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Superconductor Science and Technology

Josephson junction arrays as a variable inductor in RF circuits and tunable filters

V. K. Kaplunenko, Gerd M Fischer

Published Feb 19, 2004• 17 citations
Publisher

Abstract

We report on the investigation of the effects of the nonlinear inductance of huge Josephson junction arrays on high-quality RF circuits. The inductance of a single junction is far too small for use in many RF applications; however, Josephson junction stacks and especially intrinsic Josephson junctions in crystalline-layered superconductors open new opportunities. The stack inductance can be altered by changing a DC Josephson current either using an external bias current or an external magnetic field applied to a closed superconducting loop containing two stacks connected in parallel. Using stacks of Josephson junctions in the LC resonators, a tunable 4-pole, 15 MHz band-pass filter with a centre frequency at 1.1 GHz was designed. The filter was simulated in the time domain and the response was converted to the frequency domain. It was found that using an input power level of −62 dBm, corresponding to 0.5% of the junctions' critical current, a linear approximation for the stack nonlinear inductance can be used. By changing the applied magnetic field, a tuning range of 20% was demonstrated with a tuning speed of 2 µs or better. An estimate of the losses is also given. In addition, power handling up to −26 dBm is reported using increasing circuit complexity.

DOI
10.1088/0953-2048/17/5/011

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Central Frequency/Wideband Quasioptical Josephson Oscillator Arrays

A. Pance, G. Pance, Michael J. Wengler

In this paper we present new design of quasioptical Josephson oscillators: the Central Frequency/ Wideband design. In this design, tuning structures composed of inductances, radial stubs and quarter wave transformers are integrated with every junction of the array in order to tune out the junction capacitance and match the junction impedance to the antenna impedance for the efficient output power coupling. Each junction feeds an antenna and power from individual junctions is quasioptically combined. We present a variation of the design where a sub-array replaces every single junction of the array. Preliminary results for the array designed for 98 GHz fundamental frequency and fabricated in Hypres NIVA10xThth technology are presented. Introduction In recent years there has been a growing effort within the superconducting research community to develop oscillators based on Josephson junction arrays. 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Here we describe the basic CFW design and one of its modifications, and present preliminary results obtained from arrays fabricated in NIVA10x/Nb technology. Generic CFW array design The generic CFW design is presented in Figure 1. MS2 is a very short length transmission line whose inductance tunes out the junction capacitance. A radial stub at the end of MS2 serves as the broadband short. MS1 is the quarter wave transformer that matches the junction impedance to the antenna impedance. That way, all of the rf power produced by the junction is coupled to the * Present address: Conductus, Inc., 969 West Maude Ave, Sunnyvale, CA 94086 Page 478 Fourth International Symposium on Space Terahertz Technology antenna and radiated in the broadside direction. This design has successfully been used in SIS mixers [5] (see elsewhere in this issue). A detailed account of this and other applicable designs of tuning elements can be found in [6]. We have designed 492 GHz CFW arrays for the following parameters: critical current density je = 4000 A/cm, junction capacitance Cj = 60 fF/pm and junction area A = 71= . The impedance of the log-periodic antenna is around 79 on silicon substrate and is independent of frequency in the designed frequency range. Since there is a basic trade-off between the coupling and the bandwidth, careful design of the tuning elements provides a predicted bandwidth of 80 GHz with 75% power coupling at the central frequency of 492 GHz (Figure 2). The design of the tuning structure is performed in Touchstone [7] with effects of the superconducting kinetic inductance accounted for. The tuning element design values are: Z i = 18 CI, 1 1 = 62.5 pm (MS 1) and 12 = 3.5 pm, Z2 = 15 CI (MS2). The 360 junction array is predicted to deliver 2011W of RF power at 492 GHz. A dramatic increase in performance, in terms of both the bandwidth and the coupling is possible with advanced sub-micron and high current density fabrication processes. Figure 3 shows the fabricated 492 GHz array. It employs 360 log-periodic antennas on a chip 6 mm X 6 mm in size, with integrated tuning structures on one arm of the antenna. All junctions are DC biased in parallel. The array periods are dx = 240 gm, dy = 264 gm. Unfortunately, this fabrication run did not yield working devices because of the minor problem during fabrication. New fabrication runs should be performed in the near future. Antenna-coupled lumped array A ready extension of the generic CFW design can be made for arrays at relatively smaller frequencies. Single junction can be replaced by a lumped parallel sub-array of junctions in order to increase the output power. The overall size of the sub-array must be much smaller than the wavelength at the desired operation frequency. Usual tuning structures can be used to tune out the capacitance of the sub-array and to transform the small impedance of the sub-an-ay to the large antenna impedance. If an is composed of several antennas and sub-arrays biased in parallel, the power from different sub-arrays would be quasioptically combined. Figure 4a shows a single sub-array fabricated in Nb/A10x/Nb technology at Hypres, Inc. A compact parallel array of 64 Josephson junctions is placed on one arm of logperiodic antenna on a silicon substrate (Figure 4b). A microstrip transmission line is used as a coupling structure between the sub-array and the antenna. Its electrical length is somewhat bigger than 90° so that the excess portion tunes out the big capacitance of the sub-array and the 90° portion serves as an impedance transformer. Although the bandwidth of this design is rather narrow, it has a nice feature that it works not only at the designed frequency fo, but at a set of frequencies approximately given by the sequence fo, 3f0, 5fo, ...(2k4) f0. (1) Array from Fig. 4 was designed for the fundamental frequency of fo = 98 GHz. The fabrication process parameters were jc=983A/cm 2 , q=38fF/pm , A=12.2 gm , RN=16.4 11. In order to increase the available power, we have placed identical microstrip-coupled sub-array on the opposite arm of the antenna. The two sub-arrays feed the antenna in parallel. The schematic of the electrical circuit is given in Figure 5. The microstrip line was designed with impedance of Z=1.42 S2 and electrical length of 93° at 98 GHz. The measured dc I-V curve of the whole array reveals a series of seven resonant peaks (Figure 6a). A small amount of DC magnetic field was applied Fourth International Symposium on Space Terahertz Technology Page 479 along the chip surface to enhance the resonances. When no magnetic field is applied (Figure 6.b) one of the steps (5 counted from Vdc=0) has disappeared. The visible critical current (1.25mA , Fig. 6b) is much smaller than about 15mA expected from the size of the quasiparticle current rise at the gap voltage, which we attribute to noise. The approximate frequencies of resonant peaks are inferred from the I-V curve and are given in Table 1 below. Resonant step # Frequency [GI-14 81 2 129 3 210 4 243 5 356 6 405 7 518 Table 1. Resonant steps from the I-V curve (Figure 6) of the array in Figure 4. The first step is at the fundamental frequency fo = 81 GHz and is down-shifted from the designed 98 GHz value because of the slight discrepancy between the designed and obtained fabrication parameters. Steps #4 and #6 correspond to higher oscillator modes given by k=2 and k=3 (1). At these three frequencies, the two sub-arrays work coherently supplying the RF power to the antenna. The remaining resonant peaks roughly correspond to the sequence of modes with f0 resonant frequencies (2j-1) —2-, where j = 2, 3, 5 and 6 for the steps #2, #3, #5 and #7, respectively. In these modes, one sub-array supplies the RF power to the other sub-array, and practically no power is radiated through the antenna. From the size of the resonant steps in the oscillator modes we estimate that the available RF power is less than a RW. The experiments for coupling the array radiation to the off-chip SIS detector are in progress . For radiated power in the range ofp,W, a two-dimensional array of parallel biased antenna/sub-arrays should be employed. Discussion and Summary We have presented a new Central Frequency/Wideband design of quasioptical Josephson arrays that effectively deals with the parasitic junction capacitances. Because of the independent tuning of individual junction capacitances, CFW oscillators would tolerate large scattering in process parameters. Further, because of impedance matching between the junctions and the antennas, these arrays would be very efficient sources. The major disadvantage of the CFA' design is the size of the unit cell, i.e. much smaller number of junctions can be utilized per given array area, compared to compact 2-D arrays. This disadvantage is offset by the array efficiency. First fabricated arrays show evidence of likely coherent array operation at a set of frequencies. The design promises Josephson submillimeter oscillators of unprecedented performance. Page 480 Fourth International Symposium on Space Terahertz Technology Acknowledgments We are pleased to acknowledge Hypres, Inc. for the fabrication of the antenna-coupled lumped-array oscillator. This work was supported by the Air Force Office of Scientific Research grant AFOSR-90-0233. Gordana Pance was partially supported by the IEEE Microwave Theory and Techniques Society Graduate Fellowship.

•Apr 1, 1993•0 citations

Stacked niobium Josephson junction arrays under x-band irradiation

Alexander M. Klushin, S. Schornstein, H. Kohlstedt +3 more

Stacked Josephson junction arrays located at the rf current antinodes of a superconducting microstripline resonator were investigated. The circuits were designed to obtain highly accurate voltages at cm-waveband microwave driving and low rf-power level. Nb-Al/AlO/sub x/-Nb Josephson junctions with tunneling area of 60 /spl mu/m/spl times/300 /spl mu/m and critical current density up to 7 A/cm/sup 2/ were used. We compared the average voltages of the rf induced maximal current steps in arrays with up to three junctions per stack. Quantized current steps up to 300 mV were observed under microwave irradiation at frequency of 19.20 GHz in circuits with 384 three-junction stacks. The dynamics of stacked tunnel junctions in the presence of rf-currents will be discussed with respect to application as voltage standards.

IEEE Transactions on Applied Superconductivity•Jun 1, 1997•6 citations
We report on the investigation of the effects of the nonlinear inductance of huge Josephson junction arrays on high-quality RF circuits. The inductance of a single junction is far too small for use in many RF applications; however, Josephson junction stacks and especially intrinsic Josephson junctions in crystalline-layered superconductors open new opportunities. The stack inductance can be altered by changing a DC Josephson current either using an external bias current or an external magnetic field applied to a closed superconducting loop containing two stacks connected in parallel. Using stacks of Josephson junctions in the LC resonators, a tunable 4-pole, 15 MHz band-pass filter with a centre frequency at 1.1 GHz was designed. The filter was simulated in the time domain and the response was converted to the frequency domain. It was found that using an input power level of −62 dBm, corresponding to 0.5% of the junctions' critical current, a linear approximation for the stack nonlinear inductance can be used. By changing the applied magnetic field, a tuning range of 20% was demonstrated with a tuning speed of 2 µs or better. An estimate of the losses is also given. In addition, power handling up to −26 dBm is reported using increasing circuit complexity.
We have designed and characterized superconducting integrated circuits for the ac Josephson voltage standard that demonstrate significantly improved performance. The typical circuit consists of an array of superconductor-normal metal-superconductor Josephson junctions, which are placed in a transmission line and biased with a broad-band (dc-to-15 GHz) pulse-drive waveform. Additional low-speed (dc and audio frequency) bias and output leads contain on-chip inductors that act as low-pass filters. The operating margins of the array were improved by adding resistive shunts across these inductors to damp their intrinsic resonances. These resonances had previously degraded the integrity of the broad-band signal driving the array. We present simulations and measurements of these improved circuits that demonstrate no resonances in the range of 0.1-20 GHz. Moreover, the operating margins of the ac Josephson voltage standard were improved.
We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Qi > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition, it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.
Large-scale integration of single flux quantum (SFQ) circuits requires components as compact as possible. In this paper, we study the feasibility of integrating vertically stacked Josephson inductors (VSJIs) fabricated with self-shunted Josephson junctions into our SFQ-based circuits, and use both dc and RF electrical measurements to verify the performance of these junction stacks as compact inductors. The VSJIs consist of three Josephson junctions stacked vertically and are inserted into test structures to validate their potential as compact alternatives to geometrical inductors. The VSJIs are designed to be non-switching junctions and are combined with smaller area, switching Josephson junctions fabricated with the same junction barrier process. The VSJIs have a designed critical current of approximately 50% greater than that of the switching junctions, and their observed behavior can be modeled correctly by including the known nonlinearity of the Josephson inductance. To confirm that this nonlinearity does not degrade the expected bias margins, we simulate two common types of SFQ cells with the geometrical inductors replaced by VSJIs. The results verify that incorporating VSJIs in SFQ circuits would increase circuit density with minimal impact on circuit margins.
This work presents the dc-SQUID based tunable inductance and its relevance into the design of resonators and filters for the qubit application. The SQUID inductance depends on loop inductance, applied magnetic field and bias\ncurrent for a given thermal noise. Tunable resonators and\nfilters have been designed by replacing the inductances of the resonator with a chain of SQUIDs in series. A narrow bandpass filter with variable central frequency is useful for superconducting qubit applications, specifically for improving the line widths of Josephson junction oscillators. We have designed a tunable 3.5 GHz resonator and 2 GHz 7 stage Chebyshev filters to be fabricated in Hypres 4.5 kA/cm2 process. According to simulations, up to 50% of the operating frequency of the designed filter can be varied. We present data that shows a frequency tuning of >2 GHz.
In this paper we present new design of quasioptical Josephson oscillators: the Central Frequency/ Wideband design. In this design, tuning structures composed of inductances, radial stubs and quarter wave transformers are integrated with every junction of the array in order to tune out the junction capacitance and match the junction impedance to the antenna impedance for the efficient output power coupling. Each junction feeds an antenna and power from individual junctions is quasioptically combined. We present a variation of the design where a sub-array replaces every single junction of the array. Preliminary results for the array designed for 98 GHz fundamental frequency and fabricated in Hypres NIVA10xThth technology are presented. Introduction In recent years there has been a growing effort within the superconducting research community to develop oscillators based on Josephson junction arrays. Submillimeter Josephson arrays with power levels of the order of 11,1W have been made at Stony Brook [1] and NIST [2]. Two-dimensional array of parallel biased Josephson junctions coupled to small antennas with quasioptically combined output power has been proposed as a promising approach for achieving larger power levels and reasonable radiation linewidths [3]. It has been shown that the performance of these arrays would critically depend on the way the Josephson junctions' capacitances are tuned out [4]. We have proposed arrays with microstrip tuning structures integrated with every junction as potentially the best solution RI Because of inherent frequency limitations of tuning circuits, these arrays are designed for one central frequency with the requirement of as large bandwidth as possible. This design will be referred to as the Central Frequency/Wideband (CFW) Design. Here we describe the basic CFW design and one of its modifications, and present preliminary results obtained from arrays fabricated in NIVA10x/Nb technology. Generic CFW array design The generic CFW design is presented in Figure 1. MS2 is a very short length transmission line whose inductance tunes out the junction capacitance. A radial stub at the end of MS2 serves as the broadband short. MS1 is the quarter wave transformer that matches the junction impedance to the antenna impedance. That way, all of the rf power produced by the junction is coupled to the * Present address: Conductus, Inc., 969 West Maude Ave, Sunnyvale, CA 94086 Page 478 Fourth International Symposium on Space Terahertz Technology antenna and radiated in the broadside direction. This design has successfully been used in SIS mixers [5] (see elsewhere in this issue). A detailed account of this and other applicable designs of tuning elements can be found in [6]. We have designed 492 GHz CFW arrays for the following parameters: critical current density je = 4000 A/cm, junction capacitance Cj = 60 fF/pm and junction area A = 71= . The impedance of the log-periodic antenna is around 79 on silicon substrate and is independent of frequency in the designed frequency range. Since there is a basic trade-off between the coupling and the bandwidth, careful design of the tuning elements provides a predicted bandwidth of 80 GHz with 75% power coupling at the central frequency of 492 GHz (Figure 2). The design of the tuning structure is performed in Touchstone [7] with effects of the superconducting kinetic inductance accounted for. The tuning element design values are: Z i = 18 CI, 1 1 = 62.5 pm (MS 1) and 12 = 3.5 pm, Z2 = 15 CI (MS2). The 360 junction array is predicted to deliver 2011W of RF power at 492 GHz. A dramatic increase in performance, in terms of both the bandwidth and the coupling is possible with advanced sub-micron and high current density fabrication processes. Figure 3 shows the fabricated 492 GHz array. It employs 360 log-periodic antennas on a chip 6 mm X 6 mm in size, with integrated tuning structures on one arm of the antenna. All junctions are DC biased in parallel. The array periods are dx = 240 gm, dy = 264 gm. Unfortunately, this fabrication run did not yield working devices because of the minor problem during fabrication. New fabrication runs should be performed in the near future. Antenna-coupled lumped array A ready extension of the generic CFW design can be made for arrays at relatively smaller frequencies. Single junction can be replaced by a lumped parallel sub-array of junctions in order to increase the output power. The overall size of the sub-array must be much smaller than the wavelength at the desired operation frequency. Usual tuning structures can be used to tune out the capacitance of the sub-array and to transform the small impedance of the sub-an-ay to the large antenna impedance. If an is composed of several antennas and sub-arrays biased in parallel, the power from different sub-arrays would be quasioptically combined. Figure 4a shows a single sub-array fabricated in Nb/A10x/Nb technology at Hypres, Inc. A compact parallel array of 64 Josephson junctions is placed on one arm of logperiodic antenna on a silicon substrate (Figure 4b). A microstrip transmission line is used as a coupling structure between the sub-array and the antenna. Its electrical length is somewhat bigger than 90° so that the excess portion tunes out the big capacitance of the sub-array and the 90° portion serves as an impedance transformer. Although the bandwidth of this design is rather narrow, it has a nice feature that it works not only at the designed frequency fo, but at a set of frequencies approximately given by the sequence fo, 3f0, 5fo, ...(2k4) f0. (1) Array from Fig. 4 was designed for the fundamental frequency of fo = 98 GHz. The fabrication process parameters were jc=983A/cm 2 , q=38fF/pm , A=12.2 gm , RN=16.4 11. In order to increase the available power, we have placed identical microstrip-coupled sub-array on the opposite arm of the antenna. The two sub-arrays feed the antenna in parallel. The schematic of the electrical circuit is given in Figure 5. The microstrip line was designed with impedance of Z=1.42 S2 and electrical length of 93° at 98 GHz. The measured dc I-V curve of the whole array reveals a series of seven resonant peaks (Figure 6a). A small amount of DC magnetic field was applied Fourth International Symposium on Space Terahertz Technology Page 479 along the chip surface to enhance the resonances. When no magnetic field is applied (Figure 6.b) one of the steps (5 counted from Vdc=0) has disappeared. The visible critical current (1.25mA , Fig. 6b) is much smaller than about 15mA expected from the size of the quasiparticle current rise at the gap voltage, which we attribute to noise. The approximate frequencies of resonant peaks are inferred from the I-V curve and are given in Table 1 below. Resonant step # Frequency [GI-14 81 2 129 3 210 4 243 5 356 6 405 7 518 Table 1. Resonant steps from the I-V curve (Figure 6) of the array in Figure 4. The first step is at the fundamental frequency fo = 81 GHz and is down-shifted from the designed 98 GHz value because of the slight discrepancy between the designed and obtained fabrication parameters. Steps #4 and #6 correspond to higher oscillator modes given by k=2 and k=3 (1). At these three frequencies, the two sub-arrays work coherently supplying the RF power to the antenna. The remaining resonant peaks roughly correspond to the sequence of modes with f0 resonant frequencies (2j-1) —2-, where j = 2, 3, 5 and 6 for the steps #2, #3, #5 and #7, respectively. In these modes, one sub-array supplies the RF power to the other sub-array, and practically no power is radiated through the antenna. From the size of the resonant steps in the oscillator modes we estimate that the available RF power is less than a RW. The experiments for coupling the array radiation to the off-chip SIS detector are in progress . For radiated power in the range ofp,W, a two-dimensional array of parallel biased antenna/sub-arrays should be employed. Discussion and Summary We have presented a new Central Frequency/Wideband design of quasioptical Josephson arrays that effectively deals with the parasitic junction capacitances. Because of the independent tuning of individual junction capacitances, CFW oscillators would tolerate large scattering in process parameters. Further, because of impedance matching between the junctions and the antennas, these arrays would be very efficient sources. The major disadvantage of the CFA' design is the size of the unit cell, i.e. much smaller number of junctions can be utilized per given array area, compared to compact 2-D arrays. This disadvantage is offset by the array efficiency. First fabricated arrays show evidence of likely coherent array operation at a set of frequencies. The design promises Josephson submillimeter oscillators of unprecedented performance. Page 480 Fourth International Symposium on Space Terahertz Technology Acknowledgments We are pleased to acknowledge Hypres, Inc. for the fabrication of the antenna-coupled lumped-array oscillator. This work was supported by the Air Force Office of Scientific Research grant AFOSR-90-0233. Gordana Pance was partially supported by the IEEE Microwave Theory and Techniques Society Graduate Fellowship.
Stacked Josephson junction arrays located at the rf current antinodes of a superconducting microstripline resonator were investigated. The circuits were designed to obtain highly accurate voltages at cm-waveband microwave driving and low rf-power level. Nb-Al/AlO/sub x/-Nb Josephson junctions with tunneling area of 60 /spl mu/m/spl times/300 /spl mu/m and critical current density up to 7 A/cm/sup 2/ were used. We compared the average voltages of the rf induced maximal current steps in arrays with up to three junctions per stack. Quantized current steps up to 300 mV were observed under microwave irradiation at frequency of 19.20 GHz in circuits with 384 three-junction stacks. The dynamics of stacked tunnel junctions in the presence of rf-currents will be discussed with respect to application as voltage standards.