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Parallel Arrays of Josephson Junctions for Submillimeter Local Oscillators

A. Pance, Michael J. Wengler

Published Jan 1, 1992• 1 citation
OpenAlex

Abstract

In this paper we discuss the influence of the DC biasing circuit on operation of parallel biased quasioptical Josephson junction oscillator arrays. Because of nonuniform distribution of the DC biasing current along the length of the bias lines, there is a nonuniform distribution of magnetic flux in superconducting loops connecting every two junctions of the array. These DC self-field effects determine the state of the array. We present analysis and time-domain numerical simulations of these states for four biasing configurations. We find conditions for the in-phase states with maximum power output. We compare arrays with small and large inductances and determine the low inductance limit for nearly-in-phase array operation. We show how arrays can be steered in H-plane using the externally applied DC magnetic field.

Related papers

Dynamics of quasioptical Josephson junction arrays for submillimeter coherent sources

A. Pance, Michael J. Wengler

The dynamics of the quasi-optical two-dimensional Josephson junction arrays for oscillators is investigated. Numerical time-domain simulations of small-scale parallel arrays were performed. It is found that the DC biasing circuit determines the states of these arrays. It is also found that other states exist in which parts of the array operate in phase. The authors investigate the sensitivity of in-phase states to variations in junction critical currents and to nonvanishing fluctuations. It is found that the DC self-field effects do not provide a stable phase-locking mechanism and that RF interactions are necessary for locking the array in phase.>

IEEE Transactions on Applied Superconductivity•Mar 1, 1993•5 citations

Millimeter-wave self-radiation from high-Tc Josephson junction arrays

Kiejin Lee, Ienari Iguchi, Jeha Kim +2 more

We report the strong microwave Josephson radiation from an array of high-T/sub c/ junctions on a MgO bicrystal substrate from centimeter- to millimeter-wave ranges. The dc bias current was fed to the junction array having parallel geometry with the pair of junctions shunted by superconducting loops. The configuration of bias leads was a series of interlocking dc SQUID's geometry which guaranteed the oscillation of all junctions at the same frequency. The phase differences between adjacent junctions with different I/sub c/R/sub n/ products could be controlled by an external small magnetic field. For a five-junctions array, we observed the coherent output power of about 13 pW without external magnetic flux, which was nearly five times higher than that of a single bicrystal junction. We observed the Josephson linewidth of the self-radiation in the coherent state to be less than 1 GHz by adjustment of the external flux.

IEEE Transactions on Applied Superconductivity•Jun 1, 1997•6 citations

Quasioptical Josephson oscillator

Michael J. Wengler, A. Pance, B. Liu +1 more

Work with large two-dimensional arrays of Josephson junctions for submillimeter power generation is discussed. The basic design of the quasioptical Josephson oscillator (QJO) is presented. The reasons for each design decision are discussed. Superconducting devices have not yet been fabricated, but scale models and computer simulations have been done. A novel method for characterizing array RF coupling structures is described, and initial results with this model are presented. Microwave scale models of the radiation structure were built, and a series of measurements was made with a network analyzer. These measurements were summed in a computer to find properties of the structure when all elements in it are operating in phase. The goal of these measurements was to develop structures for oscillators which are tunable over a very broad band. Computer programs simulating a Josephson junction in any frequency-dependent coupling structure have been developed. An iterative harmonic balance technique finds the time-domain current and voltage waveforms across the junction for an arbitrary frequency-dependent RF load impedance. DC bias, and therefore oscillator frequency, can be held fixed in this technique, in contrast to time-domain techniques where the oscillation frequency is found after the waveform is found. With these programs design goals for maximum oscillator power and design limits to achieve tolerable harmonic distortion were found.

IEEE Transactions on Magnetics•Mar 1, 1991•18 citations

Microwave oscillator using arrays of long Josephson junctions

S. Pagano, R. Monaco, G. Costabile

The authors report on measurements performed on integrated superconducting devices based on arrays of long Josephson tunnel junctions operating in the resonant fluxon oscillation regime (i.e. biased on the zero field steps). The electromagnetic coupling among the junctions causes a mutual phase-locking of the fluxon oscillations with a corresponding increase of the emitted power and a decrease of the signal linewidth. This phase-locked state can be controlled by means of an external DC bias current and magnetic field. The effect of the generated microwave signal has been observed on a small Josephson tunnel junction coupled to the array via a microstrip transmission line. The feasibility of the reported devices as local oscillators in an integrated microwave Josephson receiver is discussed.>

IEEE Transactions on Magnetics•Mar 1, 1989•46 citations

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. 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.

•Apr 1, 1993•0 citations

Quasi-optical Josephson-junction oscillator arrays

Jeff A. Stern, Henry George LeDuc, Jonas Stasys Zmuidzinas

Josephson junctions are natural voltage-controlled oscillators capable of generating submillimeter-wave-length radiation, but a single junction usually can produce only 100 nW of power and often has a broad spectral linewidth. The authors are investigating 2-D quasi-optical power combining arrays of 10/sup 3/ and 10/sup 4/ NbN/MgO/NbN and Nb/Al-AlO/sub x//Nb junctions to overcome these limitations. The junctions are DC biased in parallel and are distributed along interdigitated lines. The arrays couple to a resonant mode of a Fabry-Perot cavity to achieve mutual phase-locking. The array configuration has a relatively low impedance, which should allow the capacitance of the junctions to be tuned out at the oscillation frequency.>

IEEE Transactions on Applied Superconductivity•Mar 1, 1993•12 citations
In this paper we discuss the influence of the DC biasing circuit on operation of parallel biased quasioptical Josephson junction oscillator arrays. Because of nonuniform distribution of the DC biasing current along the length of the bias lines, there is a nonuniform distribution of magnetic flux in superconducting loops connecting every two junctions of the array. These DC self-field effects determine the state of the array. We present analysis and time-domain numerical simulations of these states for four biasing configurations. We find conditions for the in-phase states with maximum power output. We compare arrays with small and large inductances and determine the low inductance limit for nearly-in-phase array operation. We show how arrays can be steered in H-plane using the externally applied DC magnetic field.
The dynamics of the quasi-optical two-dimensional Josephson junction arrays for oscillators is investigated. Numerical time-domain simulations of small-scale parallel arrays were performed. It is found that the DC biasing circuit determines the states of these arrays. It is also found that other states exist in which parts of the array operate in phase. The authors investigate the sensitivity of in-phase states to variations in junction critical currents and to nonvanishing fluctuations. It is found that the DC self-field effects do not provide a stable phase-locking mechanism and that RF interactions are necessary for locking the array in phase.>
We report the strong microwave Josephson radiation from an array of high-T/sub c/ junctions on a MgO bicrystal substrate from centimeter- to millimeter-wave ranges. The dc bias current was fed to the junction array having parallel geometry with the pair of junctions shunted by superconducting loops. The configuration of bias leads was a series of interlocking dc SQUID's geometry which guaranteed the oscillation of all junctions at the same frequency. The phase differences between adjacent junctions with different I/sub c/R/sub n/ products could be controlled by an external small magnetic field. For a five-junctions array, we observed the coherent output power of about 13 pW without external magnetic flux, which was nearly five times higher than that of a single bicrystal junction. We observed the Josephson linewidth of the self-radiation in the coherent state to be less than 1 GHz by adjustment of the external flux.
Work with large two-dimensional arrays of Josephson junctions for submillimeter power generation is discussed. The basic design of the quasioptical Josephson oscillator (QJO) is presented. The reasons for each design decision are discussed. Superconducting devices have not yet been fabricated, but scale models and computer simulations have been done. A novel method for characterizing array RF coupling structures is described, and initial results with this model are presented. Microwave scale models of the radiation structure were built, and a series of measurements was made with a network analyzer. These measurements were summed in a computer to find properties of the structure when all elements in it are operating in phase. The goal of these measurements was to develop structures for oscillators which are tunable over a very broad band. Computer programs simulating a Josephson junction in any frequency-dependent coupling structure have been developed. An iterative harmonic balance technique finds the time-domain current and voltage waveforms across the junction for an arbitrary frequency-dependent RF load impedance. DC bias, and therefore oscillator frequency, can be held fixed in this technique, in contrast to time-domain techniques where the oscillation frequency is found after the waveform is found. With these programs design goals for maximum oscillator power and design limits to achieve tolerable harmonic distortion were found.
The authors report on measurements performed on integrated superconducting devices based on arrays of long Josephson tunnel junctions operating in the resonant fluxon oscillation regime (i.e. biased on the zero field steps). The electromagnetic coupling among the junctions causes a mutual phase-locking of the fluxon oscillations with a corresponding increase of the emitted power and a decrease of the signal linewidth. This phase-locked state can be controlled by means of an external DC bias current and magnetic field. The effect of the generated microwave signal has been observed on a small Josephson tunnel junction coupled to the array via a microstrip transmission line. The feasibility of the reported devices as local oscillators in an integrated microwave Josephson receiver is discussed.>
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.
Josephson junctions are natural voltage-controlled oscillators capable of generating submillimeter-wave-length radiation, but a single junction usually can produce only 100 nW of power and often has a broad spectral linewidth. The authors are investigating 2-D quasi-optical power combining arrays of 10/sup 3/ and 10/sup 4/ NbN/MgO/NbN and Nb/Al-AlO/sub x//Nb junctions to overcome these limitations. The junctions are DC biased in parallel and are distributed along interdigitated lines. The arrays couple to a resonant mode of a Fabry-Perot cavity to achieve mutual phase-locking. The array configuration has a relatively low impedance, which should allow the capacitance of the junctions to be tuned out at the oscillation frequency.>