AD-AT27 269 DEMONSTRATION OF SQUID (SUPERCONDUCTING QUANTUM IINTERFERENCE DEVICE) PARA. (U) TRW SPACE AND TECHNOLOGYGROUP REDONDO BEACH CA APPLIED TECHN.. A H SILVER

UNCLASSIFIED NOV 82 N000 4-81-C-2495 F/G 9/5 NL

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NATIONAL SLRAL (4 F AN['AF['L I ,4

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TRW Space& Tchnology One Space ParkGmp Redondo Beach, CA 90278

213 535 4321

ANNUAL PROGRESS REPORT

TO THE

NAVAL RESEARCH LABORATORYCODE 6854

,~ .4555 OVERLOOK AVE., S.W.WASHINGTON, DC 20375

ON(

DEMONSTRATION OFSQUID PARAMETRIC AMPLIFIER

CONTRACT NO. N00014-81-C-2495SEPTEMBER 1981 - SEPTEMBER 1982

PREPARED BY

A.H. SILVERADVANCED PRODUCTS LABORATORYAPPLIED TECHNOLOGY DIVISION

TRW

NOVEMBER 1982

83 04 26 014

ARW Inc

-"b. .

(Illi m

TRW Inc. One Space ParkLw tronics & Redondo Beach, CA 90278

,efense Sector 213 535 4321

ANNUAL PROGRESS REPORT

TO THEJ h, ,Li ----

I COPY NAVAL RESEARCH LABORATORYINSPECTM CODE 6854

24555 OVERLOOK AVE., S.W.

WASHINGTON, DC 20375

ON

DEMONSTRATION OF " VgSQUID PARAMETRIC AMPLIFIER

CONTRACT NO. NOO014-81-C-2495SEPTEMBER 1981 - SEPTEMBER 1982 I.-

PREPARED BY

A.H. SILVER

ADVANCED PRODUCTS LABORATORY

APPLIED TECHNOLOGY DIVISION

TRW

NOVEMBER 1982

-mN

IINCLASSTFT FnSECURITY CLASSIFICATION OF THIS PAGE (mien Data Entered)_

READ INSTRUCTIONSREPORT DOCUMENTATION PAGE READ____NSTRU__TIONS _R PBEFORE COMPLETING FORM

I. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtite) S. TYPE OF REPORT & PERIOD COVERED

Annual ReportDemonstration of SQUID Parametric Amplifier Sept. 1981 to Sept. 1982

6. PERFORMING OG. REPORT NUMBER

7. AUTHOR(s) S. CONTRACT OR GRANT NUMBER(s)

A. H. Silver N00014-81-C-2495

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK

Advanced Products Laboratory 'REA S WORK UNIT NUMBERS

TRW Space and Technology Group P.E.62762N

One Space Park, Redondo Beach, CA 90278 XF 62-584-004

I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATENaval Research Laboratory, Code 6854 November 19824555 Overlook Avenue SW 13. NUMBER OF PAGES

Washington DC 20375 3214. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified

1Sa. DECLASSIFICATION DOWNGRADINGSCHEDULE N/A

16. DISTRIBUTION STATEMENT (of this Report)

Approved for Public ReleaseUnlimited Distribution

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20. if different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

Parametric amplifier, low noise amplifier, microwave amplifier, Josephsonjunction, SQUID, array, monolithic superconducting transformer. 1 (. %. )\

A.V

ABSTRACT (Continue on reverse side If neceeery and Identify by block number)This is the first Annual Report of an effort to demonstrate a low noisesuperconducting microwave amplifier. The amplifier is a nearly degenq4 ate,single idler parametric amplifier which uses the nonlinear inductanc7'of asingle junction SQUID (Superconducting QUantum Interference Device)i Thedesign frequency is 9 GHz, 10 dB gain, and 16% bandwidth. In orde to maxi-mize the saturation power, the device impedance was chosen near Iand amatching network was designed to transform to 50S2, In later designs, a-.

DD ,o 1473 EDITION OF NOVSSISOSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF TIS PAGE (m"en Data Entered)

* 2arAImtm~,~.. - .-

TABLE OF CONTENTS

Page

1. Introduction...............................

2. Work Plan.....................................2

3. Progress......................................3

3.1 Transformer Design.......................3

3.2 SQUID Amplifier.........................10

3.3 Fabrication ............................. 15

3.4 Analysis................................20

3.5 Measurements............................22

4. Conclusions..................................23

Appendix A ................................... 24

Distribution List............................. 27

UNCLASSIFIEDS CURITY CLASSIFICATION OF THIS PAGE(Whe Date Ented)

20. continued

K-coherent array of SQUIDs is expected to increase the power and impedance.This report includes the design and test of the 5012 to 111 broadband transfor-mer, design and fabrication of the SQUID amplifier, and both saturation and

noise analyses of the single SQUID and SQUID array. The analytical results,reported to the 1982 Applied Superconductivity Conference are: the noisetemperature of the single SQUID parametric amplifier is equal to the ampli-fier termination temperature 'J, the response is linear to several percentof the flux quantum energy in the SQUID: the amplifier will he saturated bybroad band noise if the noise source temperature is much greater than 10

1o; and the array parametric amplifier has the same noise temperature asthe single device indicating an N-fold increase in dynamic range.

UNCLASSIFIEDSECURITY CLASSIFICATION OF 1u" PAG'When Doa Entered)

LIST OF FIGURES

Page

Figure I Computed VSWR of the Optimized designof the 50R to If transformer .......... 4

Figure 2 Equivalent circuit and electrical designof the 50f to lM transformer .......... 5

Figure 3 Photograph of the 50I coplanar linesused to test dimensional changes ...... 6

Figure 4 Printout of composite masks for the50 to IS2 transformers .............. 8

Figure 5 Printout of composite masks for the5011 to 1% transformer terminated inthe I) resistor at the center ......... 9

Figure 6 Photograph of transformer test chipmounted in a brass holder and connectedto two OSM bulkhead connectors ........ 11

Figure 7 Response of 50SI tapered coaxial lineson silicon substrate measured at 4K ... 12

Figure 8 Response of the double-ended 50 toIII transformers measured at 4K ........ 13

Figure 9 Layout of six masks on the two inchwafer ................................. 14

Figure 10 Composite mask layout of amplifier

SQPI .................................. 16

Figure If Expanded plot of the six compositemasks of the SQUID amplifier SQP1 ..... 17

Figure 12 Composite mask layout of amplifier

SQP2 .................................. 18

Figure 13 Expanded plot of the six compositemasks for the SQUID parametric ampli-

fier SQP2 ............................. 19

Figure 14 Photographs of the two different ampli-fier chips as fabricated on a silicon

wafer ................................. 21

ii

'II

I. INTRODUCTION

This is the Annual Progress Report for Contract No. N00014-81-C-

2495, "Demonstration of SQUID Parametric Amplifier," covering the

period from 14 September 1981 through 14 September 1982. The objectives

of this project are the development and demonstration of a low noise

SQUID microwave parametric amplifier. These objectives were met during

this year by addressing SQUID amplifier design, circuit fabrication,

measurements, and noise analysis.

II

I

2. WORK PLAN

This is a new contract for development and demonstration of a low

noise Superconducting QUantum Interference Device (SQUID) parametric

amplifier at microwave frequencies. The focus of this contract is the

investigation and demonstration of a SQUID negative resistance amplifier

at X-band. A SQUID array is then projected to increase the available

power and operating impedance. The approach adopted utilizes monolithic

superconducting integrated circuits which were designed, fabricated, and

tested at TRW.

Three tasks were undertaken in the first year:

Task 1. Amplifier design and fabrication,

Task 2. Measurements,

Task 3. Noise analysis.

A number of the steps are very similar to those required for a contract

with the Office of Naval Research, "Application of Josephson Junction

SQUIDs and Arrays." Such steps are carried out jointly, and are reported

to both agencies. TRW is also conducting Independent Research and

Development on Advanced Josephson Devices. That research is principally

concerned with developing Josephson integrated circuit fabrication

capability. Some of the activities of that project impact on this contract

and are discussed here.

2

3. PROGRESS

3.1 Transformer Design

Since the SQUID paramp is necessarily a very low impedance device,

a suitable transformer is an essential ingredient for evaluating the

basic device, particularly with respect to available power. In order

to carry out this transformation in both impedance and dimension in a

reproducible and predictable manner, the transformer is integrated with

the active circuitry in a monolithic fashion.

The basic architecture of the transformer was presented in the

contract proposal. We have refined the design for the TRW fabrication

process and reconsidered the problems of launching from 50Q coaxial

cable into 50 coplanar line, dimensional step from I mm coplanar line

at 500, and construction of capacitors in the lumped element impedance

transformer. The electrical design was optimized numerically using

COMPACT with a computed VSWR < 1.25 over the 8-12 GHz band (Figure 1).

Figure 2 shows the equivalent electrical circuit and the geometrical

layout.

A test of the effect of changing dimensions in 50 coplanar line

was performed by fabricating three 502 transmission lines: a continuous

coplanar line at mm dimensions, a sharply stepped coplanar line, and a

short, tapered transition as shown in Figure 3. The measured performance

showed no significant differences between the three lines. Therefore,

the input LC circuit in the transformer intended to tune out the inductance

of the step in the coplanar line was deleted.

The transformer was designed to be fabricated on a 2 inch silicon

wafer 0.015 in. thick with a minimum line width of 50Pm. An OSM micro-

wave launcher drives the 50 coplanar line which has a center conductor

width equal to 1.3 mm, a ground plane spacing of 0.4 mm, and an effective

dielectric constant of 4.4. The coplanar line is tapered at 50SI to a

center conductor width of 5OPm, ground plane spacing of 30Pm, and an

effective dielectric constant of 6.4. The reduction in c and its

3

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dependence on linewidth results from the finite thickness of the Si

substrate. The 1 microstrip in the transformer is 50pm wide and

separated from the Nb ground plane by 50nm Nb205 and 200 nm SiO.

It has an effective E=13.

The transformer design incorporates short (<./4) sections of co-

planar and microstrip lines which act as lumped inductors and capacitors,

respectively. The inductive lines are 50,' coplanar lines terminated by

I.. microstrip, with L Z0 /v, where Z. is the line impedance, K the line

length, and v the propagation velocity. Capacitors are 1- and 0.52

microstrip either terminated by 50Q coplanar or used as open parallel

stubs. The capacitance of short, open lines is given by C=Z/Zov.

Photolithographic patterns were defined as 4-level masks and pro-

duced at the TRW Microelectronics Center for the combined dimensional

and impedance transformer. For the dimensions and tolerances required,

masks were fabricated directly at the reticle level in an Electromask

pattern generator. Figure 4 shows the computer-generated composite of

three I cm x 2 cm chips which will be fabricated on 2" silicon wafers,

.015" thick. Each chip has 2 coplanar inputs with tapered lines. On

one chip the reduced width coplanar line couples directly through; on

the second chip, transformers from each end are connected for in-out

transmission measurements. The third chip has each coplanar line and

transformer terminated with a matched resistive load. Figure 5 is an

expanded plot of the transformer and terminating resistor on the third

chip.

The transformers were fabricated in a I cm x 2 cm format on 2"

diameter silicon wafers with an insulating SiO2 surface. Three test

chips are produced on each wafer. Following fabrication, the wafer

was cleaved with a modified Tempress scriber and the chips mounted in

a holder suitable for connection to an OSM coaxial bulkhead launcher.

Measurements are made at T=4K with an HP-8410 Network Analyzes. The

data are in the form of the scattering matrix coefficients Sll and S 12

Only the magnitude of S is reported since the phase is difficult to

calibrate with long coaxial lines into the helium dewar.

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The test transformer chips are mounted with a coaxial connector

at each end as shown in Figure 6. As anticipated, connecting the

coplanar input to the bulkhead connector was a significant problem.

An acceptable solution is to use In solder to connect gold ribbon from

the connector center pin to the bulkhead to the coplanar lines. To

facilitate soldering to the Nb film, a gold film is evaporated over the

Nb. This is done before the Nb is patterned. Figure 7 shows the

response of the simple tapered coplanar lines at 4 kelvin; Figure 8, the

response of the double-ended transformer, in which the 50Q2 coplanar line

is transformed to IQ microstrip at the center of the chip, and then

transformed back to 500 coplanar at the other end of the chip. We have

not measured good S-parameter characteristics with the terminated trans-

formers and we attribute this to a problem in making good contact with

the resistors.

3.2 SQUID Amplifier

The first phase parametric amplifier is an rf SQUID biased at a

phase of r/2 across the junction and driven by an 18GHz pump. The SQUID

was designed to utilize the Nb/Nb 205/PbBi junctions used at TRW. The

source impedance derived by /U7/ is set at O.3Q such that the IQ trans-

former load will result in Q=3. The design valuc>, are selected by

setting the flux quantum energy = 10 4kT, producing:

L = 5pH

C = 65pF

0 =1I

ic = 67 2A

jo = 9A/cm2

Area = 50 urm x 14.9 um = 745 um2

Masks were produced at the TRW Microelectronics Center using an

Applicon computer-aided-drafting system and an Electromask Pattern

Generator. With the 50Pm linewidths required, masks were produced

directly at the reticle. Four amplifier chips were placed on each 2"

diameter silicon wafer (1 crp x 2 cm format), encompassing two different

amplifier configurations. Figure 9 is a computer generated composite

10

__ _ _ _ ____ __ __ __ _

FIGURE 6. Photograph of transformer test chip mounted in abrass holder and connected to two OSM bulkhead connectors.The tapered coplanar lines at each end are visible in thephotograph. The grey rectangle in the center of the chipis anodized Nb covered with SiO. The transformers are loca-ted in the same rectangle but are not clearly visible in thephotograph.

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Figure . Response of the double-ended 502 to li, transformecrs(ltmeasured at 4K. The upper graph is S 11 (and S 2 2 )1 the lovp I 'is S22 .

13

F :D -c-- IT -__________

FIGURE 9. Layout of six masks on the two inch wafer. The uppertwo chips are amplifiers referred to as SQP1; the lower two chipsare amplifiers SQP2.

i4.

of the multi-level mask set for the four-chip layout. Each chip contains

two coplanar line inputs along the center line, and test junctions at the

top and bottom of the chip.

Two different configurations of the amplifier were designed, SQP I

and SQP 2. Figure 10 shows the enlarged layout of SQP 1. The transformer

input to the SQUID is at the left; the pump input at the right. Figure 11

is an expanded plot of the six masks at the center of the chip, showing

the impedance matched signal line at the left and mismatched pump line at

the right. Both the microwave pump signal and the dc phase bias will be

supplied by the coaxially fed pump line.

Figure 12 shows the layout of SQP 2. This chip is symmetric with

two matching transformers (50Q to 1Q) connected symmetrically to the SQUID.

The SQUID shown in Figure 13 is two inductive sections in parallel across

the IQ microstripline. Since these inductors are the same as that of SQP

1, there is a reduction of L by a factor of two. To retain the same value

of B(=l) and resonance frequency, the junction area and hence ic and C

are doubled. Also the Q is unchanged in this configuration. In this

configuration we can operate the device as a transmission amplifier with

a 3dB loss in gain. The pump signal is injected in one of the transformer

inputs with a subsequent mismatch.

3.3 Fabrication

The amplifiers were fabricated on 2" silicon wafers using Nb/Nb2 0 3/PbBi

junctions and PbIn interconnect lines. Nb films deposited with our S-gun

system exhibit Tc>9K and a residual resistance ratio =4. The junctions

were fabricated by reactive-ion-oxidation followed by thermal PbBi

deposition in the same vacuum system.

Significant problems with contact resistance and junction quality

were encountered after the change from sapphire to silicon substrates.

This was done to permit multi-chip fabrication and to eliminate photo-

resist exposure problems at the edges of the substrate. Since silicon

is more fragile than sapphire, samples were held in place in the vacuum

system with vacuum grease rather than rigid clamping brackets for heat

sinking and mechanical support. This tends to contaminate the front

15

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surface in the lift-off process following deposition. We have been

successful at cleaning with hot xylene prior to the acetone lift-off,

but a better solution is still being sought.

In addition, the lack of in vacuo surface cleaning just prior to

deposition was judged to be another source of contamination. This was

demonstrated by carrying out other depositions in the ion gun system.

However, this approach is not a satisfactory solution since the vacuum

system is not equipped for multiple component depositions, and the

deposition of other than PbBi films contaminates the vacuum system for

junction formation. Consequently, the general purpose e-beam evaporation

system was modified under our IR&D program. This modification entailed

installation of an rf sputtering system on which the substrates are

mounted. In this configuration, the surfaces are sputter-cleaned prior

to deposition. Also, the ion-gun system is prepared with a PbBi

deposition prior to junction formation, providing a consistent back-

ground for reactive-ion-oxidation.

Figure 14 is a photograph of a SQUID paramp chip before mounting in

the microwave test setup.

3.4 Analysis

Because of the eventual importance of the noise and saturation per-

formance of the parametric amplifier in an array configuration, we have

continued with numerical analysis of noise and dynamic range. This

analysis will be reported at the 1982 Applied Superconductivity Conference

and submitted for publication in the IEEE Transactions on Magnetics. A

draft of that publication is attached.

The result of the'calculations are: 1) the nearly degenerate SQUID

paramp of the design developed here has a constant noise temperature To

equal to the device termination temperature; 2) the amplifier response

is linear to several percent of the flux quantum energy; 3) the single

SQUID paramp is easily saturated by broad-band noise if that noise tem-

perature is much greater than )OTa; 4) the coherent SQUID array paramp

20

7J

SOP I

FIGURE 14. P t~a iffvr ,t afmpli ier tisa-, fabricated

Qfl d Ii .,j' ~ fvit,, ijocs not qui te include

the on, t i The 9GH.- SQUIDS, are at the

e 11Lt r o f to.,t .t ruc turcb at the top and bottom.

has the samne_ noise temperatur' a, the single SQUID para ttr ic aiigpl i, r,

indicating fl hat th. array of N SQUIDs will hav a dyrnaicili rdrinq N ti,.

that of the singIe device. Further detail s are itcl udtd iti tI,. a a t act .d

draft of "SQUID Parametric Amplifier,"

I n conjunction with analysis of a resistiv SQUID voltagj'-coritrUl (:d-

oscillator, we have observed that the resistive SQUID biastd at 2. whre

is the SQUID LC resonance frequency, will oscillate almost exclusiVeily

at id/2 ')o for =l and Q'.2. Thi s can be viewed as a degenc rat_ parametric

oscillator similar to that predicted for the SQUID parametric amplifi.r

if Q JI(Ap)'l. Thus, it appeared very likely that a similar low noisC

amplifier could be operated with a self-pumped resistive SQUID. V'ury

recently Calander, et al have reported such an experiment although in a

non-degenerate form [J. Appl. Phys. 53, 5093 (1982)]. We have proposed

to carry out specific analysis and measurements of this ampl if ier next

year.

3.5 Measurements

Tests were made of several amplifiers at 9GHz using a cooled x-band

circulator and an H-P Spectrum Analyzer as a receiver. No useful data

was obtained, probably because of poor device quality as discussed above,

and the poor noise figure of the SA. Just at the completion of this

year, we received a NARDA low noise x-band GaAs FET amplifier to provide

improved N.F. and also increase isolation from the SA. Measurements of

new devices will proceed in the next quarter.

22

4 . CONCLUSIONS

Several fabrication problems have been resolved and we expect to

provide quantitative measurements next year. Analysis of noise and

dynamic range of the single SQUID and SQUID array continue to indicate

very useful application of the SQUID parametric amplifier.

23

APPENDIX A

SQUID PAR AnUrRC A'LIFIA X

A.H. Silver and R.D. Sanjell*TW'I Space and Technology Group

One Space Park, R sdondo Beach, CA 90278J.P. Hurell and D.C. Prire-Brown

The Aerospace CorporationP.O. Box 92957, Los Angeles, CA 90009

Consider tk* SQUID of Fig. 1 wiu. ir-.Abstract and a Josephson tanneluig ).znctio:. wi e:(..'i.

current I and capticitanoe C. For fre4,c:_.c ,,.The single 3unction SQUID was previously sh1kn Cbelow the energy] gap frequency , we neglec, l.it 7: 'en.

by analysis and si,.aation to be an attractive q asepaxicle resistance ure u tim- '- -. "candidate for a parametric amplifler. Further R. rstns corafi a " -. _ :_calculations of the noise and saturation behavior of

the nearly degenerate parametric arplifier have nowbeen performed by numerical si.nulation. These * +rsn +' -L(t)siinulations clearly show that the ar,lifier noise

ta-perature will be approxiimately the devicetemperature To , and that the amplifier will be where C is the _pbse of the J'seil .>.- .corpletely saturated in the presence of white noise I2 Ll, - L/C/R, tnme is measr/ s 11. f. schracteristic of 3,or . Signal saturaticq of, the l /

amplifier also occurs for an output power 10 f 0'/2L, 0strongly inuting the dynaric range. However, acoherent array of J single junction SQUIDS is shown to I(t) - 10+1 SOS st + 1 + S . .

have a signal saturation level increased by N relativeto a single 3ti.-D, with no increase in noise lis and I represent dc bias, s.z:_:, w. pxr*.jte-perature, resulting in an N-fold improvement in o0' sF I, epresent d i, oinput currents. For =1, O<.5, an oprd-ln p.;.:c si-dynamic range. bye =iV2, and purped at fieqjency 2-o wit. p. :-

amplitude approximately r/4, the n~arly degenera-eIntiod ct-on SQUID parametric arrpifier has high ga., a:12 a

We have previously shown I that the single gain-bandwidth relation

junction (or rf) SQUID is an attractive candidate for a G(O)( L)2 n 2

single idler parametric aiTplifier in terms of gain,bandwidth, and phase stability. Furthermore, aspecific linear array of tightly coupled SCUIh was Optznm bandwidth occurs for a loaded Q-1/1=2.

sontsptthe single c Successful performance of parametric arplifiersshown to sport a stable mlde identical tobe achieved by using circuit resonances to storeSXUID amplifier, but with power increased by N and idler power and thereby drive the system away frorinpedance by N/2, where N is the number of SQUIDs in chaotic or marginally stable ca-itions. The barethe array. The saturation and noise behavior of such Josephson tunnel junction exhibits a small siqr.a!amplifiers has now been caputed and gives further :plasma resonance which has been2 explored forsupport to the use of the SQUID as a low noise .superconducting applifier operation2. .4o usefalparametric amplifier. device, however, has resulted from either an uns-inted

single junction or multiple Junctions . Cn the otherINPT IGALhand, the low 6, tunnel junction S=1D has a shant

inductance L and junction capacitance C which allow a" ell-defined, large signal resonance to occur. This',same LC resonance can se preserved even in a largearray of oupled SQUIs This closely aproxiatesthe classical requirement for a successful anmlifier.Furthermore, for the SQUID amplifier, I in Eq. (2) ischosen to bias the junction phase e ae r /2 where thePUMP AND

DC BIAS plasma frequency is identically zero. Therefore, theJosephson plaswa resonance is not involved in theoperation of this parametric arplifier.

Saturation

L IC The gain was previously I determined from bothclosed-form analysis and nunerical simulations in thevery small signal limit in the absence of noise. Byincreasing the signal anplitude in the cor'tersimulation, the large signal response has now bee:ncalculated, providing estimates of both linearity an3saturation. Calculations wre performed for 6 -1 arv]

n-0.5 with pump amplitudes 2,,2-8 and 3.2.corresponding to a usmall signal gain'of 10 and It dri.

F1gure 1. Equivalent circuit of the externally respectively. Figure 2 shows the coapited idler powerpumped SQUID parametric amplifier, as a function of input signal power for signal

frequency at 1.05f (E -2.8) and 1.025f (L -3.2) withSSupp]orted by the Naval Research Laboratory, ontract no noise added. TCe rmalizat-ion of type A ai in,"

Nu. W0014,81-C-2495. and idler power is nfokTo, where fom- /2r and

Manuscript received Nuvenber 30, 1982

24

noise with discrete time intervals i, such that the

cutoff frequency w =/2- -3.2. It is anticif-ted

that this noise ban&idth will 3nclude all significantnoise frequencies. he noise process is generatedl by arandom walk in the phase 8 , which has a 9aussiWu1distribution of time increments with variance c , wierc

* C.o/2W)202 - 4kT Ri. (4)0] 28', 0lI" O 0

L . * 32on, Figure 3 displays the ccrpute oi',_. N OSt DOI0 temperature as a function of T for the sane twu

amplifier conditions used in determining th, gai.

saturation, E£2.8(ldB) and r3.2(15db). 5t, ll, t-.

'C the scale In -4Fig. 2, t5- Dunit of teru:.rI measurement, 10 nT I rel tes temTeraturv to th - fljx

,OS ," ,03 17 1,' qiantvz energy via TC /21k. The calculated o.r.>-

oT .!. ,2, noise temperature for oall input tenieratare irn3dites

2 that the classical reslt, 2TO) x gaiL,, is a rox-.

F-.;.e 2. Comi'tei idler response as a function of the achieved. ctioever, saturat lon of th"Inpat siinal for two values of the pump level and temperature and associated bright line gain co-Tresziiv.amplifier gain. E -2.8 (10db), and E -3.2 (15db). The exceed that anticipated by the idler performance sriv.

power is normalizid by nf 0 kT wherePnkT is equal to in Fig. 2. A comparison of the integrated braii

the flux quantum energy and ? is the resonance output power to the narrowban idler 'siq-al .frequency of the LC circuit. indicates that broadband noise can mare easily satLura-e

the amplifier.nk =: '/2L, the energy of one flux quantum in the Based on the results slo'n-, above, t .

5:U D inductance, and T is the opezating terperature SQJID is a low noise amplifier with useful but 1i-.iite,

of the SQUID. 5L7,UD arplifiersfabricated in a thin dynamic range which is potentially suscer-' t -"film 4 format can have Lt 5xlO "1, corresponding to broad and noise saturation. The ucility of a S'

.F 10 . In both cases plotted in Fig. 2, gai array to increase the total operating power and ma.,ecuipression f 14 occurs at an idler power = 10 impedance matching easier would be limited if thenf kT or 10 'f o /2L. S rog 2 saturation in the idler output noise power scales with the number of SJ*'XDs asou;pu sets in Out 3x10- f 1 /2L. We point Out that does the signal power. Therefore, wt, have perforr _ athe idler power is used V test gain canpression noise calculation on the array st.ular to tha for "'_hIebecause the coputed signal power in a two terminal single SUJJ1D. in calculations anid simulations on thedevice includes both the input and output powers. array performance, each SQUID is assined to be loadedFrequency separation of the nearly degenerate idler with a resistance R. An independent Johnson noisemakes the gain computation mcre straightforward. generator with the sane cutoff frequency 3.2 and

SSt5ong saturation near an output power of other characteristics as that used for the single 3KL:'3xl0-2f * /21. is expected on the basis of the flux was added to each resistor. Thus, each SOU;2 isMndulatRo model of the SCOJID. One expects strong independently excited by thermal noise. Fran the fr-mysaturation in output pywer below the level of the pump point-of-view, the uniform mode of the amlifier ispo~ar computed as f /L, where 0 is the amplitude of excited as well as all other modes which lie below theoscillatory flux iR e SQU[-D at the pamp frequency, cutoff frequency. As a result, the signal and idlerle maximum value of $ for a well designed amplifier ports are correctly excited by noise if the end effectswith 0 -1 is 0 ta k; more appropriate values are are neglected. Thus, the response to the effects of4W6. 2 TAhus, AIrong saturation is expected below the bath telperature are adequately simulated, althojgsi

0 0 /2L)/36, in gcod agreement with the results inFig. 2.

Noise Oto. ,- 21" 06 ,o

In practice, the noise performance willdetermine if these gains can be realized and over whatbandwidth a useful dynamic range can be sustained. Theadded noise temperature of a classical,nearly-degenerate, high gain parametric amplifier is I,

that of the idler termination. While the SOJID ...parametric a plifier obeys the classical equations at D

very mall signals, the nonlinearities in the systn 8make it necessary to determine the noise response for a '02wideband amplifier. We have performed a classicalnoise calculation to determine the ontributi i ofpotential noise sources such as pump noise orup-conversion noise from near dc. Pump noise is oexpected to be minimized if the pump afplitude is suchthat J(A) is near its maximum value, where A, is Ue

fundrental component of the phase respnse to the ,0 0pimp . Upccnversion from very 1w frequencies should ' tu'. .. iuq o

be ineffective since the resulting idlers are far frn of thethe signal band. Fgre 3. computed output noise temperature t

The calculation was performed by adding a SQUID parametric amplifier as a function of the input

Johnson noise generator in the load resistance R. 7mis noise temperature for the same two pump (gain) con-

has the effect of adding broauani noise at both signal ditions as shown-in Fig. 2. Noise temperatures are

and idler ports of the pararp simultaneously. The normalized by 10 nT , where n is the ratic of the

Hachelier-Wiener process was used to simulate the flux quantum energy ?o kTo .

25

-s-a' ?._ p ,F' m

TABLE I OmentsCOMPUTED NOISE RESPONSE OF ThESQUID ARRAY PARAMETRIC AMPLIFIER One further note aboat related measuremnts on

The output noise temperature for 4, 16, and 32 SQUIDs Josephson parametric amplifiers and chaotic beha..'or.

noualized to that of a single SQUID for the sam The simulations reported here and In Ref. I show tht

pump level and input noise temperature. the Jos-phws-n junction, 'he lxrgorate into a lo. ,

low 0 SWID which resonates the junctio, capscitr.ceINPUT OUTPUT NOISE TEMPERATURE With the SQUID inductance, has modes of operation wiuzh

PUMP NOISE are predictable, non-chaotic, and respond linearly.LEVEL TEMPERATURE 4 16 32

(t04nTo) JUNCTIONS JUNCTIONS JUNCTIONS er, at large excitations, the behavior clerly

I _ bemfes nonlinear with strong saturatio., subrmin

1 -29 Is -Is x generation. and other unexpected effects. Calendar10 0u GAIN 6 14 1.2 12 et al have recently reported low noise temperatures

264 1? 21 X (=30K) for "shunted" Josephsor tunrKl junctions AIcf.10 .3 25 x were self-puiped via internally generated Josephsoi.08 06 09 oscillations. .These devices were ir, fact low

15 36 GI is 14 0 inductance "resistive" S.UIDs with k -fact.orsI N64- 19 34approximately 2 and 4 for the lowest noise ar1lifiers.26 I 3These results strongl1 suggest that th& ex-ern-.fiy106 x 29 x hspazped configuration proposed by us will perfo a.s a

it is not an accurate representation of a broadba low nokse arplifier. Despite the s"gstion ofsignal. The latter disti.nction does not exist for the Calander', et al that the external pLrnp is a source ofsingle SCUID, noise rise in Josephson pararps, orly circunstantial

Table I sumarizes the calculated output evidence is offered that this is the case. ti sigesttemperatures for arrays of 4, 16, and 32 junctions. that low noise follows frui the low 6, low Q SX;D"he results, normalized to the single SQiD case, configuratton. Analysis of the resistive SQUID

clearly demonstrate that, in the linear response range oscillator s)xsws a variety of instabilities for evenof input temperatures, the SQUID arrays exhibit no modest values of Q or E , includLing sUbharmoric

excess noise over that for the single SQUID. At tJe generation and anharnoc oscillations. Nothigher teiperatures there is same evidence of noise surprising, the general rule to avoid theseincrease. Scatter in the numbers in Table I reflects instabilities appears to be Q6<2, similar to thethe accuracy of the noise calculations rather than requirement to avoid subharmomic geneation in thesignificant variations, externally purped parametric amplifier . Thus, the

This result means that an array of N single internally pumped amplifier should be qualitativelyjunction SQUIDS, operated as a nearly degenerate, similar to the externally pumped device withoutexternally puiped parametric amplifier , will have the flexibility in setting the pump level ,althoaghfollowing specifications relative to the single SQUID avoiding the need for a separate oscillator andparanp: adjustment for both the oscillator level and Ote dc

Gain - 1 phase value. Furthermore, a metho of generating anBandwidth - 1 internally pumped SQUID array amplifier does not appear

Impedance - 14/2 to be at hand.Saturation Power " NNoise Temperature . 1. References

Since the array responds only to noise in the uniformmode, the total noise power does not increase while the I. A.H. Silver, D.C. Pridmore-Brown, R.D. Sandell,signal par saturation level increases as 14. The and J.P. HUrrell, "Parametric Properties ofexcess noise temperature of the nearly degenerate array SQUID Lattice Arrays," UE Trans. Magn.amplifier operating at 4 kelvin is 4K, assuriin the MA-17, pp. 412-415 (1981).amplifier load is also at 4 kelvin. Hbeever, the 2. S. Whhlsten, S. Rudner, and T. Claeson,dynfuic range is limited by saturation level of "Arrays of Josephson Tunnel Junctions as10 '1nf0 kT and by a noise floor o f~okT, with a Parametric Amplifiers," J. Appl. Pnys. 49, pp.resulting %ynunic range equal to 10- - . ieasonable 4248-4263 (1978). N.F. Pedersen, "Zero-V-oltagcvalues of the ratio n- (flux quantum energy/thermal Nosdegenerate Paranetric Mode in Josphsonenergy) are about 104, with a maximul value of 10 set Tunnel Junctions," J. Appl. alys. 47, ppby the Josephson penetration length limit on junction 696-699 (1976).size. The array size may be limited by uniformity of 3. M.J. Feldman and M.T. Levinsen, "Theories ofJosephson current density and lithography, by parasitic the Noise Rise in Josepson Paraips," I1xEcapacitance or stray field, c by ispractically high Trans. Magn. MAG-17, pp. 834-837 (1981).impedance. Certainly 14-10 -10 s ho/d be realizable. 4. G.M. Jenkins and D.G. %atts, Spectral AnalysisThus, a " anic range at least 10 , and possibly as and Its Applications , Holden-Day, Inc. (1966).high as 10 , can be ccntoplated at 1C0B gain without 5. N. Calander, T. Claeson and S. Rulner. "uShteaddressing new prcbl e areas. it, the 2 more Josephson Tunnel Junctions: High Frequency,conservative value of 10 , based on n-10 , N-10 , the Self-Pumped Lw Noise Amplifier,' J. Appi.output aturation por will be 0.61W at 10G z (6tW at Pnys. 53, pp. 5093-5193 (1962).10iz); at 10 , saturation power will be 6C.W at 10GHz 6. A.I. Silver, R.D. Sandell, and J.Z. Wilcox,(6000b at 10(Xi1z). "SQUID Voltage-Controlled-scillator," I=1.

Trans. Magn., current issue.

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