn 52 is connected to the third long run 42, which is then connected to turn 53 which is again of the same handedness of first turn 51 and second turn 52. The third turn 52 is connected to fourth long run 46, which is then connected to fourth turn 54, which is again of the same handedness of the preseating turns 51, 52 and 53. A fifth long run 45 is connected to the fourth turn 54. The fifth long run 45, being the center long run, namely, the line of symmetry for the resonator, then connects to a first turn of opposite handedness 61 which in turn connects to a sixth long run 44. The run 44 connects to a second turn of opposite handedness 62, which has the same handedness as the first turn of opposite handedness 61, which is opposite to the handedness of the first turn 51. The second turn of opposite handedness 62 connects to the seventh long run 47, which connects to the third turn of opposite handedness 63 which connects to the seventh long run 42, which connects to the fourth turn of opposite handedness 64 which connects to the ninth or last long run 49.
The spiral in, spiral out structure of Fig. 4 may be implemented with varying number of long runs and turns.
Generally, the following criteria describe the topology of the spiral in, spiral out structure. The spiral in, spiral out structure includes an odd number of long runs, identified to be N, where N is > 5. Numbering the long runs sequentially from 2 to N, the first long run is connected to the N-first long run by a turn of a first handedness. Long run N-1 is connected to long run 3 by a second turn of first handedness. This sequence is repeated until a turn of the first handedness connects to long run (N+1)/2. Long run (N+1)/2 is connected to long run (N+3)/2 by a turn of opposite handedness. Long run (N+3)/2 is connected by a second turn of opposite handedness to a long run (N-3)/2.
This process is repeated until the last long run (N) is reached.
Fig. 5 shows a plan view of a lumped element spiral in, spiral out resonator having enlarged input and output pads.
In comparison to Fig. 4 where nine long runs 40, 41 ... 49 are utilized, Fig. 5 has seven long runs 71, 72 ... 77. The first long run 71 has an enlarged width relative to other runs, serving to have increased capacitance.. The first long run 71 is connected to first turn of first handedness 81 to the sixth long run 76. The long run 76 is connected by the second turn of first handedness 82 to the third long run 73, which is in turn connected by the third turn of first handedness 83 to the center long run 83. The center long run 83 is connected in turn to first turn of opposite handedness 84, which is connected to the fifth long run 75, which is connected to second turn of second handedness 85 to the second long run 72, which is in turn connected to the third turn of second handedness 86 to the last long run or output capacitor pad 77. The output capacitor pad 77 has a width which is enlarged relative to the other interior long runs, and is shown having the same width as the first input capacitor pad or long run 71.
Fig. 6 shows a plan view of a spiral snake resonator.
A first long run 91 is connected to a second long run 92 by a first turn 101. The second long run 92 is connected to a third long run 93 which is disposed between the first long run 91 and the second long run 92, by a second turn 102.
Second turn 102 has the same handedness as first turn 101.
Third long run 93 is connected to a fourth long run 94 which is disposed between the second long run 92 and the third long run 93. The third turn 103 has the same handedness as the first turn 101 and second turn 102. This structure is repeated until terminating in a last long run 95 which is centrally disposed between the first long run 91 and second long run 92.
Fig. 7 shows a spiral snake resonator with the turn portions (corresponding to 101, 102, 103 and 104 of Fig. 6) physically displaced from the long runs (91, 92 ... 95 of Fig. 6) for clarity. In operation, these portions would be connected as shown in Fig. 6. Fig. 7 differs from Fig. 6 in that it includes seven long runs, as opposed to nine long runs for Fig. 6. Adopting the same number scheme as for Fig. 6, Fig. 7 shows that the even numbered turns 102, 104, dispose collectively at one end of the long runs, are concentric with each other around a point 110. Turns 101, 103 disposed on the right hand side of the long runs are concentric with each other around a point 112. The center of radius .12 is disposed on the end of the last long run 95. In contrast, the center of curvature .110 is disposed at the end of and between the last long run 95 and the preceding last long run. If there are N long runs, and the numbering convention is to sequentially number the long runs beginning with the outermost long run, the center point 110 is disposed between long runs N and N-1.
Fig. 8 shows a plan view of a spiral in, spiral out resonator having a wide in the middle region. The spiral in, spiral out aspects of Fig. 8 are as previously described in connection with Fig. 4. In contrast, Fig. 8 includes a center long run 120 (compared to the center long run 45 in Fig. 4) which is relatively wider than other long runs 122.
The structure of Fig. 8 generally comprises a quasi-lumped element resonator structure particularly useful for bandpass and band reject filters. In the fundamental resonant mode, the peak circulating currents lie in the center of the resonator. Broadening the center conductor 120 increases the cross-sectional area of the transmission line, which allows for greater current transport. Generally, it is believed that this technique serves to alleviate the stress of large peak currents. The width of the center conductor 120 in Fig. 8 is six times as wide as the remaining conductor 122. However, resonators in which the width of the center long run 120 is at least twice as wide as the remaining long runs would utilize the concept of this invention.
Fig. 9 shows the intermodulation product as a function of input power for the structure of Fig. 5 (labeled LESISO
for lumped spiral in, spiral out) and the structure of Fig.
8 (labeled WIMSISO for wide in middle spiral in, spiral out). As can be seen, for a given power input, the wide in middle spiral in, spiral out resonator of the type shown in Fig. 8 has lower intermodulation compared to the lumped element spiral in, spiral out structure of Fig. 5.
Figs . 10, 11, 12 and 13 relate to graduated line width structures. Fig. 11 shows a zig-zag or serpentine resonator structure, but where the width of the conductors vary as a function of position within the resonator. External long runs 120 are relatively thinner than adjacent long runs 122, which are in turn thinner than next adjacent long runs 124, which are yet in turn relatively thinner than adjacent long runs 126. The center long run 128 is preferably larger than the remaining long runs.
Broadly, the technique disclosed herein is for increasing the line width of a folded HTS resonator as a function of current density. Considering a structure such as Fig. 3 with uniform width long runs 32 and uniform gaps between adjacent long runs, e.g., long run 32 and long run 34, if straightened out, would resemble a half wave resonator, assuming the fundamental mode. In this situation, the current distribution along the length of the resonator would be sin (Q~x/~,).
Fig. 10 shows a technique for simulating the resonator of the form shown in Fig. I1. If the resonator is considered to comprise long parallel runs, each having the same length, without consideration of the turns, the currents in the individual lines in terms of the maximum or minimum current in a segment is as follows:
1 .Ii~Imax Ii~Imax Adj acent Leg Ratio 1 0.158384338 1 -2 0.459649276 2.902113197 2.902113197 3 0.715920617 4.520147809 1.557536699 4 0.902112776 5.695719602 1.26007375 5 1 6.31375561 1.108508854 6 0.902112775 5.695719602 1.26007375 7 0.715920617 4.520147809 1.557536699 8 0.459649276 2.902113197 2.902113197 9 0.158384338 1 -Ideally, the structure of the graduated resonators would be smooth lines, such as shown in the smooth lines of Fig. 13. In certain applications (such as a linear, non-folded structure) it may be desirable to have the shape follow some power of the current distribution. However, when folding the resonators into the various disclosed shapes, e.g., spiral in, spiral out, zig-zag or snake, modified spiral, utilizing continuous change in the line width generally results in lines which are not parallel. By utilizing the generally parallel structures disclosed as the preferred embodiments herein, where the spacing between adjacent long runs may be made constant, modeling of such systems is made easier. However, devices utilizing the concepts of these inventions may be implemented where line widths vary continuously at some or all of the portions of the resonator.
Preferably, the ratio of widths from outside of long runs 120 at the ends of the resonator to adjacent segments is 1:3. However, under certain circumstances, this can create an impedance mismatch which becomes significant, and for practical size requirements utilizing current processing technology makes the width of the long runs too small or fine.
Fig. 12 shows a modeling of a structure of Fig. 11 where the ratio between adjacent long runs I20, 122 is 2:3.
Thus, to build a equivalent 9 long run zig-zag resonator with 0.3 millimeter lines and gaps, the total width is distributed over the lines as follows, numbers 6-9 mirroring 4-1:
i Ideal Realization Width (mm) Gap (mm) 1 1 2 .146 .1825 2 3 3 .219 .27375 3 4.5 4.5 .3285 .365 4 5.5 5.5 .4015 .41975 5 6 6 .438 Alternatively, the circuit may be modified in other ways. For example, if the circuit were split into three segments, as opposed to the nine segments described previously, the values would be approximately as follows:
i Ideal Realization Width (mm) Gap (mm) 1 1 1 .243 .243 2 1 1 .243 .243 3 1 1 .243 .3645 4 2 2 .486 .486 5 2 2 .486 Fig. 13 shows a modeling where the width of the long runs is varied as a function of a higher power of the current density. Under certain conditions, this arrangement may increase impedance mismatch at the ends of the resonator without any appreciable effect in the central region of the resonator where the currents are largest.
Fig. 14 shows a graph of the intermodulation performance as a function of input power for a zig-zag or serpentine resonator as shown for example in Fig. 3 and a resonator having varying thickness long runs as shown for example in Fig. 11. The resonators have substantially equal resonator area, that is, they occupy substantially the same amount of overall area on a HTS film. Fig. 14 shows the structure of Fig. 11 (labeled "FAT" zig-zag snake) has a reduction of up to 5dB in intermodulation product as compared to the structure of Fig. 3 (labeled uniform zig-zag snake ) .
Fig. 15 shows four resonators 130, 132, 134 and 136.
Shown above those resonators is a graphic indicating the current as a function of position within the resonator. For wavelength resonator 130, for a given resonant frequency and stored energy, the current distribution along the resonator is shown by line 130'. Similarly, clearly, for resonator 132, when in the next mode number (mode 1 where mode 0 is the lowest order mode) is shown by line 132'. For a given resonant frequency and stored energy, the peak energy density is inversely proportional to the mode number.
Utilizing higher modes serves to reduce the stress placed upon the resonator, and reduces intermodulation products.
This discovery may be utilized in connection with any of the '~ wavelength resonators described herein.

Fig. 16 shows a plot of the intermodulation product as a function of input power for the fundamental and first harmonic of a spiral in, spiral out resonator (See e.g., Figs. 4 and 5). As can be seen, the first harmonic has lower intermodulation product as compared to the fundamental harmonic.
Fig. 17b shows a zig-zag or snake resonator operable at a first harmonic, where Fig. 3 in comparison would show a zig-zag or snake resonator at the fundamental frequency. If it is desired to preserve the circuit area, but to use the first harmonic as in Fig. 17b as compared to the fundamental in Fig. 3, the width of the long runs is reduced, preferably halved, in order to double the electrical length of the resonator. Fig. 17b shows a resonator operable at a first harmonic and utilizing the wide at peak structure described in conjunction with Figs. 15 and 16, above. Thus, the structure of 17b when operated at the first harmonic has two regions corresponding to the relatively wider regions of the long runs at which the current density is reduced. This wide at peaks resonator structure advantageously improves the intermodulation performance. The principals of the wide at peaks technique may also be applied to spiral in, spiral out snake resonators. In such resonators, due to the nature of the spiral in, spiral out folding, the odd harmonics of the resonator are closer to that of a spiral resonator in its fundamental mode.
Figs. 18a and 18b show the magnitude and phase, respectively, on a modeled system of a spiral in, spiral out resonator. The modeled structure is based upon a resonator of the structure shown in Fig. 4 and described above. As shown , the system is modeled as having 'single turns' which are linear and substantially parallel to adjacent 'turns'.
While this structure is advantageously utilized for modeling, it may also be utilized in physical implementations of the structures. Indeed, the structures described herein may be utilized with round or rounded turns, squared turns, mitred turns, or any turn serving as 5 an interconnection between the long runs which does not materially negatively impact the achieving the goals or objects of these inventions. One source for modeling software is Sonnet Software, Incs., Suite of Planar 3DEM
Tools (referred to either as "Sonnet" or "em") and is 10 available from Sonnet Software, Inc., 10207 North Street, Suite 210, Liverpool, New York 13088. The magnitude shown in Fig. 18a increases from the ends of the resonators to a maximum value in the middle of the center line. The frequency of modeling is 0.71742 GHz. The phase shows that 15 segments in the odd numbered long runs (40, 43, 45, 47, and 49 in Fig. 4) have a phase substantially 180° opposite to that of the even numbered long runs (40, 42, 44, 46 and 48 in Fig. 4).
20 Figs. 18c and 18d show the magnitude and phase respectively for the simulation of the same spiral in, spiral out resonator but at the first harmonic. The magnitude shows that the magnitude rises from the ends of the resonator to two peaks situation roughly at 1/4 and 3/4 of the length of the line, with the magnitude decreasing from the peaks to the center of the resonator. The phase shown in Fig. 18d shows that the resonator in substantially the upper half is of one phase, whereas the resonator in substantially the bottom half is of 180° phase difference.
The phase change is at substantially the center of the middle long run (long run 45 in Fig. 4). It has been discovered that the use of a symmetric mode, that is, one in which currents flow in the same direction in adjacent legs of the resonator, such as is shown in Fig. 18b, provide superior results. Specifically, the use of the symmetric mode serves to reduce current densities relative to the asymmetric mode. One of the direct beneficial results of reduction in current density is the reduction in intermodulation effects. While the asymmetric mode, that is, one in which currents flow in opposite directions in adjacent legs of the resonator, are beneficial respecting far field shielding, if the far field effects can be pushed sufficiently away the symmetric mode has the benefit described previously.
Experimental Results The following table provides data regarding spiral resonators, and spiral in, spiral out snake resonators of the size and area identified.
Topology SpiralSpiral SISO SISO SISO SISO

Snake Snake Snake Snake Length (mm]10.91 10.41 8.8175 8.8175 16.25 16.37 Width [mm] 4 9 6.9 6.4 3.6009 7.0025 Area [cm2] 0.91640.4164 0.56432 0.56432 0.58519621.1463092 LineWidth 0.9 0.4 0.4 0.9 0.4 1 [mm]

Gap [mm] 0.2 0.2 0.2 0.2 0.9 0.5 Frequency 829.28829.5 849.291 849.19 865.866 869.206 [MHZ] 5 Unloaded 39800 Q

Loaded Q 4130 -76 -62.5 -58.5 -66 -69 IMD @- -55.5 20dBm[dBc]

SpiralSpiralSISO SISO SISO SISO

Topology Snake Snake Snake Snake IMD @-20dBm -80.1 -100.1-87.1 -85.0 -88.1 -90.5 [dHc]

(QL~1000) Fig. 19 shows Sonnet cross-sections for zig-zag, spiral in, spiral out, spiral and higher mode (ALF) spiral in, spiral out resonators. Specifically, Fig. 19 shows quantitative results far a resonator if cut in a vertical direction such as labeled on cut 19 in Fig. 18a and Fig.
18b. Thus, for the spiral in, spiral out structure in the fundamental mode (Figs. 18a and 18c and lower left figure in Fig. 19 labeled SISO) the current can be seen to alternate in direction from adjacent long runs. Thus, in Fig. 19 SISO, the external most long runs correspond to values 141, 149, the adjacent long runs corresponding to values 142, 148, and so on to the value 145 of the center resonator. As can be seen, the current is opposite directions for adjacent lines (compare the positive value of 141 with the negative value of 142). In the higher mode spiral in, spiral out resonator (Figs. 18b and 18d and lower right graph in Fig.
19 labeled ALF SISO), again utilizing the same number convention, shows that adjacent resonators corresponding to signals 151, 152, 153 and 154 are all negative, indicating current flow in the same direction. In contrast, current in long runs corresponding to signals 156, 157, 158 and 159 run in the same direction, that direction being opposite to the direction of current in the long runs corresponding to signals 151, 152, 153 and 154. As shown, the signal 155 corresponding to the center resonator is shown substantially at 0. As can be seen in the graphics of Fig. 19, the current shows divergences at the edges of the long runs of the resonator. Further, while the ALF SISO of Fig. 19 is at a higher frequency (then a harmonic) as compared to the fundamental frequency such as used in the SISO of Fig. 19, the ALF SISO shows a lower envelope, corresponding to lower current density as compared to the other structures shown.
Fig. 20 shows a plan view of a hairpin resonator 160.
The hairpin resonator 160 is characterized in having a first long run 162 having a length L and a width W, and a second long run 164, also having a length L and width W, the first long run 162 and second long run I64 being substantially parallel to each other, and separated by a gap G. The long runs 162, 164 are connected to turn 166. The hairpin resonator 160 is spaced a distance S from conductor 168, and is generally parallel to the long runs 162, 164. It has been discovered that the particularly geometry affects both the losses and intermodulation in these resonators. The first harmonic mode gives less intermodulation relative to the fundamental mode, though the first harmonic mode has relatively higher losses relative to the fundamental mode, believed to be due to the more extended fields of that mode.
In operation, microwave energy may be coupled to these resonators in a band reject fashion via the transmission line 168. The spacing S between the transmission line 168 and the resonator 160 determines the strength of the coupling and thus the energy stored in the resonator, which may be characterized in terms of the loaded quality factor QL
of the device.
The response of the band reject resonator may be characterized in terms of three quantities, the resonance frequency, Fo, and the loaded and unloaded quality factors, QL and QU. Fo and QL are determined by the geometry of the resonator 160 and substrate.

For the actual experiments performed, the width of the runs 162, 164 was fixed at 0.4 mm, with L, G and S being adjustable parameters. The resonance frequency of 7.4 GHz was chosen.
Fig. 23 shows a graph of the current in the hairpin resonator of Fig. 20 in the fundamental mode. The current can be seen to flow in opposite directions in adjacent legs of the hairpin resonator 160. Fig. 23b shows the current distribution in the hairpin resonator 160 in the harmonic mode. The current can be seen to run in the same direction in adjacent long runs 162, 164, thus operating in the symmetric mode.
[NOTE: ADD TEST DATA REGARDING RESONATOR WITH A >
100,000]
Four sets of resonators were designed:
1. For gap widths of g-0.4, 0.2, 0.1 and 0.05 mm 1 and s were adjusted so that the first resonance was at fo=7.4 GHz with QL =2000, resulting in 1~4 mm and s~l mm. As the microwave currents flow in opposite directions in the two legs of the resonator these will also be referred to as anti-symmetric resonators.
2. For gap widths of g=0.4, 0.2, 0.1 and 0.05 mm 1 and s were adjusted so that the second resonance was at fo=7.4 GHz with QL =2000, resulting in 1~7 mm and s~2 mm.
Since the currents flow in the same direction in the two legs of the resonator these will be referred to as symmetric resonators.
3. For a gap width of g=0.4 mm 1 and s were adjusted so that the second resonance remained at fo=7.4 GHz but the coupling strength varied at QL =2000, 1000, 500, 200.
4 . A straight resonator ( g-->oo) was designed so that its first resonance was at fo=7.4 GHz with QL =2000, resulting in 17.7 mm and s~2 mm.

The circuits were clipped into gold plated test fixtures using Indium foil below the circuit to ensure proper thermal and electrical contact. The microwave circuit was then completed by wire bonds at both ends of the 5 50 S2 thru line. Note that the electrical ground plane seen by the resonator is, for the most part, provided by the unpatterned film on the back side of the substrate.
The microwave transmissions, SZ1, was measured using HP
10 8720B Vector Network Analyzer in order to determine fo, Q~
and Qt, which characterize the linear response of the circuit at low microwave powers. The Qs are obtained from direct measurements of the fractional bandwidths at -3 dB, ~f_2 aB, the insertion loss, S21(fo), and the width of the resonance 3 15 dB above the minimum, Of+3dB. In all cases the input power to the resonators was held fixed in PIN=-20 dBm.
The measured and calculated Qs are presented in Fig.
21A. In the calculations a surface resistance of RS=210,52 at 7.4 GHz and a penetration depth of ~,(77K)=0.3~,m were 20 used.
For the antisymmetric resonators the calculations are in good agreement with the measurements. For smaller gap sizes Q~, is degraded. This can be understood from the antiparallel currents running in the gap region. Therefore, 25 high current densities have to flow at the inner edges of the legs to screen out this field from the superconducting films. These high current densities lead to increased losses and to higher intermodulations. In contrast, for the symmetric mode the parallel currents lead to fields that cancel within the gap and no such degradation is expected.
For this mode we find almost exactly double what is measured (the dotted line shows half of the calculated values), using the same surface impedances used to evaluate the anti-symmetric mode Qs.
The circuits were tested with and without an Aluminum lid placed 0.150 inches above the circuit. For the first set of resonators the effect of removing the lid was only a slight shift in the resonant frequency with no detectable change in QU or QI,. For the resonators which made use of the first harmonic (sets 2 and 3), the effect was far more severe; there QU dropped close to an order of magnitude as the lid was removed. This is an indication that the microwave fields associated with the resonator are far more extended for the symmetric modes than for the anti-symmetric ones.
The two microwave signals required to produce intermodulation products were symmetrically placed 15 kHz above and below fo, for a signal separation of 30 kHz.
Continuous Wave (CW) Signals were produced using HP 8341B
and HP 83640A synthesized sweepers, and the signals detected using a Tektronix 3784 Spectrum Analyzer. The output power of the two sources was measured using an HP 437B power meter, and adjusted so that the two signals arrived at the sample with the same magnitude.
The absolute magnitude of third order intermodulation products. PIMP, as a function of input power provided to the device, PIN was measured. For the 30 kHz signal separation we are using here these signals are generated at fo+ 45 kHz.
As can be seen in Fig. 22 PIMD has a slope much closer to 2:1 (dotted Line) than the 3:1 (dashed line) expected from a pure third order nonlinearity.
PIMD at a fixed input power of PIN+-20 dBm is presented as a function of gap width for the first two sets of resonators and the straight one in Fig. 21b. PIMP was set to Q=1700 using the intermodulation value as proportional to the fourth power of Q. The open symbols denote the raw data while the full ones denote the adjusted values.
Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity and understanding, it may be readily apparent to those of ordinary skill in the art in light of the teachings of this invention that certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims.

Claims

1. A spiral in, spiral out resonator having a fundamental resonant frequency, comprising:
a plurality of long runs, a plurality of turns connecting the long runs, the turns connecting the long runs in a spiral in, spiral out configuration, wherein said spiral in, spiral out configuration defines an electrical length sufficient to support resonance either at said fundamental resonant frequency or at harmonics of said fundamental resonant frequency, the configuration characterized in that there are an odd number of long runs N where N > 5, wherein a first long run is connected to a second long run by a turn of a first handedness, and the second long run is connected to a third long run by a turn of said first handedness, wherein said first handedness is such that a current traveling from a given long run, through a turn of said first handedness and into another given long run would travel in one of either a clockwise or counterclockwise direction with respect to said spiral in, spiral out configuration, and long run N-2 is connected to long run N-1 by a turn of opposite handedness to said first handedness and long run N-1 is connected to long run N
by a turn of said opposite handedness, wherein said opposite handedness is such that a current traveling from said a given long run, through a turn of said opposite handedness and into another given long run would travel in the other of said clockwise or counterclockwise direction with respect to said spiral in, spiral out configuration, and an indirect coupling for coupling to a signal source.

2. The spiral in, spiral out resonator of claim 1 wherein N is 5.

3. The spiral in, spiral out resonator of claim 1 wherein N is 7.

4. The spiral in, spiral out resonator of claim 1 wherein N is 9.

5. The spiral in, spiral out resonator of claim 1 wherein N ~ 9.

6. The spiral in, spiral out resonator of claim 1 wherein the resonator has a Q of at least 1,000 at or above 77 K.

7. The spiral in, spiral out resonator of claim 1 wherein the resonator has a Q of at least 10,000 at or above 77 K.

8. The spiral in, spiral out resonator of claim 1 wherein the resonator has a Q of at least 50,000 at or above 77 K.

9. The spiral in, spiral out resonator of claim 1 wherein some of the long runs are subject to larger current density and some of the long runs are subject to smaller current density, and wherein the long runs subject to larger current density are wider than the long runs subject to lesser current density.

10. The spiral in, spiral out resonator of claim 9 wherein the (N + 1)/2 long run is wider than the other long runs.

11. The spiral in, spiral out resonator of claim 10 wherein the (N + 1)/2 long run is at least twice as wide as the other long runs.

12. The spiral in, spiral out resonator of claim 10 wherein the (N + 1)/2 long run is at least six times wider than the other long runs.

13. The spiral in, spiral out resonator of claim 1 wherein the plurality of long runs and turns are comprised of a high temperature superconducting material.

14. The spiral in, spiral out resonator of claim 13 wherein the high temperature superconducting material is a thallium containing superconductor.

15. The spiral in, spiral out resonator of claim 13 wherein the high temperature superconducting material is a YBCO high temperature superconductor.

16. The spiral in, spiral out resonator of claim 1 wherein the plurality of long runs and turns are a thin film disposed on a substrate.

17. The spiral in, spiral out resonator of claim 16 wherein a ground plane is disposed on the substrate.

18. The spiral in, spiral out resonator of claim 1 wherein the turns are semicircular.

19. The spiral in, spiral out resonator of claim 1 wherein the turns are mitered turns.

20. The spiral in, spiral out resonator of claim 1 wherein the turns are linear and at substantially right angles to the long runs.

21. The spiral in, spiral out resonator of claim 1 wherein said resonator possesses a current distribution which is symmetric.

22. The spiral in, spiral out resonator of claim 1 wherein said resonator possesses a current distribution which is antisymmetric.

23. A resonator comprising:
a plurality of long runs, a plurality of turns connecting the long runs to each other in a spiral snake configuration, characterized in that a first long run is connected to a second long run by a first turn of a first handedness, the second long run is connected to a third long run by a turn of said first handedness, the third long run being disposed between the first long run and the second long run, the remaining long runs being connected in like manner, the Nth long run having a turn at only one end.

24. The spiral snake resonator of claim 23 wherein there are three long runs.

25. The spiral snake resonator of claim 23 wherein there are four long runs.

26. The spiral in, spiral out resonator of claim 23 wherein N is 5.

27. The spiral in, spiral out resonator of claim 23 wherein N is 7.

28. The spiral in, spiral out resonator of claim 23 wherein N is 9.

29. The spiral in, spiral out resonator of claim 23 wherein N ~ 9.

30. The spiral in, spiral out resonator of claim 23 wherein the resonator has a Q of at least 1,000.

31. The spiral in, spiral out resonator of claim 23 wherein the resonator has a Q of at least 10,000.

32. The spiral in, spiral out resonator of claim 23 wherein the resonator has a Q of at least 50,000.

33. The spiral in, spiral out resonator of claim 23 wherein the long runs subject to larger current density are wider than long runs subject to lesser current density.

34. The spiral in, spiral out resonator cf.claim 23 wherein the plurality of long runs and turns are formed from high temperature superconducting materials.

35. The spiral in, spiral out resonator of claim 34 wherein the high temperature superconducting material is a thallium containing supercondutor.

36. The spiral in, spiral out resonator of claim 34 wherein the high temperature superconductor is a YBCO high temperature superconductor.

37. The spiral in, spiral out resonator of claim 23 wherein the plurality of long runs and turns are formed in a thin film disposed on a substrate.

38. The spiral in, spiral out resonator of claim 37 wherein a ground plane is disposed on the substrate.

39. A resonator comprising:
a plurality of long runs, the long runs having a width, a plurality of turns adapted to connect the long runs, the resonator characterized in that the long runs have varying widths, with at least one having a width which is greater than at least some of the other long runs.

40. The resonator of claim 39 formed in a zig-zag configuration having varying width long runs.

41. The resonator of claim 40 wherein the ratio and the ratio of widths of adjacent resonators is 1:3.

42. The resonator of claim 40 wherein the ratio of widths of adjacent long runs is 2:3.

43. The resonator of claim 39 wherein the resonator has a wide in the middle long run configuration.

44. The resonator of claim 39 wherein the resonator is adapted for operation in a harmonic mode.

45. The resonator of claim 38 wherein the resonator is adapted for operation in the first harmonic mode.

46. A method for operation of a resonator having a plurality of long runs, the long runs being arranged iii a generally parallel configuration to each other, the long runs being connected one to another by turns in a configuration selected from the group consisting of spiral in, spiral out resonators operated at a harmonic, and spiral snake resonators, characterized in that a current in a plurality of adjacent long runs is in the same direction, and that the current in a second plurality of adjacent long runs is in a direction opposite to that first direction.

47. A method for reducing current density in a resonator having a plurality of long runs, the long runs being substantially parallel to one another, the long runs being connected to turns, the resonator being formed into a structure selected from the group comprising: zig-zag resonators, spiral, spiral out resonators, spiral snake resonators, as compared to a resonator of the same structure and equivalent area, having uniform width W in the long runs the improvement comprising utilizing width W' for at last one long run, where W'>W, and the resulting current density is less than in the comparable run.

48. A high temperature superconductor quasi-lumped element resonator comprising:
a high temperature superconducting hairpin resonator, the hairpin resonator including:
a first long run, a second long run, the first and second long runs being substantially parallel, turn connecting the first and second long run, a transmission line, the transmission line being substantially parallel to the long runs, the resonator having a first harmonic mode of operation where the current is symmetric in the first long run and the second long run.

34a

49. The spiral in, spiral out resonator of claim 1 wherein said indirect coupling comprises a capacitive coupling.

50. The spiral in, spiral out resonator of claim 1 wherein said electrical length of said spiral in, spiral out configuration is substantially equal to 1/2 wavelength of said fundamental resonant frequency.