A Superconducting Analog Track-and-Hold Circuit

A superconducting analog track-and-hold circuit has been designed, fabricated, and tested. Experimental results demonstrate a 1.2-GHz bandwidth and a 25-dB dynamic range. Model calculations indicate that an optimized circuit with a critical current density of 10 000 A/cm2 can achieve a 4-GHz bandwidth and a 35-dB dynamic


I. INTRODUCTION HERE ARE TWO different types of Josephson sam-
T pling circuits.The pulse method developed by Faris [I] and Hamilton [2] consists of a sampling pulse generator and a single-junction threshold detector.On each repetition of the signal, the sampler compares the signal at a given sample time to a reference level, and a binary output indicates whether the signal is above or below that reference level.In order to determine the signal amplitude, repeated sampling is required.A time resolution of 2.1 ps has been reported with this technique [3].The other method, invented by Zappe [4], uses a switching junction to trap a sample of the signal in a superconducting loop.A SQUID readout device is used to determine the amount of current in the loop.While this method is slower, it can capture a single shot sample of the signal rather than just comparing it to a reference level.With integrated-circuit technology, 100 or more of these sampling circuits will fit onto a single chip allowing many samples of a single shot signal waveform to be taken and stored for later readout and analysis.In this way the track-and-hold can be used as a multipoint transient recorder.This paper discusses the design, analysis, and testing of the loop-type superconducting analog track-and-hold circuit.magnetic flux produced by the gate current Ig couples into J1 suppressing its critical current I,,,.A sine-shaped junction is used because its threshold curve has very low side lobes [5].In the experimental data of Fig. l(b), the critical current is suppressed to less than 3 percent of its maximum value for all gate currents greater than 10 mA.When the critical current of J1 is suppressed, signal current I, flows through LI + L 2 to ground.When the gate current is removed at sample time T, J1 returns to its zero-voltage state, trapping the signal current at time Tin loop L1, L 2 , L 3 , and J1.Since the loop is superconducting, the signal will not decay and can be read out at any later time using the read SQUID circuit L 2 , L 4 , J 2 , and J 3 .

THE TRACK-AND-HOLD CIRCUIT
111.DESIGN CONSIDERATIONS In designing the circuit, the following must be considered: 1) Suppose that the signal current range is centered around zero with max and min values of +Iso and -ZSo.If a signal value +Iso is trapped in the loop and the signal changes to -I,,, the current through J1 will be 2Zso.Since this current must be less than I, (0), the allowable signal range is -I,(O)/2 < I, < +1,(0)/2.3) The shaped junction switch is not an ideal switch because it can carry a small supercurrent I , ( I , ) , even when it is in its open state.Thus, signal-current changes less than I, ( Zg ) will not be tracked by the circuit and the dynamic range is limited by the ratio I , (0) / I , ( I,).It has been found that a sine-shaped junction with a length of several times the Josephson penetration depth can achieve a critical current suppression ratio I,,, (0) /Im ( I , ) on the order of 50, for all values of Ig greater than about 10 mA 4) Another nonideal characteristic of the switch is the existence of a small parasitic inductance L 3 .Because of this inductance, there is coupling between the gate signal and the read SQUID and signal variations in the hold mode are not completely shorted to ground.A small fraction L 3 / ( L 1 + L 2 + L 3 ) of the signal and gate current is coupled into Ll + L , , resulting in unwanted feedthrough.In many applications the signal level can be set to zero when the circulating current is read so that signal feedthrough is not a problem.Coupling of the gate signal into L , + L 2 is the same for every sample and therefore can be easily subtracted from the sampler output.
5 ) The read-SQUID critical current is a periodic function of the circulating current to which it is coupled.Therefore, in order to avoid ambiguity in reading the circulating current, the nearly linear portion of the theshold curve should span the full range of possible circulating currents.This requirement is met if I, ( 0 ) ( L 2 + L 4 ) = 0.7 Oo.The inductances L 2 and L4 and the critical currents of J 2 and J 3 are chosen to optimize the shape of the SQUID threshold curve In the track mode the loop current will follow the signal with a bandwidth of approximately 0.20 R , / L .R, also plays a role in helping J , to reset promptly when Ig goes to zero especially for rapidly slewing input signals.The simulations discussed below show that the optimum value of R, is somewhat lower than that given above.

IV. CIRCUIT DESIGN A N D SIMULATION
The first column of Table I shows the circuit parameters chosen to satisfy the above conditions.In order to perform a numerical simulation of the circuit, it is necessary to replace the shaped junction with the lumped-element equivalent circuit shown in Fig. 2(a).At least 30 sections are required to properly model the shaped junction [ 5 ] .A simulated equivalent-time response to an arbitrary input signal I,,( t ) is generated from the following sequence: 1) Beginning with all currents and voltages equal to zero, IR is ramped up to IRo = 10 mA to set the circuit in the track  mode.
2) The input waveform I , ( t ) is started.3) Beginning at time to, I8 is ramped to zero in 50 ps.This sets the circuit in hold mode.4) 500 ps after I, (r) has returned to zero, the sampled value, represented by the current in L , , is saved.This procedure is repeated many times as a function of to.Fig. 2(b) is the equivalent time response to a pulsed input made by plotting the sampled values as a function of to.The original waveform I , ( t ) is also shown for comparison.The circuit parameters are the design values of Table I.The transition times indicate that the loop current tracks the input with a 4.3-GHz bandwidth.It has been pointed out by Klein [7] that the time at which JI resets to the voltage state becomes erratic for high signal slew rates.This problem was investigated by using a fullscale sinewave for the input signal.At frequencies above 1.5 GHz the sampled response was found to degrade rapidly.As R, is reduced, the performance improves until the bandwidth is limited by the L / R , time constant of the loop.A tradeoff between these two constraints sets the practical bandwidth to about 2 GHz for the design values of Table I.
V. EXPERIMENTAL RESULTS Circuits were fabricated with critical current densities of 350 and 1000 A/cm2.Most of the experimental results are from the 350-A/cmZ circuit because the performance of the read SQUID was better at the lower current density.The measured circuit parameters of the tested track-andhold are shown in column 2 of Table I.
The circuit was tested by sampling a repetitive waveform at different times and then plotting the sample value as a function of sample time.This is exactly the technique used in conventional sampling oscilloscopes.As shown in Fig. 3, signal pulses are triggered from a clock at about a 60-kHz repetition rate.The clock also triggers the 150ps-wide gate current pulse through an electronically variable delay.The delay is swept to generate many sample points along the signal waveform.The sample values, represented by the current in L 2 , are read out by using a flux-locked loop around the read SQUID.This loop uses the critical current of the SQUID to sense the current in L 2 and adjusts the SQUID control current Zc,,t,,I to maintain a constant value of SQUID critical current.This technique maintains a linear readout in spite of the somewhat nonlinear SQUlD threshold curve.By plotting -Zcontrol versus the delay time, the signal waveform is reproduced.
Fig. 4(a) shows an input signal pulse with a 250-ps transition and Fig. 4(b) shows the 150-ps-wide gate pulse used to trigger the sampler.Fig. 4(c) is the equivalenttime sampler response curve showing a fall time of 300 ps, corresponding to a bandwidth of 1.2 GHz.Note that the gating pulse is not a perfect square wave.Since the sample value is averaged over the fall time of the gating pulse, the response curve will be distorted when the fall time of the gating pulse approaches the transition time of the signal waveform.Fig. 5 shows the equivalent-time response to a sinewave input, demonstrating the ability of the track-and-hold to operate at 1 GHz.Simulation of the equivalent time response using the measured circuit parameters predicts a 1.0-GHz bandwidth in good agreement with the experimental result.The signal-to-noise ratio demonstrates a 25-dB dynamic range.
Improved performance can be obtained by using a higher critical current density to reduce the size and capacitance of J I .The reduced capacitance allows J , to reset properly at higher signal slew rates thereby improving the bandwidth.For example, at a current density of 10 000 A/cm2, simulations show that the sampler can follow a full-scale sinewave up to 4 GHz.
In order to construct a multipoint transient recorder using an array of track-and-hold circuits, the track-andhold circuits must be coordinated to sample the signal waveform at successive times.This can be accomplished by gating the track-and-hold circuits with a delay-line network.One area that must be addressed is the readout and correlation of the outputs of each read SQUID needed to reconstruct the original waveform.In order to accomplish this, the suppressed critical current of each read SQUID must be translated into the corresponding loop current via the SQUID threshold curve and plotted versus the delay time of the gating pulse.
VI. CONCLUSIONS A superconducting analog track-and-hold has been analyzed and tested.The experimental circuit demonstrates a 1.2-GHz bandwidth with a dynamic range of 25 dB.These results are consistent with our circuit simulations and calculations.By fabricating a similar circuit with a higher critical current density, simulations indicate that a bandwidth of 4 GHz and a dynamic range of 35 dB should be possible.Integrating many of these track-and-hold circuits on a single chip could produce a multipoint transient recorder with a signal input bandwidth that is not currently achievable in any technology.

2 )
Since the magnetic flux stored in the loop is quantized into integer multiples of the flux quantum +o, the dynamic range of the circuit is limited by the number of U .S .Government work not protected by U.S. copyright flux quanta that can be stored in the loop.Therefore, the maximum dynamic range will be I,,,(O)(L] + L 2 + L 3 ) / O o , where Oo = 2.07 mA .pH.

[6]. 6 )
Optimum frequency response in the track mode is achieved by choosing the shunt resistance R, to critically damp the resonance formed by the capacitance CJI, of J , and the inductance L I + L,.This leads to the condition R, = d ( L , + L 2 ) / 4 C J , .