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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-22, NO. 4, APRIL 1974 549 Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications STUART A. WOLF, JOHN R. DAVIS, SENIOR MEMBER, IEEE, AND MARTIN NISENOFF Abstract-Theferromagnetic-coretype of solenoid ‘that is used as atrailedantennaforcommunicationsreception by submarines has not demonstrated adquatesensitivity to satisfy the performance requirements for deeply submerged submarines receiving extremely low frequency (ELF) transmissions from the planned Sanguine com- munications system. It is possible, however, that a superconducting quantum interference device (SQUID) can be adapted to this role successfully and can permit all requirements of platform depth, speed, and maneuverability to be met. The present status .of SQUID’S is described, and some laboratory measurements that prove the potential of these devices for the ELF communications reception capability are presented. The engineering developmentthat must be pursued in the areas of 1) sensor and electronics dynamic range, 2) sensor orthogonality, and 3) refrigera- tion systems to make SQUID ELF sensors available as operational receiving antennas is also discussed. C I. INTRODUCTION URRENT submarine deployment plans require greatly improved communications performance between sur- face or airborne transmitting terminals and deeply sub- merged receivers. Improvements must be made, most particularly, in restrictions upon receiver depth, speed, and maneuverability. The attenuation of radio waves in seawater at very low frequencies (VLF) requires the receiving antennato be relatively neartothe surface. Furthermore, the long trailing wire antennas and ferro- nagnetic-core solenoids (which may bebuoymounted) low in normal use at these frequencies hamper the sub- narine’s operating flexibility. The prospect that the extremely low frequency (ELF) )and may be employed in the near future for submarine lommunications provides a potential solution to some of hese requirements that avoids the limitationsof the VLF ommunications systems. Principally, ELF waves pene- rate so deeply into seawater that sensors need no longer le towed close to the surface. However, two serious roblems remain. 1) Trailing wire (distributed electrode) and ferro- lagnetic-core solenoid sensors must be long and conse- uently unwieldy, hence limiting maneuverability. 2) Omnidirectionality requires either an infeasible de- loyment of widely separated electrode pairs(one pair tn be trailed, but the other pair must be deployed per- Manuscript received December 6, 1973. This paper was pre- nted at the 1973 National Telecommunications conference, tlanta, Ga., Nov. 26-28. The authors are with the U. S. Naval Research Laboratory, ‘ashington, D. C. 2037.5. pendicular to the direction of submarine motion) or development of a relatively noise-free solenoid. As will be indicated in Section 11, present solenoid sensors cannot satisfy the noise requirements for adequate performancein likely operating areas with the planned ELF transmitting capacity and the required message delivery rate. It is the purpose of this paper to propose the development of a magnetic-field (H-field) sensor that can satisfy the performance requirements and can, in fact, provide fully omnidirectional receiving capability without the need for an electric-field (E-field) sensor a t all. This proposed sensor will employ a superconducting quantum interference device (SQUID) and wil,l permit ambient noise level performance to be achieved in the bandwidth required for ELF communications. Section I11 of thispaper contains a description of a typical SQUID, a discussion of laboratory measurements performed recently atthe Naval Research Laboratory that confirm SQUID sensitivity in the ELF range, and a presentation of the three major hurdles to effective, employment of a SQUID in an operational receiving sys tem : 1) achievement of adequate dynamic range; 2) achievement of adequate orthogonality among three 3) refrigeration. planar sensors; 11. REQUIRED SENSOR PERFORMANCE I. In the particular case of the proposed Sanguine ELF communications system, a submarine ELF H-field sensor must have a sensitivity equal to or greater than -200 dB relative to 1 V/m/(Hz)1’2, in a bandwidth 100 Hz wide centered at a frequency of 80 Hz.’ This sensitivity will permit the requirements previously listed to be met in the ordinary sea operating areas at the noisiest season. The bandwidth requirement of 100 Hz will permit wide- band noise processing to be used to reduce the impact of sensitivity for submarine ELF communications is to use the equiva- 1 The convention in the literature for expressing H-field antenna lent E-field sensitivity. To avoid confusion, the a propriate con- versions for seawater with a conductivity of 4 m h o h at 50 Hz are -200 dB//1 V/m/(Hz)l/z = -162 dB//1 A/m/(Hz)l/Z = 10-14 T/(H~)I/*. When discussing SQUID’S the more common unit is T/(Hz)’12. Therefore these units will be used Interchangeably.

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Page 1: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-22, NO. 4, APRIL 1974 549

Superconducting Extremely Low Frequency (ELF) Magnetic Field

Sensors for Submarine Communications

STUART A. WOLF, JOHN R. DAVIS, SENIOR MEMBER, IEEE, AND MARTIN NISENOFF

Abstract-The ferromagnetic-core type of solenoid ‘that is used as a trailed antenna for communications reception by submarines has not demonstrated adquate sensitivity to satisfy the performance requirements for deeply submerged submarines receiving extremely low frequency (ELF) transmissions from the planned Sanguine com- munications system. It is possible, however, that a superconducting quantum interference device (SQUID) can be adapted to this role successfully and can permit all requirements of platform depth, speed, and maneuverability to be met.

The present status .of SQUID’S is described, and some laboratory measurements that prove the potential of these devices for the ELF communications reception capability are presented. The engineering development that must be pursued in the areas of 1 ) sensor and electronics dynamic range, 2) sensor orthogonality, and 3) refrigera- tion systems to make SQUID ELF sensors available as operational receiving antennas is also discussed.

C I. INTRODUCTION

URRENT submarine deployment plans require greatly improved communications performance between sur-

face or airborne transmitting terminals and deeply sub- merged receivers. Improvements must be made, most particularly, in restrictions upon receiver depth, speed, and maneuverability. The attenuation of radio waves in seawater a t very low frequencies (VLF) requires the receiving antenna to be relatively near to the surface. Furthermore, the long trailing wire antennas and ferro- nagnetic-core solenoids (which may be buoy mounted) low in normal use at these frequencies hamper the sub- narine’s operating flexibility.

The prospect that the extremely low frequency (ELF) )and may be employed in the near future for submarine lommunications provides a potential solution to some of hese requirements that avoids the limitations of the VLF ommunications systems. Principally, ELF waves pene- rate so deeply into seawater that sensors need no longer le towed close to the surface. However, two serious roblems remain. 1) Trailing wire (distributed electrode) and ferro-

lagnetic-core solenoid sensors must be long and conse- uently unwieldy, hence limiting maneuverability.

2 ) Omnidirectionality requires either an infeasible de- loyment of widely separated electrode pairs (one pair tn be trailed, but the other pair must be deployed per-

Manuscript received December 6, 1973. This paper was pre- nted at the 1973 National Telecommunications conference, tlanta, Ga., Nov. 26-28. The authors are with the U. S. Naval Research Laboratory, ‘ashington, D. C. 2037.5.

pendicular to the direction of submarine motion) or development of a relatively noise-free solenoid.

As will be indicated in Section 11, present solenoid sensors cannot satisfy the noise requirements for adequate performance in likely operating areas with the planned ELF transmitting capacity and the required message delivery rate. It is the purpose of this paper to propose the development of a magnetic-field (H-field) sensor that can satisfy the performance requirements and can, in fact, provide fully omnidirectional receiving capability without the need for an electric-field (E-field) sensor a t all. This proposed sensor will employ a superconducting quantum interference device (SQUID) and wil,l permit ambient noise level performance to be achieved in the bandwidth required for ELF communications.

Section I11 of this paper contains a description of a typical SQUID, a discussion of laboratory measurements performed recently at the Naval Research Laboratory that confirm SQUID sensitivity in the ELF range, and a presentation of the three major hurdles to effective, employment of a SQUID in an operational receiving sys tem :

1) achievement of adequate dynamic range; 2) achievement of adequate orthogonality among three

3) refrigeration. planar sensors;

11. REQUIRED SENSOR PERFORMANCE I .

In the particular case of the proposed Sanguine ELF communications system, a submarine ELF H-field sensor must have a sensitivity equal to or greater than -200 dB relative to 1 V/m/(Hz)1’2, in a bandwidth 100 Hz wide centered at a frequency of 80 Hz.’ This sensitivity will permit the requirements previously listed to be met in the ordinary sea operating areas at the noisiest season. The bandwidth requirement of 100 Hz will permit wide- band noise processing to be used to reduce the impact of

sensitivity for submarine ELF communications is to use the equiva- 1 The convention in the literature for expressing H-field antenna

lent E-field sensitivity. To avoid confusion, the a propriate con- versions for seawater with a conductivity of 4 m h o h at 50 Hz are

-200 dB//1 V/m/(Hz)l/z = -162 dB//1 A/m/(Hz)l/Z = 10-14 T/(H~)I/*.

When discussing SQUID’S the more common unit is T/(Hz)’12. Therefore these units will be used Interchangeably.

Page 2: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

550 IEEE TRANSACTIONS ON COMMUNICATIONS, APRIL 1974

the highly non-Gaussian noise in the ELF band on the communications signal.

Current efforts to achieve omnidirectionality in sub- marine reception are centered upon efforts to supplement the E-field trailing wire antenna with an H-field antenna of the ferromagnetic-core solenoid type. Such an antenna

’ is Iimited by several types of noise, including motion- induced noise of two kinds (end effect and distortion noise) , and magnetostriction noise, in addition to thermal noise of the core winding. The best documented sensitivity for an H-field antenna to date is -170 dB relative to 1 V/m/ (Hz) l / 2 (unpublished work by the RCA Corpora- tion), 30 dB worse than the required performance. Re- searchers at the Naval Underwater Systems Center may have achieved somewhat better sensitivity in initial tests of a new design, but these tests are incomplete [l]. Near- maximum performance for this type of device may now have been achieved, and it now is possible that satisfactory performance cannot be achieved with the ferromagnetic- core solenoid; a new approach seems warranted.

As will be indicated in Section 111, SQUID sensors have been shown at the Naval Research Laboratory to be capable of detecting about 2 x T/ (Hz)’” [-213 dB// l V/m/ (Hz)’~~] in the ELF band above 100 Hz. Measurements a t lower frequencies were not possible because of power frequency interference in the vicinity of 60 Hz, but there is no reason to doubt that this same sensitivity is available over the entire planned communications bandwidth. SQUID’S are subject t o mo- tion-related noise, but unlike the magnetostriction and cable-distortion noise to which a long solenoid is subject, which are due to internal motion, the major noise prob- lem in SQUID’s is one of .controlling the relatively rigid rotations of the sensors in the earth’s magnetic field. Provided this motion-related noise can be eliminated, the SQUID sensor can provide a self-contained omnidirec- tional receiving capability equal to the requirements listed previously.

The motion-related noise to be accommodated consists of the effect of sensor rotation in the earth’s magnetic field of 0.5 X T. Because the earth’s field is uniform on the physical scale of a typical SQUID, a set of orthog- onal sensors can. be used to sum the vector components continuously and thus permit the large earth’s field component to be removable as a dc component. The problem areas are 1) providing enough dynamic range in the parts of the system ahead of the vector summing stage to prevent the SQUID electronics from being saturated, and 2) achieving orthogonality among the sensors. The total dynamic range requirement is about 194 dB. Using techniques that have been developed for magnetic air- borne detection, physical rotation of the sensor can be constrained to less than 10-3 rad, thus lowering the re- quired sensor and electronics dynamic range to 134 dB. Present-day SQUID electronics have a dynamic range of 140 dB. The 134-dB electronics dynamic range and 100-Hz bandwidth can be achieved by using 24-b digital elec- tronics and a 9.6-kHz sampling rate. A means by which

Fig. 1. A typical SQUID sensor consisting of a superconducting ring 2 rnm in diameter and about 1 mm high evaporated on a

one point along the circumference. The object on the right sidc quartz cylinder. The ring has a “bow-tie” type of constriction at

of the picture is the tip of a ball-point pen for reference.

effective orthogonality among the sensors can be achieve( will be discussed in Section 111.

111. APPLICATION OF SUPERCONDUCTING QUANTUM INTERFERENCE DEVICES

Measured SQUID Characteristics

The required sensitivity of 10-14 T / ( H Z ) ~ / ~ should b achievable with a presently available, SQUID syster combined with a superconducting flux transformer. 1

typical thin-film SQUID sensor as shown in Fig. 1 is 2-mm-diameter cylindrical film of superconducting matt rial in the form of a ring deposited on an insulating sut stratum with a submicron constriction at one point alon the circumference (see, for example, [Z]). This ring coupled inductively to a resonant circuit tuned to 30 MH and the RF voitage across the coupled structure is mea; ured as a function of the external magnetic field. In th configuration the SQUID sensitivity is nearly constal over the 0-30-kHz frequency range. The impedance I

the ring is a function of the external magnetic field on1 a characteristic drive current has been exceeded, and it this quality that makes a SQUID useful as a magnet field sensor. The response of the superconducting ring the applied field is periodic, with the period being 0: quantum of flux defined as h/2e = 2 x 10-15 Wb (h Planck’s constant, and e is the electronic charge). Tyl ically, the signal-to-noise ratio is such that 1 part in 3 of a flux quantum can be resolved in a 1-Hz bandwidl For a 2-mm-diameter ring, which was the size of t available SQUID, this circumstance yields a sensitivj of 6 X lo-” T/ (Hz) 1’2.

The sensitivity of this SQUID can be substantia improved by using a superconducting flux transformer couple it to the external field. A flux transformer consi of two coils made of a continuous simply connected w or ribbon of superconducting material. One coil is coup inductively to the SQUID cylinder, and the other coi: exposed t o the external flux. If the external field is chang the properties of the superconducting state demand tl a current will flow in the flux transformer to keep I

enclosed flux constant, and this current causes a COI

Page 3: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

WOLF et al.: SUPERCONDUCTING MAGNETIC FIELD SENSORS 5.51

Fig. 2. The 15-cm-diameter 5-cm-long lead foil flux transformer primary, which when coupled to the basic SQUID as described in the text, has a 2 X lO-*5 T/(Hz)"* sensitivity. The two larger

vide the calibration field. The SQUID itself is mounted between copper coils are the 20-cm-diameter Helmholtz pair used to pro-

the two Helmholtz coils on the axis of the flux transformer. The long rod and large circular plate are Dewar flask mounting apparatus.

stantially relaxed for noise components outside the oper- ating bandwidth.

If the sensors are completely free to rotate, each sensor would have to be capable of tracking a field from 10W4 T to 0.5 x T, resulting in a required 194-dB dynamic range. In addition, if the orthogonality of two sensors was in error by 0, then the change in the vector sum of the outputs of these sensors for a 90" rotation of the sensors would be equal to H,B, where He is the earth's field. Thus, if no signal above T due to the rotation of misoriented sensors is to be allowed, then e must be 2 x rad or less; equivalently, the sensors must be orthogonal to 2 parts in 1O'O. These requirements are very stringent but can be greatly relaxed if one of the sensors is in the direction of the earth's field.

A simple calculation (see the Appendix) indicates that

sponding change in field to be produced at the SQUID. A simple calculation taking into account the relative areas of the two coils, the inductance of the coils, and the

1 coupling of the SQUID coil to the SQUID indicates that field amplification can be obtained in this fashion [3].

Two such flux transformers were fabricated at the Naval Research Laboratory and coupled to a SQUID which had a peak-to-peak instrumental noise corresponding to 6 x T/(Hz)'j2 for signals from dc to 30 kHz. One flux transformer provided a field amplification of 7 and had a peak-to-peak noise a t dc and in the frequency range from 100 Hz to 10 kHz such that a signal corre- sponding to (9 f 5 ) X T/ could be readily detected. Data were not taken in the vicinity of 60 Hz because the ambient noise near 60 Hz was about T peak to peak. The attenuation provided by two super- conducting shields reduced the noise at the flux trans- former t o about 1 flux quantum, which is a factor of lo3 larger than the signal that was detected a t frequencies away from 60 Hz. The other flux transformer gave a field amplification of 300 and consisted of a single turn of 5-cm-wide lead foil 15 cm in diameter (see Fig. 2). The measured sensitivity in this case was such that the peak- to-peak noise was (2 f 2) X T/ (Hz) measured a t dc and from 100 Hz to 30 kHz. At frequencies near 60 Hz the environment introduced additional noise above that intrinsic to the system. Additional shielding was provided in this case by a large metal Dewar flask. One important result of the experiments was that in spite of the large 60-Hz noise, as much as several flux quanta in the second experiment described, it was still possible to resolve signals of of a flux quantum at frequencies removed from the frequency of the noise.

if one sensor's alignment is maintained along the earth's field H , to within an angle a, and if the worst misalign- ment in orthogonality of sensors is e, then the largest motion-induced signal is (for small a, e) approximately He&. A reasonable goal for (Y might be lov3 rad, because this degree of stabilization has been achieved in opera- tional airborne magnetic anomaly detection systems. With this degree of alignment, the dynamic range required would be 134 dB, and dynamic ranges of 140 dB have already been achieved electronically in the frequency' range of interest. However, this circumstance also requires effective orthogonality of the sensors to 2 parts in 10'. Assuming a flux transformer diameter of 10 cm, this degree of orthogonality correspond: to alignment of the plane of the flux transformer to 200 A. Clearly, a subsidiary alignment procedure must be incorporated.

It can be shown that the variation with 0 of the signal from two misoriented sensors is proportional to (sin a cos C Y ) 0 (see the Appendix). If the best alignment possible results in e of about 1 part in 104, then a feedback scheme could be used to electronically cancel the motion- induced signal associated with the residual misalignment.

A conceptually simple method of employing such a compensation scheme would begin by placing the mechan- ically rigid three-sensor system in a uniform calibration field, with one sensor (say, the x sensor) aligned in the direction of the field. Small departures of the other two sensor axes from orthogonality with the x sensor could be compensated by combining their outputs with just enough of that from the x sensor to null them. The sensors then could be rotated by 90" so that one of the others (say, the y sensor) is aligned with the field, and the x sensor is nulled. Then the remaining ( z ) sensor output could be combined with just enough of the y sensor output 'to

Stability Requirements yield a null. Other more sophisticated methods also could be employed. For example, two flux-gate sensors with a

One of the most serious problems in utilizing the sensitivities of 10-10 T and orthogonal t o 1 part in lo4 T/ (Hz) sensitivity of a SQUID is the spurious signal would, if their outputs were electronically multiplied, give generated by the device moving in the earth's magnetic a signal that varies as sin CY cos CY. A part of this signal field. Since the field of the earth is 0.5 X T, it is could be fed back into the SQUID coils to cancel the necessary to cancel the within-band effects of motion in signal due to the SQUID'S motion in the field. Two flux this field to 2 parts in 1O'O. The requirements are sub- gates would be required for each SQUID not aligned

Page 4: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

552 IEEE TRANSACTIONS ON COMMUNSCATSONS, APRSL 1974

along the earth’s field. Balancing the system would be done empirically by adjusting the amount of feedback from each pair of flux gates until the output from the SQUID’S was no longer sensitive to small motions. If a could be kept below rad, then sin a’cos a is approxi- mately equal to CY, and one flux gate per misaligned sensor is all that is needed. Although cumbersome, this procedure should be quite workable.

Frequency components of the motion-induced noise outside the signal band also need to be considered. The product of this noise amplitude, measured in flux quanta,’ and the noise frequency must be less than the rate at which the SQUID electronics can “count” flux quanta, or its slewing rate. The presently achievable slewing rate is about 1 0 6 quanta per second. For a T / ( H Z ) ’ ’ ~ sensitivity SQUID plus flux transformer, a quantum cor- responds to 10-1’ T. So, for example, noise a t 10 Hz could be tolerated up to 10“ T. For frequencies in the motion-induced noise that are outside the signal band, if one of the orthogonal sensors is oriented along the earth’s field to rad, then orthogonality of the sensors would no longer be required to keep the error signal due to rotation smaller than T but would only be neces- sary to insure that the vector-summed signal amplitude remains constant for a signal of arbitrary polarization.

Cryogenic Environment and Refrigeration The remaining major problem associated with the utili-

zation of SQUID’S is their cryogenic environment. Present- day SQUID’S require a liquid helium bath to provide an operating temperature in the vicinity of 4.2 I<. If (assum- ing the worst case in which hull-mounting might be pre- vented by excessive noise at that location) the SQUID must be located in a separate vehicle towed a considerable distance behind the submarine, the refrigeration must either be aboard the towed vehicle or it must contain a sufficient reservoir of liquid helium to provide adequate deployment time. Three alternatives are possible: a vehicle containing a Dewar flask, a vehicle containing a Gifford- McMann closed cycle refrigerator with its compressor aboard the submarine, and a vehicle containing a Joule- Thomson refrigerator using three working gases and com- pressors or gas cylinders aboard the submarine.

In the simplest case, a large portion of the vehicle would be a vacuum-insulated container or Dewar flask to hold the liquid helium required to provide the necessary refrigeration. The cable to, the submarine would be rela- tively simple and would consist of a tension member and electrical leads. However, using a reasonable size Dewar flask the vehicle would have to be brought aboard the submarine for helium replenishment a t intervals of less than 30 days. This fairly short deployment time may be unsatisfactory for operational situations but would not be a drawback in initial tests.

In the second alternative the vehicle would contain a Gifford-McMann closed-cycle refrigerator with the com- pressor located aboard the submarine. The main advan- tage of this system is that the vehicle could remain de-

Fig. 3. A commercially available Joule-Thomson refrigerator (the cylindrical object adjacent to the ruler), which liquifies both bottled hydrogen and helium without the use of any moving parts. The nitrogen in this version is supplied as a liquid; with an additional expansion valve, the nitrogen could also be liquified. This would not introduce significantly more complexity or size.

ployed indefinitely. The disadvantages are that the refrig- erator has a moving piston with a frequency of motion of about 1.3 H z and this might cause motion to the SQUID mounting. (It could, however, be made with nonmagnetic parts which would not give rise to any magnetic signa- ture). The high-pressure helium gas and the low-pressure return would have to run in cables from the submarine to the vehicle, and these cables would be quite heavy because they would have to handle a large volume of gas. The refrigerator could be made quite small (about 0.03 m3) ; several built for space applications have demon- strated 8000 h between required maintenance.

In the third alternative, a Joulc-Thomson refrigerator using three working gases would be located on the vehicle and the compressors or compressed gas cylinders would be located on the submarine. This type of refrigerato1 would use nitrogen, hydrogen, and helium as the working gases and would have no moving parts; it would USE

expansion valves for refrigeration. While this method requires nitrogen and hydrogen a t a pressure of aboul 100 atm and helium a t 30 to 40 atm on the high-pressure sides, it does not use a large volume of these gases, and the high-pressure lines could consist of tubing of extreme13 small inside diameter. These tubes could be concentric with the low-pressure return lines. This method require! six passages for gas flow, but the cabling would weigk less than in the Gifford-McRilann case. The drawback: to this system are that three compressors are requirec which in their present form are large and cumbersome and the refrigerator in its present form is not very reliable Further development work on both the. compressors an( refrigerator would be required. A research type of corn mercially available refrigerator of this type is illustrate( in Fig. 3.

To summarize, the first alternative, employing a Dewa flask in a towed vehicle, could be implemented wit1 existing cryogenics provided the time between refillin! could be made adequately long and the servicing timl

Page 5: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

WOLF et al.: SUPERCONDUCTING MAGNETIC FIELD SENSORS 553

which can be simplified using the following identities:

cos y sin 6 = cosa sin p

cos y cos 6 = sin a.

If 8,cp <( 1, then sin 8 x 8; sin cp x cp, cos 8 = 1 - 02/2, cos cp = 1 - cp2/2, and after extracting the square root,

H,,,, = H e ( 1 + 4 cos2 a[02(sin2 p - cos2 p )

- 28 sin p cos p] + 3cp2[cos2 a sin2 p - sin2 a ]

-cpcosasinpsina) + ..-. (2)

Taking’derivatives with respect to a and p and multiply- ing by Aa and A@, respectively, the amplitude of the noise generated by small rotations a and /3 is

AH;,,, = ( d H / d a ) A a

= H e ( -cos a sin a[02(sin2 p - cos2 p )

- 28 sin p cos p ] - cp2 sin a cos a[sin2 p + 13

+ cp sin p[sin2 a - cos2 a ] ) Aa (3)

and

AHLeas = (dH/d@)Ab

= H e ( 4 cos2 a[402 sin p cos p

- 28(c0s2 p - sin2 p ) ] + cp2 cos2 a sin p cos p

- cp cos a sin a cos 0) A@. (4)

For H e aligned along the x axis, p = go”, a = 0, then from (3) and (4) ,

AH;,,, = -H@Aa

AH&,,, = - H , o A ~ .

Thus for one sensor aligned along H e the error is of first order in the angles describing nonorthogonality of the sensors as well as first order in the deviation in alignment of the x sensor with He. There are combinations of angles a and 0 where one or the other of AH,,,; and AHmea! varies quadratically with the angles describing non- orthogonality, but there is no combination where both of the terms are quadratic.

The form of the deviation of the measured field Hme,,, from the actual field H e will now be considered. From ( 2 ) ,

Hmea, - He

= He ( + cos2 a[B2(sin2 p - cos2 p ) - 28 sin p cos p ]

+ +p2[cos2 a sin2 p - sin2 a] - cp cos a sin a sin p ) .

For p = go”,

H,,,, - H e = H e ( cos2 a + +cp2 cos2 a’ - cp sin a cos a )

so to first order in the angles which measure nonorthog- onality, but to higher order in a,

H,,,, - He = -H,cp sin a cos a.

$1“ Fig. 4. H , is the earth’s field. It makes an angle a with the x-y

the y axis. He makes an angle y with the x-z plane, and the pro- plane and its projection on the x-y plane makes an angle p with

axis. The three orthogonal sensors are “1,” “2,” and “3”. “ ” ’ jection of He on the x-z plane makes an angle of 6 with the z

1 1s

x-y plane, and “3” makes an angle cp with the z axis in the x-z aligned with x, but “2” makes an angle e with the y ax& in the

plane.

acceptably short. The Gifford-McMann refrigerator’s noise characteristics would have to be studied and a reliable compressor developed before it becomes a viable

I option. This method also has the disadvantage of requir- ing heavy cabling. The Joule-Thomson refrigerator also requires compressor development and lighter but more complicated gas coupling between submarine and towed vehicle. Each alternative requires some development be- yond what is available now.

APPENDIX A

ANGULAR DEPENDENCE OF THE MOTION- INDUCED NOISE OF A THREE-COMPONENT

MAGNETOMETER UPON DEVIATIONS FROM. ORTHOGONALITY

If it is desired to make a magnetic-field sensor using SQUID’S that is insensitive to motion in the earth’s field, one technique would be to take the output of three pre- cisely orthogonal sensors and form the vector sum of their outputs. Motion of a system of misaligned sensors will cause noise to be generated. This noise will be calcu- lated in the case where one sensor is along the x axis, one sensor is misaligned with the y axis by an angle Bin the e y plane, and one sensor is misaligned with the x axis by an angle cp in the e x plane. This is not the most general case but it has all the types of error terms which would enter the general calculation. Fig. 4 illustrates the angles involved in the calculation.

From Fig. 4 it may be seen that the field measured by the three sensors would be

Hmeasa = [ H e cos a sin @I2 + [ H e cos a cos (6 + 8 ) 1’ + [He cos y cos (6 + cp)? (1)

Page 6: Superconducting Extremely Low Frequency (ELF) Magnetic Field Sensors for Submarine Communications

554 IEEE TRANSACTIONS ON COMMUNICATIONS, APRIL 1974

Similarly, for CY = 0,

H,,,, - H e = H e { 4O2(sin2 p - cos2 0) - e sin p cos 0 + +@[sin2 p ] 1 .

Thus, to first order in the angles which measure non- orthogonality, and higher order in p,

H,,, - H e = -HeO sin p cos 0.

ACKNOWLEDGMENT

The authors would like to thank J. Kennedy for help in performing the noise and sensitivity measurements and Prof. S. C. Collins for useful discussions on cryogenic refrigeration systems.

REFERENCES [l] J. Merrill, Naval Underwater Syst. Cen., New London, Conn.

[2] Proc. I E E E (Special Issue on Applications of Superconductivity),

[3] J. E. Zimmerman, J . A p p l . Phys., vol. 42, p. 4483, 1971.

personal communiCation.

vol. 61, pp. 8-144, Jan. 1973.

* Stuart A. Wolf was born in Brooklyn, N. Y., on September 15, 1943. He received the A.B. degree in physics from Columbia College, New York, N. Y., in 1964 and the M.S. and Ph.D. degrees from Rutgers University- The State University, New Brunswick, N. J., in 1966 and 1969, respectively.

From 1969 to 1972 he was a Research Associate with the Physics Department, Case Western Reserve University, Cleveland, Ohio. In 1972 he joined the Applied Superconduc-

tivity Section, .Naval Research Laboratory, Washington, D. C. He has done research on the superconducting proximity effect, the thermal and electrical properties of both bulk and thin film super-

conductors, and the fabrication and operation of SQUID’s. H i s current research interests include the fabrication of SQUID’s from high transition temperature superconducting materials by RF sputtering, the behavior of SQUID’s at microwave frequencies, and the application of SQUID’s to ELF and VLF communication systems.

Dr. Wolf is a member of the American Physical Society and Sigma Xi.

* John R. Davis (SM’74), for a photograph and biography, see t.his issue, page 492.

* Martin Nisenoff was born in New York, N. Y., on December 25, 1928. He received the B.S. degree in physics from Worcester Polytechnic Institute, Worcester, Mass., in 1950 and the M.S. and Ph.D. degrees in physics from Purdue University, Lafayette, Ind., in 1952 and 1960, respectively.

From 1961 to 1970 he was a Research Scientist with the Scientific Laboratory, Ford Motor Company, first in Dearborn, Mich., and then in Newport Beach, Calif.

From 1970 to 1972 he was a member of the Cryogenics Application Group, Stanford Research Institute, Menlo Park, Calif. In 1972 he joined the staff of the Naval Research Laboratory, Washington, D. C., where he is in charge of the Applied Superconductivity Sec- tion, Solid State Division. He has done research in the effect of particle irradiation on the properties of semiconductors, the excita- tion of standing spin waves in thin ferromagnetic films, the electrical properties of thin superconducting films and the fabrication and theory of operation of SQUID’s. His current research interests include the fabrication of SQUID’s from high-temperature super- conducting materials, the behavior of SQUID’s excited at microwave frequencies, and the application of SQUID’s as magnetic sensors for ELF and VLF communication systems and for MAD applications.

Dr. Nisenoff is a member of the American Physical Society, Tau Beta Pi, Sigma Xi, and Sigma Pi Sigma.