a josephson-array calculable-waveform generator

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1999 469

A Josephson-Array Calculable-Waveform GeneratorLaurie A. Christian and Karl J. H. Millar

Abstract—This paper proposes a new method for using aJosephson array to create a voltage waveform with a root-mean-square value calculable to better than 2 in 106 at frequenciesbelow 50 Hz. A novel method of reliably switching the dc voltagefrom one known voltage step to another at precisely definedtime intervals is investigated. In this method, transients in themicrowave voltage driving the array are used to induce switchingbetween steps. We consider two possible implementations ofthis concept. The first is for an array similar to that used inconventional dc voltage standards. The second uses the binarysequence of individually biased arrays introduced by Hamiltonet al. Computer simulation and theoretical analysis is used todemonstrate that the uncertainties in switching times are po-tentially limited only by the speed of the available microwaveattenuators, which is currently of the order of a nanosecond.

Index Terms—Digital-to-analog conversion, electrical variablesmeasurement, Josephson arrays, Josephson device measurementapplications, Josephson junctions, measurement standards, mi-crowave modulation.

I. INTRODUCTION

JOSEPHSON junction arrays used in dc voltage standardscomprise typically between 2000 and 22 000 Josephson

junctions connected in series. Each junction behaves as afrequency-to-voltage converter generating a dc voltage thatis strictly proportional to an input microwave frequency.Direct comparisons of array-based dc voltage standards giveagreement of the voltages produced to a few parts in 10[1].

Several approaches have already been considered for trans-ferring this exceptional dc voltage accuracy to ac voltagemeasurement and generation [2]–[5]. For ac waveform synthe-sis, the voltage generated by the array must be rapidly switchedfrom one value to another at precisely determined times. A keyissue is how quickly this can be done since switching timeswill largely determine how accurately the ac voltage can becalculated. This paper describes a novel fast voltage switchingconcept [6] in which switching is initiated by a transient inthe microwave voltage that drives the array. Switching timesof the order of a nanosecond are possible, limited principallyby the speed of the currently available variable microwaveattenuators. With appropriate array design, the result is avoltage waveform with calculable characteristics. The analysispresented in this paper indicates that an uncertainty of 2

V/V in the root-mean-square (rms) value of a 0.73-V 50-

Manuscript received June 21, 1996; revised November 13, 1998.L. A. Christian is with the Measurement Standards Laboratory of New

Zealand, IRL, Lower Hutt, New Zealand.K. J. H. Millar was with the Measurement Standards Laboratory of New

Zealand, IRL, Lower Hutt, New Zealand. He is now with the Center forTheoretical Physics, Massachusetts Institute for Technology, Cambridge, MA02139 USA.

Publisher Item Identifier S 0018-9456(98)09815-5.

Fig. 1. The dcI–V characteristic of a single junction forVrf=�V = 1:40

and�V=(IcR) = 0:016 [see (1)].

Hz waveform could be achievable with existing p-i-n diodeattenuators.

At present, the most promising scheme for ac waveformsynthesis uses Josephson arrays with groups of independentlybiased junctions [2]. Changing the voltage of the array isachieved by switching the individual dc bias currents to eachgroup in the manner of a digital-to-analog (D/A) converter.In this case, high switching speed requires fast pulses inthe dc bias circuit. Our design concept exploits the highbandwidth of the microwave circuit feeding the array to switchthe voltage. This offers an alternative and potentially fasterswitching technique which would allow the dc bias circuit tobe optimized for other requirements.

II. M ICROWAVE TRANSIENT INDUCED JUNCTION SWITCHING

A. Voltage Selection in Conventional DC Arrays

In use, a Josephson array is irradiated with microwavesof known frequency at appropriate amplitude. Fig. 1 showsan example of the resulting dc current versus voltage (– )characteristic for a single junction where the dc voltage is amultivalued function of the dc current. The voltage differencebetween the constant-voltage steps is given by the quotient ofthe microwave frequency and the Josephson constant-which has a value of 483 597.9 GHz/V. The array typicallyis irradiated with a 70–96-GHz microwave frequency, and for75 GHz, the voltage difference is 155V.

Selection of a particular voltage from the series array ofjunctions is done by biasing the array either with an externalvoltage source coupled with a series resistor or an externalcurrent source coupled with a shunt resistor. These generatea load line similar to that shown in Fig. 1, and the circuit

0018–9456/98$10.00 1998 IEEE

470 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 2, APRIL 1999

Fig. 2. Simplified equivalent circuit for a single Josephson junction biasedwith dc and microwave voltage sources.

Fig. 3. Assumed Bessel function form of the dependence of step width onthe microwave voltage amplitude.

operates stably only at those dc voltages determined by theintersection of the load line with the array– characteristic.

The current width of the voltage steps can be estimatedusing the Stewart–McCumber model for the Josephson junc-tions in the array. As shown in Fig. 2, this model describes ajunction as an ideal Josephson element with critical currentshunted by a subgap resistanceand a capacitance .

The current width of the resulting constant voltage steps hasa dependence upon the amplitude of the microwave voltageacross the junction given approximately by

(1)

Here, is the voltage difference between steps,is thedc current flowing through the junction, is the integerstep number, and is the Bessel function of the first kind.The dependence for the first three steps is shown in Fig. 3.Equation (1) is valid when the microwave bias source can bemodeled as a voltage source or, when a current source is moreappropriate, has most of the junction current passing through

or . Experimentally, we expect to observe narrower stepsdue to the effect of noise [7].

For the array to be used as an accurate digital voltagewaveform generator it must be switched rapidly from oneknown voltage step to another at a precisely defined time. Inprinciple, if the bias resistance is small enough that only onevoltage step is available at a time, the array can be forcedbetween predetermined voltage steps by rapidly changingthe output of the voltage or current bias source. Low biasresistances, however, may cause unstable array behavior [8]. In

addition, connection leads to conventional arrays are normallyfiltered to prevent electrical interference from switching thearray voltage. This filtering will increase the uncertainty inthe switching time and hence decrease the accuracy of thevoltage waveform.

B. Principles of Voltage Switching Inducedby Microwave Transients

The waveguide that conveys the microwave voltage to thearray may have a bandwidth of over 10 GHz for typicaloperating frequencies. A variation in the microwave voltagesupplied to the array will change the relative current width ofthe constant-voltage steps. Thus a transient in the microwavevoltage driving the array may be used to destabilize onevoltage step and force the array onto another. This paperestablishes the conditions under which this can be achievedin a controlled manner.

The values of junction parameters used in this paper aresimilar to those used in series-array dc voltage standards.Representative values are: 200 A, 5035 pF, and 75 GHz. The steady-state value of ischosen to be about 1. Fig. 3 shows that such values ofcorrespond to the and steps having large currentwidth and higher step numbers having significantly smallerwidth. If the microwave voltage is decreased from a value inthis range, the size of the step will increase, and thatof all other steps will decrease, destabilizing any junctions onthose steps. Similarly, increasing the microwave voltage willdecrease the size of the step, and enhance the othersteps.

Consider a single junction with an– characteristic andload line shown in Fig. 1. With the junction initially on the

step, the dc bias voltage is changed slowly to make theload line pass through the center of the step. At thisstage the current through the junction is near the limit of the

step. A decrease in the microwave voltage will thendestabilize this step while enhancing the current width of the

step and forcing the junction onto it.The amplitude of the microwave transient is maintained at

a level where higher order steps do not intersect the loadlineand so are not available. After the voltage transition, themicrowave voltage may be returned to its normal level, andthe junction will remain stable on the new voltage step. Thebias voltage merely has to slowly track the desired outputvoltage and put the junction current near the edge of the stepsometime before the microwave transient occurs. Thus, tran-sients in the microwave voltage induce a transition betweentwo dc voltage steps defined by the loadline. Because of thehigh bandwidth of the microwave circuit, these transitions can,in principle, be induced at very well defined times.

In voltage switching induced by microwave transients, theload line of the dc bias circuit is selected so that the arrayhas only two voltage steps available at any one time. Theload line in Fig. 1 is an example that meets this condition. Inderiving the conditions under which this is the case we assumethe functional form of the width of the step given by (1).The parameter values used in our analysis and, in particular,

CHRISTIAN AND MILLAR: A JOSEPHSON-ARRAY CALCULABLE-WAVEFORM GENERATOR 471

the values of used make this Bessel-function form for thestep amplitudes a reasonable approximation. While the stepamplitudes need not follow this functional form, the change instep width with change in must be known and must showthe same trends as in Fig. 3, with one of the andsteps increasing while the other is decreasing.

Consider a single Josephson junction, biased by a dc voltagethrough a resistor and with a microwave voltage

applied across it, as shown in Fig. 2. If the junction is phase-locked to the th step, then a dc currentwill flow through the junction. As the microwave voltageamplitude is increased or decreased (depending on whetheris zero), the size of theth step will decrease, until the pointwhere the step is no longer stable with the dc current passingthrough it. At this point, the junction will cease to be phase-locked, and may take on any of the available voltage steps.The manner of choosingwhich step is selected is chaotic andthus is unpredictable in general. However, the external circuitcan be designed to allow only one of the steps to the side ofthe original one to be available, i.e. only one of the steps.Now, if the microwave amplitude is temporarily changed towhere the th step is not stable, then the junction will beforced to stabilize on the chosen one of .

To allow only one of the steps either side of theth stepat the time of switching to be available, we require that,which is the parallel combination of and , satisfies

(2)

and also

(3)

where solves

(4)

At the microwave voltage levels we are using, these equationshave a consistent solution only for , , so with thisswitching concept we must demand thatat all times everyjunction in the array is only on these steps. This constraintalso ensures that there are no small amplitude steps, whichmay dislodge at times other than during the microwave voltagetransient. The assumed parameter values above requiretobe of the order of 1 .

Note that the stability of the junction voltage depends on itsstep number, the current passing through it, and the directionof the microwave transient. When the current puts the junctionat the center of its step, it is stable irrespective of the directionof the transient. Similarly transients in the “wrong” directionwhen a junction is operating away from the center will notcause transitions because they make those steps more stable.

C. Effect of Series Inductance

When the bias resistance satisfies (2)–(4), and the voltageacross the junction becomes either too large or small, thejunction current will respond. This prevents the junction fromphase-locking on any step other than the desired one. However,if the dc voltage bias circuit contains a significant series

Fig. 4. An example of a computer simulation of the microwave transient in-duced switching of a single junction. The circuit parameters areIc = 300�A,R = 50, C = 45 pF, RS = 1:5, andf = 75 GHz.

inductance , then the junction may lock to a voltage stepbeforethe current responds. This state will be stable until thecurrent approaches the end of the step, which will then becomeunstable, and another step will be chosen. Even if the desiredstep is found before the end of the transient, this process ishighly undesirable as it lengthens the time taken for transitionsto occur. In addition, there is the possibility of continuousoscillations occurring in some circumstances.

To avoid this, the reaction time of the external circuit needsto be no longer than the time in which a junction may changestates. The limiting factor for the external circuit is the reactionof the inductance, which has a time constant of ,whereas the time for a junction to switch voltage states iscontrolled by the time taken to charge the capacitance, whichis approximately . Thus, we require

(5)

For a typical junction, this value will be around 100 pHor less. It should be noted that is the inductance tothe nearest voltage source, which over the short time scalesinvolved may be some nearby voltage buffering system. Forthe first implementation of the switching concept describedin Section II-B, this may be a capacitor mounted on the chip(see Fig. 5).

D. Computer Simulation

Fig. 4 shows a numerical computer simulation of the mi-crowave transient induced voltage switching process for a


Fig. 5. Circuit diagram for fast switching of a modified form of a conven-tional array (the microwave bias source is not shown).

single junction, with the voltage averaged over each drivecycle to remove high frequency components. The behaviorobserved here is typical of that seen over a range of parametervalues and initial conditions that satisfy the constraints given in(2)–(5). Simulations were performed for up to 17 junctions inseries with bias circuits of the form discussed in Sections IIIand IV.

It is well known that the driven pendulum equations gov-erning the dynamics of the junction response to the externalmicrowaves and dc currents yield chaotic behavior [8]. Ouranalysis showed that the parameter values used in the nu-merical simulation introduced large errors (e.g., 2radians inthe junction phase) after only a few tens of microwave drivecycles. However, the purpose of these simulations is merelyto determine whether the array switches reliably betweenpredetermined voltage steps and to establish approximatelyhow long it takes to do so. The consistency of the resultsindicates that the bias circuit, while it may not determine theexact path through– -time space, will nevertheless reliablydetermine the voltage steps that the array finally settles on.

III. I MPLEMENTATION WITH A CONVENTIONAL

ZERO-BIASED SERIES ARRAY

Two possible implementations of this design concept areconsidered in the following sections. The first uses a voltagebiasing circuit with a series array having junctions withdesign parameters like those used in conventional dc voltagestandards. For these arrays, the same dc bias current passesthrough each junction, and the dominant interaction betweenjunctions is through the common source impedance. If thesource inductance satisfies some constraints, each junctioncan switch approximately independently of the others. Thisimplementation of the design concept then sets out to switchthe voltage of only one junction during each microwavetransient and to arrange for all junctions to be on the ,

stepsat all times. In this case, the slew rate is limited tovolts per second, where is the time required for

a junction to switch states and the current to drop. This timeis at least

A. Effect of Identical Junctions

The process of generating an arbitrary waveform beginswith the array of junctions all in the state. Whenthe array is biased as in the single-junction case above, acurrent passes through each junction. We considera transient that increases the microwave voltage so that the

junctions will become less stable. However, all of thesejunctions will become unstable at about the same time, withonly a small variation due to the small differences betweenjunctions, and also due to noise. If several junctions aredislodged at once, it becomes possible to get steps other thanthe , steps, as the requirement forced on the array bythe loadline only restricts the total voltage, and combinationssuch as an step with an step rather than an

and combination become possible. Half-integersteps have also been observed in numerical simulations in thiscase.

To prevent voltage steps other than , being chosen,we require that only one junction is allowed to switch voltagestates. We also require that the current quickly drops so thatall the other junctions can restabilizebefore they lose phase-lock. In this way, the junction that does dislodge is forcedto switch by one step and all the other junctions to remainwhere they were. Increasing the risetime of the microwavetransient will encourage one junction at a time to switch evenif they have nearly identical parameters and therefore behaveidentically. With a long risetime the junctions in the arrayspend sufficient time close enough to the edge of the stepfor the small differences in junction parameters or noise tocause them to become unstable at significantly different times.However, the noise in common to all the junctions must besmall relative to the noise for each.

When noise is present, the junction is no longer stable nearthe ends of a voltage step, but has a finite probability per unittime of switching to another voltage state [7]. The probabilityof a second junction changing voltage states in the time inwhich the first junction switches and the current settles to thenew voltage step must be made to be extremely small so thatonly one switches at a time. An increase in the risetime ofthe microwave transient coupled with an appropriate level ofnoise can be used to considerably improve the reliability ofthe junction switching to the desired , steps, asthe simulations showed. However, irrespective of the risetimeused there will always be a nonzero probability of more thanone junction switching at a time. The need to increase therisetime of the microwave transient and slew rate limiting inthis case means that the application of the switching concept toconventional arrays probably does not offer significant speedadvantages over using rapid dc bias switching.

B. Compensating for the Series Inductance

The problems encountered with inductance in the biascircuit for the single junction case also occur for multiplejunctions, but with greater consequences. Our simulationsshowed that steps other than , can also be createdin this case that will lead to the array voltage changing attimes other than during the microwave transient. To removethe effect of any inductance in the leads to the array, the arraycan be buffered with a capacitor across the input, as shownin Fig. 5.

The capacitance is selected because of the requirementthat the voltage remain steady during the time in which thetransient takes place, or that the time constant of the capacitive


Fig. 6. TheI–V characteristic for a single junction in the binary sequenceof arrays implementation (V

rf=�V = 1:42 and�V=(IcRjj) = 0:56).

circuit is longer than the transient width. In practice, thecapacitor would need to be placed on the array chip itself,as shown in Fig. 5, so that the inductance between it andthe junctions is kept significantly below the 100-pH valuedescribed in Section II-C. The resistance is then selectedto maintain the required loadline during the transition while

has a lower limit set by the requirement that it criticallydamp the – resonance.

IV. I MPLEMENTATION WITH A BINARY SEQUENCE OFARRAYS

The second implementation uses a D/A converter compris-ing a binary sequence of series arrays introduced by Hamiltonet al. [2]. In their design, every junction is individually shuntedby a resistor which is chosen to be small enough to makethe – characteristic nonhysteretic. The voltage of eachjunction in an array can be set to the same step by altering thecommon bias current. A desired voltage can be obtained byappropriately biasing each array. The accuracy of the rms valueof an ac waveform synthesized by this method is limited by thetime taken to switch the bias current. The degree of filteringin the Hamiltonet al. design can be less than that commonlyused in conventional dc voltage standard arrays. Nevertheless,the bandwidth of the bias current circuit is unlikely to be asgreat as that of the microwave one. The microwave transient-switching technique therefore offers an alternative method withthe possibility of higher switching speeds.

The design of Hamiltonet al. employs current-biasedshunted junctions. For the microwave transient switchingconcept to work, the junction parameters need to be modifiedto produce a hysteretic– characteristic like that shownin Fig. 6. The circuit can be modeled using its Theveninequivalent voltage source and bias resistor. The junctionshunt resistance subgap resistance and their parallelcombination are equivalent to those used in (2)–(4). Eachjunction is therefore effectively biased in the same way as forthe single junction in Section II, and the methods and analysisused there are directly transferable to this implementation.Here , and satisfy (2)–(4), and for a given biascurrent no more than two steps are stable. The inductance

is the inductance of the shunt arm, which can be madeas small as 1 pH [2].

As each junction is biased in a nearly identical manner,and the absence of a common load prevents the junctionsfrom coupling, they are expected to behave almost identically,with variations again only due to the small differences in theindividual junctions’ characteristics and to noise. It is thuspossible to cause all the junctions in the array to switchpredictably between steps at the same time. Because theswitching produces a very fast voltage change the leads biasingthe array are required to be inductive to ensure the currentremains approximately constant during the transition. In thisimplementation, it is an advantage to have identical junctionsand to have some inductance in the bias circuit leads.

This implementation of the switching concept then uses anarray design comprising a number of arrays in series, each indi-vidually current biased, and controlled by the same microwavesource. To obtain any required voltage, the bias currents toeach array are set in advance of the microwave transient,and two closely spaced microwave transients (one increasingand one decreasing) are used. The increasing transient inducesswitching of the arrays with junctions that have beenprepared for a transition to . Similarly, the negativetransient will switch the arrays with junctions thathave been prepared for a transition to . Groups ofjunctions that are not intended to be switched will have theirbias current centered on the existing steps and the transientswill not disturb them. This process sets the overall array to therequired voltage state at a time controlled by the microwavetransients.

In practice, the best performance obtainable by this methodis limited by the speed of the microwave attenuator used tocreate the transients. The time constant to charge the capacitorsin the array is which, for the values used here, isapproximately 50 ps, and the time constant for the junctionto settle into the new voltage state is . This impliesthat times to change between voltage states as short as 150ps are possible, in principle at least. As changes between twovoltage states will normally require two transients, this allowsswitching between any two voltage states in a time as shortas 300 ps. If the junctions are designed to use conductingbarriers, and have large critical currents, and thus smallerresistances as suggested by Hamiltonet al., then thisswitching time limit may be made very short. As the speedof microwave attenuators available at present is slower thanthis, the attenuator speed sets the limit on the accuracy of thetiming.

V. FILTERING AND NOISE

The voltage of a phase-locked Josephson junction, or anarray of junctions, is a dc value with large ac componentsat the drive frequency and its harmonics. There will alsobe a noise voltage component arising from thermal noisein the junction resistance . When using Josephson arraysto generate a dc voltage, the output is filtered or averagedto remove these frequencies. To generate a waveform withcalculable rms value, we need these ac components removed as


well, but we also require the timing of the voltage transitionsto be preserved. Because the microwave drive and junctionvoltage noise frequencies are separated by only a few ordersof magnitude, an ac voltage uncertainty calculation would needto include the effect of any filtering in the output leads.

Thermal noise causes voltage noise to appear across thejunction oscillating with a dominant frequency given by [7]

(6)

Equation (6) is valid when the noise is small and whenThis frequency may be as much as 20

GHz for the parameter values considered here. Our simulationsshowed a thermal noise voltage with an rms amplitude ofapproximately 0.4 V for a single 4.2-K junction with1.3 pF, driven by a microwave frequency of 75GHz and operated near the center of its step. Lower frequencycomponents were present with amplitudes several orders ofmagnitude lower than that of the dominant frequency. It isnoted that in operation the current flowing through the junctionwould not be allowed to approach too close to the edge of thestep. Filtering of this internal junction noise would be easieror unnecessary in some situations because the dominant noisefrequency would then typically remain in the gigahertz range.

Any real ac waveform synthesizer constructed using thisdesign concept would also be exposed to noise sources externalto the array. These sources would include the noise fromthe bias current source, the noise generated by the voltmeterbeing calibrated and appearing at its input terminals, and thenoise arising outside the synthesizer and voltmeter. Filtersmay be required on the current bias and voltage leads to thearray to prevent these sources disturbing the operation of thesynthesizer.

Effective filtering of the current bias leads should be pos-sible because these leads only require a bandwidth extendingto several times a frequency determined by the separation ofthe microwave transients. Filtering the voltage leads wouldnot be desirable because the uncertainties associated with thefilter characteristics would degrade the overall accuracy ofthe synthesizer. Measurements made on several commerciallyavailable high accuracy ac voltmeters indicate that the noiseappearing at the input terminals has an rms amplitude consid-erably less than 1 A. This should be too small to disturb thearray between microwave transients and filtering the voltageleads would not be required for this noise source. Eliminationof the effect of the other noise sources, those outside thesynthesizer and voltmeter, is likely to be one of the moredifficult system design issues to be overcome in building thesynthesizer.

VI. L IMITING ACCURACY

Several factors affect the accuracy of the calculated rmsvalue of a waveform synthesized in this manner: the un-certainty in the timing at which transitions occur; the effectof noise on the output voltage; and the presence of high-frequency components in the output. The value of the voltage

steps is known to be accurate to better than 1V/V. Thevoltage may be written as the sum of an ideal synthesizedwaveform plus an error term due to timing, noise andhigh-frequency component effects. Then the rms value ofis given in terms of the rms value of as

(7)

where the angled brackets denote time averages. For un-correlated error sources such as the thermal noise and highfrequency components, the middle term averages to zero, andso to first order, the fractional uncertainty is

(8)

Thus, the errors introduced are at a10 level if these factorscan be made to have rms amplitudes as little as a thousandtimes smaller than the amplitude of the waveform generated.

In the case of the uncertainty in the timing of the transitions,there is a systematic error which does not average to zero.Because the mechanism for switching from step 0 to 1 isdifferent to that from step 1 to 0, there will be a consistenterror in the length of time the array stays in each state,limited by the rise time of the microwave transient . Thefractional uncertainty caused by this can be calculated for thetwo different implementations in Section III.

For a triangular waveform of period synthesized using azero-bias array, the fractional uncertainty is less than

(9)

A binary switching array producing a triangular waveformwith a peak amplitude corresponding to the lowerbits allturned on has a fractional uncertainty less than

(10)

where .Equations (9) and (10) include the uncertainty introduced by

oscillations or other transients that are or less in magnitudeand which last less than . When generating a waveformusing the binary switching array, there are transient voltagesresulting from the need to switch bits off at a different time toswitching bits on. These transients are calculable and would beincluded in . These transients may be as short as 10 ns.

For a 1.27-V 50-Hz waveform synthesized in 155-V stepsusing a binary switching array and with a of 1 ns, (10)gives an uncertainty in the rms value equal to 2V/V. Factorssuch as the output filtering and external noise may increasethis value. The uncertainty, however, improves as the outputfrequency tends to zero and would be useful for calibratinglow-frequency ac voltage measuring instruments.

The above analysis applies to the unloaded output of thewaveform generator. Hamiltonet al. [2] discuss how a con-ventional D/A converter on the output may be used to supplythe bulk of the output current.


VII. CONCLUSION

We have shown that microwave transients can be used toswitch the voltage of a Josephson array very rapidly withoutrequiring the removal of filtering from the current bias leads.Two possible implementations of this concept have beenconsidered.

The first using a series zero-biased array has several draw-backs which make it difficult to implement as an ac voltagestandard. The limitation on the inductance in the array andthe leads connected to it require very careful design andfabrication. Identical junctions have been shown to create thepossibility of locking to steps other than the 0 and1 ones.The speed of timing achievable is as a result relatively slowand is unlikely to be faster than that available using directbias current switching.

The application of microwave transient switching to thebinary sequence array, however, allows very fast, reliableswitching. The design parameters required for the array circuitincluding the allowed values of inductance are achievable.The method is currently limited in speed by the availablemicrowave attenuators and not by the speed of the currentbias circuit. As the speed of microwave attenuators improves,this design concept offers potential advantages in the speed ofswitching the array voltage.

ACKNOWLEDGMENT

The authors thank K. Jones for his assistance in the prepa-ration of this manuscript.

REFERENCES

[1] D. Reymann and T. J. Witt, “International comparisons of Josephsonarray voltage standards,”IEEE Trans. Instrum. Meas., vol. 42, pp.596–599, Apr. 1993.

[2] C. A. Hamilton, C. J. Burroughs, and R. L. Kautz, “Josephson D/Aconverter with fundamental accuracy,”IEEE Trans. Instrum. Meas., vol.44, pp. 223–225, Apr. 1995.

[3] R. L. Peterson and N. M. Oldham, “Josephson ac voltmeter,”J. Appl.Phys., vol. 63, no. 10, pp. 4804–4810, May 15, 1988.

[4] S. B. Chapman and R. B. D. Knight, “A new AC-DC transfer standard,”in CPEM 92 Dig., June 1992, pp. 328–329.

[5] B. D. Inglis, “Standards for AC-DC transfer,”Metrologia, vol. 29, pp.191–199, May 1992.

[6] L. A. Christian and K. J. H. Millar, “A Josephson array based arbitrarywaveform voltage generator with calculable value,” NZ ProvisionalPatent Application 272322, June 9, 1995.

[7] R. L. Kautz, “The ac Josephson effect in hysteretic junctions: Range andstability of phase-lock,”J. Appl. Phys., vol. 52, no. 5, pp. 3528–3541,May 1981.

[8] , “Design and operation of series-array Josephson voltage stan-dards,” in Proc. Int. School of Physics Enrico Fermi, 1989, 1992, pp.259–296.

Laurie A. Christian was born in Invercargill,New Zealand, on September 19, 1950. He receivedthe B.Sc. (Honors) degree in 1973 and the Ph.D.degree in 1983 in physics, both from the Universityof Otago, Dunedin, New Zealand.

He is employed as an electrical metrologist atthe Measurement Standards Laboratory of NewZealand, which is part of Industrial Research Ltd.His research interests include Josephson technology,cryogenics, electrostatic hazards and nuisances, lowcurrent and high resistance measurement. He has

developed the New Zealand Josephson standard of dc voltage. Recently, hespent nine months as a Guest Researcher at the NIST Boulder Laboratoriesworking on the design of an ac voltage standard based upon pulse-drivenJosephson array devices.

Karl J. H. Millar received the B.Sc. (Honors)degree from Victoria University of Wellington,Wellington, New Zealand, in 1995, and is workingtoward the Ph.D. degree at the MassachussettsInstitute of Technology, Cambridge.

His primary field of research is in superstringtheory.

a josephson-array calculable-waveform generator

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