1022 IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-21, NO. 2, MARCH 1985

LOW NOISE MICROWAVE PARAMETRIC AMPLIFIER*

A. D. Smith, R. D. Sandell, J. F. Burch, and A. H. Silver TRW Space & Technology Group

One Space Park, Redondo Beach, CA 90278

Summary

We report the lowest noise temperature of any microwave amplifier except the maser. This amplifier is a nearly degenerate superconducting ,parametric amplifier at X-band consisting of a low B , thin film, single junction SQUID, a monolithic 50Q to 1 R impedance matching network, and a cooled circulator. Nb/Nb 0 /Pb alloy junctions were incorporated into Nb and P6-?n circuitry on 1 x 2 cm silicon chips. The SQUID was phase-biased near 90' and driven by an external pump at approximately twice the operating frequency. The self-resonance frequency of the SQUID inductance and junction capacitance was set at the operating frequency of 8.2GHz. The operating charac teristics depended on the pump amplitude, the junction phase bias, and the SQUID parameters. For small values of B < 1, the maximum gain in both the signal and idler channels was = IOdB, the bandwidth 1 170MHz, and the single-sideband noise temperature was 6K with an uncertainty of (+I 5 to -7)K. For higher B , the gain increased to nearly 30dB with increased noise and parametric oscillations occurring near the pump subharmonic frequency.

Introduction

Microwave/millimeter-wave detection and analog signal processing are potential applications for superconductive electronics utilizing quasiparticle detectors, superconductive amplifiers, local oscillators, pumps, dispersive delay lines, convolvers, and correlators integrated in monolithic thin film structures. For most of the last decade, the major effort in superconductive electronics has centered on the development of digital logic systems. Considerably less investment has led to the development of quantum-noise-limited quasiparticle detectors, low noise amplifiers, and analog signal processing devices. We have demonstrated low noise microwave parametric amplifiers for such applications

junctions imbedded in a single junction, or rf, SQUID. ' utilizing the parametric inductance of Josephson

This paper presents a brief history of Josephson parametric amplifiers followed by the design, fabri cation parameters, and the experimental performance of a nearly degenerate low noise superconducting para metric amplifier at X-band. We report gain, band- width, noise, and power saturation measurements and discuss the future direction of this research. The measured noise temperture at a gain of 10dB is 6K with an uncertainty of (+15,-7)K. At large values of the SQUID B , the amplifier exhibits higher gain, parametric oscillations at the pump subharmonic, and increased noise.

The design' of this amplifier differs from others by utilizing low impedance, low inductance SQUIDS with low current density junctions. The low inductance SQUID allows high power capability while the low. junction current density provides low and large

*Supported by the Naval Research Laboratory under Contract No. NO001 4-81 -C-2495

Manuscript received September IO, 1984

capacitance to resonate with the SQUID inductance at the signal fre uency. The junction phase is current- biased near 90 and the pump signal modulates the junction over a large fraction of the phase space from 0-180'. By controlling the junction phase in a single-valued, low B SQUID, this design avoids the instabilities and noise rise of previous super- conducting amplifiers. A low circuit Q is required to achieve bandwidth and stabiliz2 the ju2ction dynamics. The design requires j = 9A/cm , 745p junctions, and 50wn line widths at 88Hz.

a

Background

Parametric amplifiers rely on a harmonically driven, nonlinear reactance to produce a low noise negative resistance reflection amplifier. Conventional paramps use the voltage-dependent capacitance of reverse-biased semiconductor diodes. Room temperature paramps do not achieve sufficiently low noise temperatures and have been replaced by transistors or by cooled varactors which achieve noise temperatures as low as 12K at L band. Such devices are not extendable to significantly higher frequencies because of parasitic losses. The maser achieves microwave noise temperatures near 3K at LHe temperatures. Higher frequency masers require large magnetic fields and high power pump sources at millimeter-wave frequencies.

Current-dependent kinetic inductance of superconducting films and of Josephson junctions have been considered as parametric amplifying devices. The Josephson phase-dependent reciprocal inductance,

where L = 2ai / @ , is cap ble of producing large Josephson amplifiers is th4 potential for self-pumping by means of the iprnal Josephson oscillations. Kanter and Silver used a point contact SQUID to produce a low noise internally pumped parametric amplifier at 3OMHz, and Kanter3 reported similar operation at 9GHz with a point contact in a reduced height waveguide cavity. These devices suffered from noise saturation, poor coupling to the resonant circuit, and, in the latter case, from large values of the SQUID B and poor control of the microwave impedance. In most circuits studied, the junction phase did not vary uniformly with time and one Id not

When the critical current is reached, most juhtions switch to the voltage state or to an arbitrary phase with response times dependent on the frequency- dependent damping. A significant body of work which was devoted to developing Josephson amplifiers has been rev'ewed by Richards' at IC ,SQUID 1976 and Pedersen' at IC SQUID 1980. Most: of these devices were beset by problems including impedance mismatch, low saturation power, small bandwidth, gain dependent noise, and operational instabilities. Since that time, there has been further development of both internally and externally pumped Josephson parametric amplifiers. I

-1 fractiogal variagiogs in L.- B . A unique attraction of

produce a nearly harmonic time-variation of L.- 9. .

The externally pumped monolithic thjn'film SQUID and SQUID array amplifiers were proposed as an approach to eliminate these problems. The Chalmers

0018-9464/85/0300-1022$01.00@1985 IEEE

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group rep~rted"~ low noise performance of internally pumped amplifiers which were similar to resistive SQUIDS. We have now demonstrated low noise parametric amplification with B < 1 rf SQUIDs for which the total SQUID parametric inductance varies as

L = L-Ql + BCOSO), -1 (2) P where L is the SQUID inductance and B = Lo/L.. For such devices, the phase is single valued andjvaries smoothly over the full period.

Parametric amplifiers have a number of different operating modes represented by the relative frequencies of the signal; pump, and idlers. The pump is the power source for eventual amplification of the signal. Because of the nonlinearities in the device, all sum and difference frequencies of the signal and pump are generated. Those spurs which are important to the device performance are referred to as idlers. The most common mode of operation is the single idler amplifier, where

f. = f - fs. 1 P Typically the pump frequency is approximately twice the signal frequency, so that the signal and idler frequencies are nearly degenerate and have the same impedance termination. Other principal idlers are near zero and 2f , and can be terminated in either open or short ciycuits. The amplifier discussed in this paper is of the single idler, nearly degenerate type. This amplifier requires a dc phase bias in order to break the even symmetry of the inductance- pump current dependence. On the other hand, the unbiased Josephson junction retains even inductance but operates in the doubly degenerate mode where f * f f f.. The latter design wgs first iRvestf'gate4 by the Berkeley group .

Amplifier Design

The amplifier design is based on that of Silver, et a1 and has the following req-yirements: (a) the junction phase and therefore L. is a smoothly varying, single-valuTd functiod of the current, (b) the variation of L. approaches 2L , (c) the circuit responds at the siinal frequency an8 has a low Q, and (d) the circuit has a low impedance and a matching network to a conventional 500 microwave connector. In

I I 4 - 2 0 1 2 4 6 8 0 n 2ir 8,

INDUCTANCE u L n - 2 2

- Figure 1. Graph of the SQUID phase (0) versus current (0 ) (top,right) and SQUID inductance L versus O and OxXfor a low B SQUID shown in the lowerPleft.

order to satisfy (a) and (b) , we use a single junction SQv;FD with B ( 1 . Figure 1 shows the variation of L. as a function of both o and source current I for B J = 1 and T. The equation of motion of this SQUID representyd by the circuit of Fig. 1 is, in dimension- less form , 0 t n0 t Bsin'Ot 0 = E(t), ( 4 ) .. "

where the coefficients are n=R-' AT, E=BI/i , and time is measured in ~ 6 . This equation is dentical to that for a damped junction except for the addition of the term linear in 0 which represents the flux in the inductance. Since the homogenous response is measured in terms of the resonance frequency of the SQUID L and the junction capacitance C, we tune the resonance to the center of the signal frequency band, f , where,the impedance is R and the damping parameter qsis the inverse Q.

The inductance L is chosen to maximize power handling capability and noise immunity within the bounds of reasonable impedances. The device functions by the manipulation of a fraction of $ in the SQUID inductance L. Since the voltages associated with this process depend only on the frequency, the power will be maximized by selecting the lowest impedance, hence the smallest L. Selection of L also deteynines the immunity to thermal noise by 3he ratio $ /23 to kT. Values of L 5pH provide ( @o /2L)/kT 8x10 and impedance near l a .

The amplifier was designed as a single junction SQUID whose inductance is a section of 1 0 super- conducting microstripline. The monolithic I 0 to 500 thin film transformer connects to the SQUID with a I n stripline. The transformer output is a 50um, 500 coplanar line which is then expanded to the dimensions of an SMA connector as shown in Fig. 2. The entire assembly is connected to a LHe cooled coaxial circulator with semirigid coax.

Operation of the singly degenerate reflection amplifier requires both a microwave pump signal at ~ 2 f and a dc hase bias. The junction phase is biaged near 90 and the pump garies the phase over a large portion of the 2; - 180 region producing a large variation in L for B 5 1. Operation with zero phase bias woul8 be analogous to the doubly degenerate mode. Operation at 90' bias destroys the even symmetry and produces the largest component of odd symmetry in the parametric susceptance.

8

SQUID Diagnostics

The parametric amplifier response was, influenced by i , pump power and frequency, signal power and freqaency, and de control current. The output was observed on a spectrum analyzer (SA) for various values of'these parameters. The design requires low current density junctions to achieve the required small B and large C. By suppressing the critical current with a magnetic field, these amplifiers were

Figure 2. Photograph of the SQUID parametric amplifier chip. The signal is connected through the transformer at,the left. The pump is connected just to the right of the junction at the right side of the figure.

1024

operated with higher current density junctions than the design value. In this way, 3 was adjusted to several values for measurement of the amplifier. For single junction amplifiers, this method may be useful for tuning operational devices with on-chip control current inductors. Values of both greater and less than unity were inferred, and we were able to distinguish significant differences in the device operation.

The effect of the magnetic field suppression of the critical current in the SgUID parametric amplifier can be calculated directly from the field dependence of the Josephson inductance. Parametric amplification results from the phase-dependent inductance of the SQUID, Eq. (2). When a magnetic field is applied to a junction, 0 becomes a function of position across the junction. For a small junction in a uniform magnetic field, the resultant inductance becomes

where = @sin(X)/X, X = ( n @ / @ ) , C is the spatial average junction phase, and ig the'magnetic flux in the junction. For junctions small compared with the Jcsephson length, the flux in the junction is nearly equal to the applied f1u.x coupled to the junction. Equ-ation ( 5 ) has the same form as Eq. (2) except that 8' varies by the same sin(X)/X factor as the junction critical current. For large current suppression factors, such as that used here, a magnetic vortex is essentially situated on the junction.

With the single junction or rf SQUIDS required for these amplifiers, there is no direct measurement of the junction critical current. Although test junctions on the sides of the chip were monitored during magnetic field adjustment, one cannot quantitatively specify (or measure) the value of B because of both the field and j7jnction nonuniform- ities. Values of B were estimated from the observed amplifier characteristics and from independent measurements of the microwave reflectance as described below.

The oniy diagnostic test available to characterize the SQUID, except for the amplifier performance itself, is the microwave reflectance. In the mail signal limlt we assume the unpumped SQUID to be a linear LCR circuit, where the inductance at any control current C is given by Eq. (5) where e is a function of e . The SQUID load admittance Y = G t iB xis connected to a transformer which represents a source admittance Y = GS + iBS. The mismatch reflectivity of the SQUTD is L L L

We can express the reflectivity directly in terms of the source and load resistances, R and RL, the resonance frequency f , Q, 0 , and d where the source admittance is presume8 to be real. At a fixed frequency f, the quantities in REFL. are constant except for BL which depends on C and hence 3 . This variation for a strongly coupled SQUID is uderstood to be the result of the large variation of the SQUID resonance frequency f with 0,. Minimum reflectivity occurs at B = -E = 8. For a real source admittance the minimum occur8 when the test frequency is equal to the resonance frequency of the SQUID circuit.

B

L

In the amplifier circuit, the SQUID is integral to the resonant ci-rcuit (unity coupling) and the resonance frequency varies over a very wide range from

zero to [ltl+~f,'LC]-~'~. Comparison of the observed dependence of the reflected power on 0 with the analytical predictions, as shown in Fi2. 3, provides information on the SQUID parqmeters 9 . For sufficiently small frequencies and B, B is always positive and the SQUID frequency is always greater than test frequency; the reflected power has one minimum per cycle at 0 = IT. For higher frequencies or larger 8, B passesXthrough zero and the reflected power has two mlnlma per cycle of 0

L

L. . X'

The minimum reflectivity provides a direct measure of the match between the source and the SQUID damping resistance. A major contribution to the damping at the junction is the low voltage quasi- particle conductance of the junction because of the higher conductance of the junction compared with the design'value. Measured zero-voltage resistances of test junctions on the same chip were several ohms. From t'ne measured microwave reflectance minimum of -4dB, the mismatch resistance ratio at resonance is calculated as f 1.5. Assuming a perfect transformer, the effective damping impedance is either 1.5nor .67Q. This value remains ambiguous because of the quadratic root.

Microwave Probe

The experiments were carried out with a semirigid coaxial cable and a cooled X-band coaxial circulator. All coaxial lines were dc-connected at only one point to prevent both ground loops and thermal currents between the cold and warm ends. D.c. blocks-were used

-I U w K

P - o . 5 , ~ = 2 1 I I 0 11 2s

0,

7.9 GHz 5 -1OdB PC

0 211

-1 8 5 GHz

k -1OdB IT:

0

Figure 3. Comparison of the computed (top) and measured microwave reflectivity (bottom) of the SQUID for different frequencies.

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for all microwave cables. Both the signal and pump lines were decoupled from room temperature noise by 20 o r 30dB attenuators cooled to 4K. The coaxial circulator did not produce a measurable leakage magnetic field. In order to minimize the circulator stray field, the paramp chip was isolated from the circulator by a 5cm long coaxial line. No effect of the circulator field was observed. All de lines into the probe were filtered to reduce RFI.

A small persistent superconducting coil was placed around the amplifier chip with the field orientation parallel to the surface of the substrate and the SQUID microstrip in order to control i (and hence B ) with minimum flux coupling to the SQUPD inductance. Field-induced depression of the critical current was monitored using test junctions on the edge of the chip. This permitted variation of 6 for any paramp chip. Because the magnet is operated in the persistent mode, there is no measurable noise from field instability. In fact, the persistent mode magnet probably serves as an additional magnetic shield.

Experimental Method

Paramp power gain was measured in a two-step process. First, the input power, line losses , and GaAsFET amplifier gain were calibrated by applying a small fixed input signal to the SQUID. With no pump power and zero phase, the SQUID is a nearly perfect reflector of very small signals and is nearly ideal for calibration purposes. After the detected output power level is noted, the pump is turned on and the de phase adjusted for maximum output signal. The increase in output power constitutes the parametric amplifier gain.

Noise temperature measurements were made by recording the corresponding rise in the background noise floor with amplifier gain. Noise level measurements were difficult because of the extremely small noise contribution from the SQUID amplifier, especially compared with the noise of the following lllow noise" GaAsFET amplifier and SA. Line losses and amplifier gains from the paramp to the spectrum analyzer were measured component by component. A calibration factor for paramp output power relative to observed spectrum analyzer power was obtained. As before, the noise level was determined in a two-step process. The SA was set at a frequency removed from the signal frequency but well within the response

KLYSTRON CMAs F ET AMPLIFIER-

SPECTRUM ANALYZER

COLD 4 1 ATTENUATOR

CIRCULATOR I .. . . -

SQUID AMPLIFIER

KLYSTRON 116 - 18 G H d

Figure 4. Block digram of the experimental microwave arrangement for measuring the SQUID amplifier.

bandwidth. A set of measurements with the amplifier off determined the baseline noise which was due mainly to the GaAsFET amplifier. A second set of measurements with the amplifier on determined the total system noise. The difference in noise levels represents the paramp noise. This was converted to the input noise measurement by dividing by the previously measured paramp gain and subtracting the known residual blackbody noise in the input channel.

Figure 4 shows a block diagram of the experimental arrangement for measuring amplifier performance. A klystron.supplied a stable X-band signal to the SQUID through a cooled 30dB attenuator and circulator. The attenuator reduced room temperature blackbody noise by 30dB, effectively eliminating this wide band "signal". The reflected signal was circulated to a room tempera.ture GaAsFET low noise amplifier before being supplied to a spectrum analyzer for power spectrum measurement. Operation of the SQUID amplifier was controlled by adjusting the applied pump frequency and power, the SQUID de phase control current, the junction critical current (i.e., B ) , and the signal power and frequency. The pump signal was supplied from a second klystron at approximately twice the signal frequency through a cold attenuator and an intentional 50:l impedance mismatch.

Amplifier Response

The a lifier performed qualitatively as expected' "* with variation in B , control current (i.e., average junction phase), and pump power. As indicated above, the noise was sufficiently low that it was very difficult to measure for low B where the gain was near 10db. For B > 1 , the noise increased with the higher gain developed and strong subharmonic oscillations and noise floor increases were observed with high values of pump power.

Figure 5 shows a typical small signal amplifier response observed on the spectrum analyzer. The lower curve is the SA record with an applied signal on the order of IpW at 8.42GHz with the paramp off; the upper curve was obtained with the pump on (+4dBm measured at the pump klystron in this case) and the SQUID phase adjusted for maximum gain. The signal gain is 10.9dB and an idler appears at f - f with gain 10.5dB relative to the input signal? Insthis case the noise floor increased by 1 0.2dB when the amplifier gain is turned on, representing amplification of the background input noise.

The observed yyar levels were consistent with the proposed model of thqamplifier. The pump

-50 1 -60 t SIGNAL IDLER

FREQUENCY i - 4 0.5 MHz

Figure 5 . Small signai response of the SQUID parametric amplifier. The lower curve is the applied signal; the upper-curve, including the idler, is the amplified response. The linewidth is determined by the SA bandwidth.

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power at the SQUID is difficult to quantify because of the intentional, but uncalibrated, mismatches in the pump feed line. Pump power required for typical 10dB gain varied over more than 10dB for different values of B.

Figure 6 shows the response for a higher B case as a fudction of the signal power. With the small signal gain set at 17dB, the (nearly) symmetric spectrum shows nonlinear increase in the amplified signal and idler as well as the appearance of higher order frequency components at higher power. The shifts in the main signal and idler peaks at high power were the result of frequency drift in the klystrons. Each successive trace represents a 5dB increase in input signal power. Some of the nonharmonic structure results from pickup and subsequent upconversion amplification of extraneous rf signals. Figure 7 shows the output signal power as a function of the input power. The 3dB compression point is :: -80dBm referred !pl8he output, consistent with the previous estimates .

Figure 8 shows typical observed bandwidths of the amplifier for both low gain (IldB) and high gain (22dB). In the low gain case, the pump subharmonic frequency was equal to the passive circuit resonance frequency (8.42GHz) and the gain curve was well- behaved with a bandwidth = 170MHz. In the high gain case, parametric oscillations were observed at the pump subharmonic for high values of the pump power. The pump subharmonic frequency was offset by 220MHz to 8.2GHz and the response was double peaked. The signal gain maxima occurred when either the signal or idler frequencies were within the circuit resonance. The

.- 5 dB INCREASE0 POWER PER SWEEP GAIN = 17.1 dB

-80

dBm -90

-100

I 4 0.5 MHz

Figure 6. Response at the signal and idler of a high gain SQUID amplifier for increasing input signal power.

-70 - GAIN =,17.1 dB'

-80-

- E 4 40- !i

6 0

-100 -

INTERMODULATION PRODUCT

-1lOt- I I I I -1 20 -100

POWER I N (darn)

Figure 7. Graph of the power dependence of the high gain SQUID amplifier showing both the signal and first nonlinear term.

m 9 2 a 0

-

gain was higher and more sharply peaked when.the signal was within the resonance bandwidth. The lower gain case in Fig. 8 represents the conditions for which we measured the smallest noise temperature. This bandwidth is smTller than the 840MHz bandwidth originally predicted . One exppnation is that the amplifier figure-of-merit, GxBW , is reduced because B was <I. For the high current density junctions used for these experiments, the proper operating point was on a very steep portion of the i versus field curve and it was difficult to establisfi B = 1 . Another possibility is that Q was too large. This cannot be resolved without performing curve fitting to measure both Band Q.

Noise Temperature Table 1 shows the measured values of the signal,

idler, and baseline noise levels for the parametric amplifier at 8.2GHz. All power levels are referenced to the SA. A -91.OdBm correction was subtracted from the measured values in order to adjust for baseline noise levels. The signal gain was observed to be 1 greater than the idler gain, as expected f o r a well- coupled SQUID.

TABLE 1 SQUID PARAMP POWER LEWEXS AT 8.2 GHZ -------

Measured Corrected For -- Level (dBm) Baseline Noise

Pumped Signal -73.9 Pumped Idler

-74.0 -74.2 -7L. 3

Unpumped Signal -83.5 -84.3 Pumped Baseline -90.8 -104.3 Unpumped Baseline -91.0 Signal Gain = 10.3 dB = 10.7 Idler Gain = 10.0 dB = 10.0

Table 2 shows the analysis of the noise

--

-- ---

temperature of the amplifier. Turning on the amplifier raised the baseline measured at the SA by

-

20 -

-

10 ,-

0

0 - 7.8

I I I I 8.0 8.2 8 A 8.6 I

FREQUENCY (GHzl

Figure 8. Frequency-dependent response of the SQUID amplifier. The lower curve was obtained at low gain with the pump subharmonic at the SQUID resonance; the upper curve at high gain and the pump detuned as shown.

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TABLE 2 Future Directions NOISE TEMI?EXAm ANALYSIS

..

- Noise detected -104.3 dBm Bandwidth (0.1 MHz) +10.0 GaAsFET Amp. Gain -26;9 Warm Cable LOSS +I .7 Cold Cable Loss +2.0 Circulator LOSS - +0.9 Excess Output Noise

With Pump -1 16.9 dBm/MHz =I 60 K Blackbody Level (SSB) - + 4 . 5 g Total Output Noise -1 16.5 dBm/MHz 164.5K Paramp Gain -10.3 dB

-126.8 dBm/MHz = 15 K Blackbody Level (DSB) - -9 I( Noise Temperature 6 K N o i s e Uncertainty (+15/-7) K

--

-104.3dBm over the 0.1MHz SA bandwidth. The observed noise level was corrected for amplifier gain and cable loss, resulting in -116.6dBm noise level referred to the amplifier output. We calculated a total noise rise of 160K above the unamplified case. The unpumped baseline consists of blackbody radiation of 4.2K from the cold attenuator with an additional 0.3K (300K - 3OdB) leakage through the attenuator. This produced a total estimate of the output noise of 164.5K.

The amplifier referenced-to-input noise level was obtained by normalizing the output noise by the signal channel gain, leaving 15K. We attribute 9K of this amount to attenuator and feedthrough noise from the signal and idler channels. The best value of the amplifier input noise temperature TN was determined to be

TN (SSB) = 6K (+15/-7)K.

for a signal gain = 10.3dB and idler gain = 10.0dB. The uncertainty in the noise temperature estimate is largely from uncertainty in the measurement of the baseline noise rise. In the low noise condition, the pump subharmonic oscillation and-baseline noise rise did not appear. In another case with higher 6 and gain = 17dB, the measured SSB noise temperature was 34K *

PblnAu

Figurfio9. Equivalent circuit and drawing of the SQUID array . The structure shows the coupling of alternate single junction SQUIDS. Damping resistors are not shown. . .

. .

The future directions for this research will be to improve the accuracy of the noise temperature measurements, increase the gain and dynamic range, increase both the instantaneous bandwidth and operating frequency, and incorporate this device in a monolithic system.

Work is in progress to lower the total measurement.system noise and thereby decrease paramp noise uncertainties. This will consist of a second SQUID paramp stage followed by a cooled low noise GaAsFET amplifier. We expect to achieve greater bandwidth by reducing the Josephson current density near the design value in order to make it easier to achieve 6 = 1. Also improvement in data acquisition will make it possible to carry out a curve fitting process to measure B and n in order to optimize the amplifier figure-of-merit.

Greater saturation power and dynamic range should be achieved by arraying simi+aSosingle junction SQUIDs as proposed by Silver, et a1 ' . The equivalent circuit for this array is shown in Fig. 9 along with a sketch of an integrated circuit implementation. We have carried out a full design for both 50 and 100 element arrays which have a design impedance of 5051 and are directly connected to a monolithic 5051 coplanar waveguide. Figure 10 is a photograph of a portion of one such array. Critical currents within 10% of the design value may be required to properly operate these devices. Dynamic range is expected'to increase by 50-100 over the single device because of the increasyllaower with no increase in noise temperature .

The design parameters for the SQUID parametric amplifier are suffickently easy to accommodate that extension to higher frequencies poses no real fabrication problems. Assuming that the flux quantum energy, and hence the inductance, remains constant, the junction area is reduced (and the current density increased) by. the square of the frequency ra3io. Thus at 90GHz the curren2 density becomes 900A/cm and the junction area 7.5vm ; the 50Um linewidths will be reduced to 5~m. The major new problems will be those of microwave coupling since coaxial cable connectors are no longer feasible at this frequency. One does not expect the noise todincrease significantly at SOGHz, indicating that one can produce a quantum- noise-limited. amplifier. On the other hand, saturation power should increase by a factor of 10 because of the increased frequency.

Figure IO. Photograph of a "section of a 50 element SQUID array as, sketched in Fig. 9. Damping resistors are on the outside of the alternating junction array.

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1.

2.

3.

4.

5.

References

A.H. Silver, D.C. Pridmore-Brown, R.D. Sandell, and J.P. Hurrell, "Parametric Properties of SQUID Lattice Arrays", IEEE Trans. Magn., Vol. MAG-17, pp.412-415 (I981 ).

H. Kanter and A.H. Silver, "Self-Pumped Josephson Parametric AmplificationIf, Appl. Phys. Lett., Vol. 19, pp.515-517 (1971). H. Kanter and A.H. Silver, 'IResponse of the Self-Driven, Weakly Connected Superconducting Ring (ac-SQUID)", IEEE Pub. No. 72CH0682-5-TABSC, PP-592-596 (1972).

H. Kanter, llTwo-Idler Parametric Amplification With Josephson Junctions", J. Appl. Phys., Vol. 46, pp.4018-4025 (1975). H. Kanter, IIParametric Amplification With Self-pumped Josephson Josephson junctions11, IEEE Trans Magn., Vol. MAG-11, pp.789-793 (1975).

P.L. Richards, "Superconducting Devices for Millimeter and Submillimeter Wavelengths", SQUID Superconducting Quantum Interference Devices and Their Applications", Ed. by H.D. Hallbohm and H. Lubbig, Walter de Gruyter, Berlin pp.323-338 (1977).

N.F. Pedersen, I'RF Applications of Superconducting Tunneling Devices", SQUID 80 Superconducting Quantum Interference Devices and Their Applicationsr1, Ed. by H.D. Hallbohm and H. Lubbig, Walter de Gruyter, Berlin pp.739-762 (1980).

6. N. Calander, T. Claeson, and S. Rudner, llLow-Noise Self Pumped Josephson Tunnel Junction Amplifier", Appl. Phys. Lett., Vol. 39, pp.650-652 (1981 ) .

7. N. Calander, T. Claeson, and S. Rudner, "Shunted Josephson Tunnel Junctions: High Frequency, Self Pumped Low Noise Amplifiers", J. Appl. Phys., Vol. 53, pp.5093-5103 (1982) -

8. P.T. Parrish and R.Y. Chiao, llAmplification of Microwaves by Superconducting Microbridges in a Four-Wave Parametric Mode", Appl. Phys. Lett., Vol. 25, pp.627-629 (1 974). R.Y. Chiao and P.T. Parrish, lIParametric Amplification by Unbiased Josephson junctions", J. Appl. Phys., Vol. 46, pp.4031-4042 (1975). M.J. Feldman, P.T. Parrish, and R.Y. Chiao, llOperation of the Suparamp at 33GHz", J. Appl. Phys., Vol. 47, pp.2639-2644 (19'76).

9. A.D. Smith, R.D. Sandell, J.F. Burch, and A.H. Silver, to be published.

IO. A.H. Silver and R.D. Sandell, SQUID Parametric Amplifier", IEEE Trans. Magn., Vol. MAG-19, pp.622-624 (1983).