Hard magnetic bubble domain analog multiplier

Hard magnetic bubble domains are propagated in displaced orbits in response to the product of two cyclically varying propagation control fields. The control fields modulate the hard bubble domain diameter and a driving field gradient. Repulsive boundaries establish a restricted propagating channel in a layer of bubble domain material to maintain the net displacement of orbital movements of the bubble domain along a predetermined axis. The axis of the bubble domain net displacement is perpendicular to the direction of the driving field gradient and preferably along a neutral axis of the driving field gradient. The net displacement of the hard bubble domains provide an improved analog multiplication of two alternating current computational input signals controlling the propagation control fields.

CROSS-REFERENCE TO RELATED PATENTS 
This application is related to U.S. Pat. No. 3,845,478, issued Oct. 29, 
1974, assigned to the assignee of this invention. 
BACKGROUND OF THE INVENTION 
This invention relates to a hard magnetic bubble domain analog multiplier 
having an improved linear response of bubble domain propagating velocities 
produced by the product of two propagation control magnetic fields. More 
particularly, the invention relates to a hard magnetic bubble domain 
analog multiplier having repulsive boundaries defining a propagating 
channel perpendicular to the direction of a driving field gradient 
established by one of the two control fields. 
Prior magnetic domain analog computational arrangements are known utilizing 
drive control magnetic fields for propagating single wall magnetic domains 
or bubble domains with predetermined responses. The velocity and direction 
of bubble domains are controlled in a domain multiplier computational 
arrangement by the combined response to at least two drive control fields. 
Computational inputs are formed by electrical signals related to 
quantities to be computed upon. These electrical input signals control or 
produce the drive control magnetic fields directed into a predetermined 
magnetic bubble domain propagating path or channel. Examples of analog 
bubble domain computational arrangements are disclosed in the above 
cross-referenced Pat. No. 3,845,478 and also in U.S. Pat. No. 3,825,910 
issued July 23, 1974 also assigned to the assignee of this invention. 
Magnetic bubble domains are propagated in accordance with the disclosure of 
U.S. Pat. No. 3,825,910 by a self-induced magnetic drive field established 
when a bubble domain is moved above a semiconductor drive layer having a 
uniform current density. Various analog computational arrangements are 
described in the aforementioned patent with a bubble domain being 
propagated by a field carried with the domain. In one arrangement, an 
additional control magnetic field is applied to a predetermined 
propagating channel so that the velocity of the magnetic bubble domain is 
proportional to the product of the controlled magnetic field and the level 
of the uniform current density layer producing the induced field. In the 
latter arrangement, the net displacement of the bubble domain produces a 
computational output proportional to the product of two quantities 
controlling the control magnetic field and the uniform drive layer 
current. Some limitations are found in the device just described in the 
difficulty of obtaining semiconductor materials having proper Hall effect 
characteristics. The complex interactions of magnetic fields including 
those including the Hall effect field interactions produce some difficulty 
in controlling the resultant bubble domain movement. It is noted that the 
basic mode of propagating bubble domains in the above-described device 
differs from that of the present invention. 
The present invention is more directly related to and is an improvement of 
the bubble domain computational arrangement disclosed in the above 
cross-referenced U.S. Pat. No. 3,845,478. The arrangement disclosed 
propagates magnetic bubble domains in response to the product of two drive 
control magnetic fields controlled by two alternating current input 
signals. The first drive control field is effective to modulate the bubble 
domain size or diameter and the second drive control field produces a 
modulated field gradient applied across the bubble domain. Bubble domains 
are driven at an average velocity associated with a net displacement 
proportional to the product of the variations in the domain size and the 
level of the field gradient. Input signals, proportional to voltage and 
current components of an electric power consumption quantity to be 
computed, are effective to separately control the first and second drive 
control fields. The net velocity of the magnetic bubble domain is a 
computed measurement of electric power. Accordingly, the detected 
displacement of the magnetic bubble domain provides an indication of the 
time integral of the multiplied voltage and current quantities and thus a 
computed measure of electrical energy. 
The direction of the magnetic bubble domain net displacement in the U.S. 
Pat. No. 3,845,478 is along the direction of the controlled magnetic field 
gradient with the magnetic bubble domains being soft or normal magnetic 
bubble domains. The described propagated movement is oscillatory with 
reciprocating motion rather than with a cyclical orbital motion produced 
in the present invention. It has been observed that in the operation of 
the propagating device of the aforementioned patent, the controlled field 
gradient may produce substantial modulation of the magnetic bubble domain 
diameter in addition to the variations in the bubble domain diameter 
produced by the size modulating field. Since the domain size is directly 
interrelated to associated driving field gradient, the dynamic range of 
input signals is sometimes limited. Undesirably, the magnetic bubble 
domain is propagated so that its velocity is not directly related to the 
product of the two drive control fields. This occurs since the two fields 
do not independently modulate the domain diameter and field gradient. The 
domain diameter variations due to the controlled field gradient are 
referred to as a self-multiplication effect of the magnetic bubble. 
Accordingly, it is desirable to avoid self-multiplication, drift 
components in the net bubble domain displacement, and other effects 
producing non-linear response in a magnetic bubble domain analog 
multiplier device and especially those effects causing unacceptable mixing 
of the two drive control field contributions to domain computational 
movement. To improve these undesired effects, the present invention 
utilizes the propagating characteristics of hard magnetic domains having 
what is believed a more complex magnetically defined wall structure to 
provide an oscillatory cyclical motion that produces a net displacement 
more linearly responsive to the product of two propagating control fields. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, a hard magnetic bubble domain 
analog multiplier includes an elongated strip layer of bubble domain 
material having a propagating channel defined by substantially parallel 
repulsive boundaries extending between the strip ends. A bias field 
establishes a hard magnetic bubble domain in the channel. Two propagation 
control fields are applied into the channel such that a first and domain 
diameter control field modulates the bias field in response to a first 
alternating current input signal related to a first quantity to be 
computed upon. A second control field effects a driving field gradient in 
a direction across the width of the channel. The driving field gradient is 
varied in response to a second alternating current input signal. The 
latter input signal is related to a second quantity to be computed upon by 
being multiplied by the first quantity. The two propagation control fields 
are cyclically varying to propagate the hard magnetic bubble domains in 
orbital paths so as to have a net displacement along a predetermined axis. 
The measured net displacement or time for a predetermined net displacement 
distance is an indication of a computed time integral of the product of 
the two quantities to be computed upon. The repulsive boundaries restrict 
the hard bubble domain orbital travel that is transverse to the 
predetermined axis of net displacement as the bubble domain moves in 
controlled orbits having substantially equal and opposite transverse 
displacement components and a net longitudinal displacement component 
along the channel axis. The resulting net displacement is proportional to 
the product of the magnitudes and the phase angle between the two 
alternating current computational input signals. Net displacement of the 
magnetic bubble domains is sensed by domain detectors. 
It is a general feature of this invention to provide an improved hard 
magnetic bubble domain analog multiplier for multiplication of two 
alternating current signals. In a preferred form of this invention, a 
channel is formed by repulsive boundaries adjacent the narrow parallel 
edges of a strip of domain material extending transversely to a driving 
field gradient. The channel contains the driven orbital excursions of hard 
bubble domains produced by the field gradient and the domain diameter 
control field. It is a further feature of this invention to produce 
channel boundaries by repulsion magnetic field sources which are effective 
to repel the transverse movement in the bubble domain orbital trajectory 
that is directed away from a predetermined longitudinal axis of measured 
bubble domain net displacement. A still further feature of this invention 
is to effect net displacement of cyclical and orbital hard bubble domain 
motion along a neutral axis of a driving field gradient to reduce 
propagation errors in an analog multiplier. In a bubble domain analog 
multiplier having a strip layer of hard bubble domain material and an 
adjacent ribbon of conductive material carrying a uniform current density 
so as to produce a driving field gradient having a neutral field axis, the 
side edges of the domain material are disposed equidistant from the 
neutral field axis so that the repulsive boundaries maintain the bubble 
domain net displacement along the neutral axis. A still further feature of 
this invention is to provide a hard bubble domain analog multiplier 
wherein a driving field gradient source is formed by spaced current 
carrying conductors having current flow in predetermined directions to 
generate a field gradient having a centrally disposed neutral axis 
relative to repulsive boundaries extending perpendicular to the direction 
of the gradient field. 
Other features and advantages of this invention will be apparent from the 
description of the preferred embodiments of the invention shown in the 
drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now to FIG. 1 of the drawings, a magnetic bubble domain computing 
system 12 is illustrated including a hard magnetic bubble domain analog 
multiplier 14 which is made in accordance with the present invention. The 
multiplier 14 includes a strip layer 18 of magnetic bubble domain material 
of a type capable of having a hard magnetic bubble domain 20 established 
and moved therein. The multiplier 14 is an improvement of the magnetic 
bubble domain propagating device disclosed in U.S. Pat. No. 3,845,478, 
issued Oct. 29, 1974 and issued to the assignee of this invention. Both 
the device of the aforementioned patent and the multiplier 14 move or 
propagate a magnetic bubble domain at a velocity directly related to 
variations in the bubble domain diameter and the modulated strength of a 
magnetic field gradient produced across the bubble domain diameter. As 
explained more fully herein below, the characteristics of the bubble 
domains and domain propagation relative to the field gradient differ in 
the present invention. 
The hard magnetic bubble domain 20 is moved in the strip layer 18 in 
response to first and second cyclically varying drive or propagation 
control fields Hd and Hg directed perpendicularly through the plane of the 
strip layer 18. The propagation control field Hd is effective to vary the 
bubble domain diameter hereinafter referred to as the domain diameter 
control field and the propagation control field Hg is effective to produce 
a driving magnetic field gradient across the bubble domain diameter and is 
referred to hereinafter as the driving field gradient. As described more 
fully in connection with the description of FIGS. 2 and 4, the magnetic 
bubble domain 20 is movable toward either end 21A or 21B of the strip 
layer 18 at a net or average velocity related to the product of the 
control fields Hd and Hg. Thus, the desired net domain propagation is 
perpendicular to the direction of the driving field gradient rather than 
along the direction of the gradient control field as disclosed in the 
aforementioned U.S. Pat. No. 3,845,478. 
The hard bubble domain 20 is a type of single wall magnetic domain having a 
substantially cylindrical bubble configuration wherein the direction of 
magnetization within the bubble domain is opposite to the direction of 
magnetization of the material of the strip 18 as it is in a normal or soft 
bubble domain. It has been observed that some bubble domains have 
different mobility and direction of movement characteristics. It is 
believed that these differences are distinguished by characterizing the 
bubble domains as being normal or soft bubble domains or hard bubble 
domains as is the bubble domain 20. These differences are explained by 
differences in the magnetic structure of cylindrical walls of the bubble 
domains which have a finite thickness. The cylindrical walls separate the 
opposite directions of magnetization inside and outside of the bubble 
domain with the opposite directions being perpendicular to the top and 
bottom surfaces of layer 18. Hard bubble domain generation is achieved 
using principles and methods described in a paper "Extraordinary Bubbles 
In Epitaxial Garnet Films" by H. Nishida, T. Kobayashi and Y. Sugita; 
A.I.P. Conference Proceedings No. 10, Part 1 (Magnetism and Magnetic 
Materials - 1972), pages 493-497, American Institute of Physics, N.Y. 
1973. 
One different characteristic of hard bubble domains is the direction of 
domain propagation in response to the direction of a magnetic field 
gradient applied across the domain diameter. Hard bubble domain motion is 
at an angle to the direction of the driving field gradient rather than 
parallel to the field gradient as described in the U.S. Pat. No. 
3,845,478. It is to be understood that the direction of a field gradient 
is the direction in which the rate of change in the intensity or strength 
of the magnetic field gradient is greatest, keeping in mind that the 
driving field gradient is oscillatory. In the bubble domain propagating 
device disclosed in the aforementioned U.S. Pat. No. 3,845,478, a desired 
bubble domain motion is described for a normal or soft bubble domain which 
has motion which is along or parallel to the direction of the field 
gradient exerted thereacross, as noted above. The present invention 
advantageously utilizes the characteristics of hard bubble domains in 
which the cyclical orbiting bubble domain movement has a net displacement 
in a direction perpendicular to the direction of the magnetic field 
gradient as described further hereinbelow. 
To produce the driving field gradient Hg, forming one propagation control 
field, the domain analog multiplier 14 has associated therewith a ribbon 
layer 22 of conductive material, in one preferred embodiment. The layer 22 
may have different length and width dimensions than the layer 18. An A.C. 
input current signal Ig is applied through the ribbon layer 22 so as to 
have a uniform current density throughout the ribbon layer which has a 
thin uniform thickness. The current signal Ig in the ribbon layer 22 
generates the control field Hg described further hereinbelow. To produce 
the domain diameter control field Hd, forming the other propagation 
control field, a conductor loop 24 is formed in a parallel plane 
relationship above the strip layer 18. The A.C. input current signal Id is 
applied to the conductor loop 24. The current Id generates the magnetic 
field Hd uniformly and in a perpendicular direction into the plane of the 
strip 18 where the bubble domain 20 is to be moved. Accordingly, the input 
current signals Id and Ig form first and second computational input 
signals, respectively, for generating the two propagation control fields 
being related to first and second quantities to be multiplied together in 
operation of the multiplier 14. 
Before describing in detail the operation of the bubble domain analog 
multiplier 14 and the response of the bubble domain 20 to the associated 
magnetic fields, the magnetic bubble domain computating system 12 is now 
generally described as an example of one typical use of the bubble domain 
analog multiplier 14 made in accordance with this invention. The 
computating system 12 is arranged to measure the electrical energy 
supplied through the conductors 26 and 27. An A.C. voltage quantity Vp and 
an A.C. current quantity Ip define the components of electrical power 
occurring in the conductors 26 and 27. It is well known that the 
electrical energy carried in the conductors 26 and 27 and measured in 
kilowatt hours is equal to the time integral of the power flow in these 
conductors. 
Signal conditioning circuits 29 and 30 develop the A.C. input current 
signals Ig and Id respectively, so that they are directly related, for 
example, in magnitude and phase, to the voltage and current quantities VP 
and Ip. The levels of the input signals are controlled by the signal 
conditioning circuits 29 and 30 to be appropriate for producing the 
related magnetic bubble domain driving characteristics of the propagation 
control fields Hd and Hg. A phase reverser circuit 31 is connected between 
the signal conditioning circuit 30 and the ribbon layer 22 to selectively 
reverse or shift the phase angle of the current signal Ig one hundred 
eighty degrees for purposes described in detail hereinbelow. 
For the computating system 12 to initiate and synchronize magnetic bubble 
domain propagations for the desired analog computational operation, a 
control circuit 32 is provided. A bias field is provided by a permanent 
magnet, not shown, which produces the constant D.C. bias field Hb. A hard 
magnetic bubble domain generator 34 is controlled by the control circuit 
32 to develop a hard magnetic bubble domain 20 preferably adjacent one end 
of the strip layer 18 and along a predetermined axis 36 of the strip layer 
18. The axis 36 extends longitudinally between the ends 21A and 21B of 
strip layer 18 as a reference path for net displacement in the domain 
orbital travel between the ends 21A and 21B. The bubble domain 20 may 
progress in opposite directions in the strip layer 18 and along the axis 
36 when the differences in phase relationship between the alternating 
current input signals Id and Ig is reversed. The control circuit 32 
controls the phase reverser circuit 31 to effect reversal of the direction 
of the domain net displacement. An optionally provided bubble annihilator 
source 40 is also controlled by the control circuit 32 so that when the 
magnetic bubble domains have traversed to the ends of the strip layer 18 
they can be eliminated and a new domain can be generated when the 
reversing operation is not desired. Successive domains are moved in a 
common direction of net displacement in the latter mode of operation. A 
computational output circuit formed by a pulse counter 41 provides an 
indication of measured electrical energy as described more fully 
hereinbelow. 
A pair of bubble domain detectors 42 and 44, which may be of a known type 
utilizing magnetoresistive, Halleffect or like devices, are effective to 
generate a signal across output conductors connected to the domain 
detector circuits 46 and 48, respectively in response to the magnetic 
field associated with a bubble domain passing thereunder. The detectors 42 
and 44 are positioned adjacent the ends 21A and 21B at opposite ends of 
the axis 36. The detector signals are applied as pulses 50 and 52 to the 
circuit 32 upon originating from the detectors 42 and 44. The pulses 50 
and 52 are effective to produce pulses 54 from the circuit 32 to the pulse 
counter 41. The output pulses 54 are proportional to the time between the 
instant the bubble domain 20 is generated under one of the domain 
detectors 42 or 44 and the instant it reaches the other one of the 
detectors. The time between the pulses 54 provides an indication of the 
elapsed time that a bubble domain 20 is moved under control of the 
propagation control fields Hd and Hg along the axis 36 between positions 
beneath first one of the detectors 42 and 44 and then the other. Upon 
reaching a detector, the pulses 50 or 52 are effective to operate the 
phase reverser circuit 31 and reverse the domain travel. Alternatively, 
one of the pulses 50 or 52 can activate the annihilator 40 and the domain 
generator 34 to repeat domain travel in the same direction. 
The domain analog multiplier 14 moves the bubble 20 in cyclical orbits with 
a net displacement along the axis 36 at an average velocity proportional 
to the product of the propagation control fields Hg and Hd. Domain 
propagation is in a channel 58 of the layer 18 extending substantially 
parallel to the axis 36 and the side edges 59 and 60 of the strip layer 
18. The channel 58 has side repulsive boundaries 62 and 64 extending 
between the opposite ends 21A and 21B of the strip layer 18 where the 
detectors 42 and 44 are positioned. The repulsive boundaries 62 and 64 are 
formed substantially equidistant from the axis 36 of the layer 18 and are 
immediately adjacent the edges 59 and 60. The side edges are effective to 
form the boundaries 62 and 64 as described more fully hereinbelow in 
connection with the detailed description of the magnetic fields associated 
with the hard bubble multiplier 14 hereinafter and more particularly in 
accordance with the description of FIG. 3. 
FIG. 2 illustrates an enlarged perspective view of the multiplier 14 shown 
in FIG. 1 for purposes of illustrating the magnetic fields associated 
therewith. The bias field Hb established by steady D.C. field maintains an 
average or optimum hard magnetic bubble domain size and diameter and is 
represented in FIG. 2 by the directional arrows 66 directed by the bias 
magnet perpendicular to the flat top and bottom surfaces of the strip 
layer 18. As is understood by those skilled in the art, the direction of 
magnetization of the hard bubble domain 20 is downward to be opposite to 
the direction of magnetization of the remaining portion of the strip layer 
18 and to the bias field Hb. The bias field Hb is constant with time and 
uniform in space throughout the area of the strip layer 18. 
The input current signal Id is taken as having a sinusoidal waveform by way 
of illustration and not limitation in this invention to produce a 
sinusoidally cyclically varying domain diameter control field Hd. The 
directional arrows 68 indicate the direction of the control field Hd at 
one instant of time. The field Hd varies between maximum magnitudes in 
opposite directions in a sinusoidally varying manner uniformly so as to be 
time varying in accordance with the frequency of the input signal Id. 
Also, the loop 24 produces the field Hd so that it is uniform in space at 
any given instant through the area of the strip layer 18. The control 
field Hd effectively modulates the bias field Hb to modulate the diameter 
of the hard bubble domain 20. When the field Hd is in the direction of the 
directional arrows 68 in FIG. 2 and opposite to the bias field Hb, the 
magnetic bubble 20 is enlarged from its average or neutral diameter, which 
is when the control field Hd is zero. Accordingly, when the direction of 
the control field Hd is reversed from that shown in FIG, 2, the bubble 
domain diameter is smaller than that of its neutral diameter. 
The driving field gradient Hg is represented at one instant of time by the 
directional arrows 70. The field Hg is generated by the uniform current 
flow of the input current Ig flowing in the ribbon layer 22. Due to the 
width of the ribbon 22 and the current flow parallel to the sides of the 
strip and therefore parallel to the channel 58, there is a neutral 
magnetic field axis 71 substantially coinciding and aligned with the 
center of the layer 18 and axis 36 along which the vertically directed 
magnetic field Hg generated by the current Ig is substantially zero. There 
are substantial magnetic fields generated that are horizontal and parallel 
to the plane of the layer 18 but these horizontal fields do not produce 
propagating forces on the bubble domain 20. The intensity of the field Hg 
progressively increases, vertically to the plane of the layer 18, from the 
axis 36 to the side edges of the strip 18 in opposite directions. As 
viewed in FIG. 2, the directional arrows 70 are perpendicular to the top 
and bottom surfaces of the strip layer 18 and upward to the left-hand side 
of the axis 36 and downward along the right-hand side of the axis 36. The 
gradient direction of the field gradient Hg is then along the axis 72 in 
the plane of the strip layer 18 and perpendicular to the axis 36 and also 
perpendicular to the side boundaries of the channel 58. 
The input current Ig has a sinusoidally cyclically varying waveform, by way 
of example, so that the field Hg varies in time between maximum magnitudes 
in opposite directions. Accordingly, at another instant of time, for 
example one hundred eighty electrical degrees in the cycle of the current 
signal Ig, the directional arrow 70 would be downward and upward along the 
left-hand and right-hand sides, respectively, of the axis 36. It is to be 
noted that the phase relationship between the control fields Hg and Hd 
varies in accordance with the phase relationship between the input signals 
Ib and Ig. The latter phase relationship is directly related to the phase 
relationship between the voltage and current quantities Vp and Ip and, 
therefore, the power factor of the electric energy flow in the conductors 
26 and 27 which is to be measured by the multiplier 14 of this invention. 
For purposes of describing this invention, the input current signals are 
taken as being in phase or one hundred eighty degrees difference upon 
operation of the phase reverser circuit 31. 
The hard magnetic bubble 20 is propagated at a net velocity proportional to 
the product the domain diameter control field Hd and the driving field 
gradient Hg with a net displacement along the axis 36. It is noted in the 
aforementioned U.S. Pat. No. 3,845,478 that net bubble domain velocity is 
controlled by the combined effects of the magnetic bubble domain diameter 
and the gradient of the magnetic field across the diameter with net 
displacement in the direction of the field gradient. Translational travel 
of the hard bubble domain 20 is at an angle to the direction of the field 
gradient Hg, indicated by the directional arrow 74 rather than 
substantially along the axis 72 and in the direction of the field gradient 
as in the case of a simple or normal magnetic bubble as disclosed in the 
U.S. Pat. No. 3,845,478. The orbital hard bubble motion effected by the 
cyclic magnetic fields is described hereinafter. 
FIG. 4 illustrates two different modes of propagating a hard magnetic 
domain in accordance with the present invention. The lower portion of the 
strip layer 18 illustrates the preferable mode wherein the net 
displacement is along the axis 36 in the channel 58 having repulsive 
boundaries 62 and 64, as shown in FIGS. 1 and 2. As noted above, the field 
gradient neutral axis is coincident to the axis 36 such that there is zero 
strength of the field Hg along the axis 36. In the upper portion of FIG. 
4, boundary 62 immediately adjacent to the side 59 of the strip layer 18 
is one boundary of a channel 76 and an opposite boundary 77 is associated 
with the immediately adjacent axis 36 so that net domain displacement is 
along a mutual parallel axis 78. 
Directional arrows in FIG. 4 indicate the trajectory of orbital movements 
of a hard bubble domain at various translational positions when the domain 
diameter and driving gradient propagation control fields are oscillating 
through the sinusoidally cyclic variations. With the directions of the two 
control fields as shown in FIGS. 1 and 2, the directional arrow 80 shows 
the movement from an initial hard bubble domain position 82 to a second 
bubble position 83. The bubble domain diameter at the position 82 is 
smaller than that of the position 83 on the axis 36 since the bubble 
domain position 82 is adjacent the repulsive boundary 62 and has a neutral 
size established by the D.C. bias field Hb when the field Hd is passing 
through zero. There is essentially zero domain velocity at the domain 
position 82 which at the maximum left-hand transverse position when field 
gradient is also passing through zero strength. It is noted that this 
repulsive boundary 62 magnetically opposes the hard bubble domain as 
described more fully in connection with the description of FIG. 3. The 
hard bubble domain moves in the field gradient with motion toward lower 
bias fields and generally at an angle to the direction (along the axis 72) 
of field gradient. Increased hardness characteristics of a hard bubble 
domain results in motion more perpendicular or transverse to the direction 
of the field gradient. During the instant when the driving field gradient 
Hg at the left-hand side of the axis 36 and is out of the plane of the 
strip layer 18, the gradient field decreases in strength toward the axis 
36 and produces a force moving the bubble at an angle to the direction of 
the gradient field and along the arrow 80. As noted hereinabove, there is 
more tendency of harder bubble domains to move perpendicular to the field 
gradient, therefore the angle of the directional arrow 80 will be more 
parallel to the axis 36 and perpendicular to the direction of the driving 
field gradient. Concurrently, the direction of the domain diameter control 
field Hd is into the plane of the strip layer 18, the bubble domain 
diameter is increasing so that the propagating force increases due to the 
larger domain diameter. As the control fields Hg and Hd reach a maximum at 
the first ninety degree quadrant of their sinusoidal cycle, the field Hd 
has maximum opposition to the bias field Hb so that the domain diameter is 
maximum and the domain velocity is highest toward the right at the 
position 83. 
The directional arrow 84 indicates the movement of the magnetic bubble 
domain from the position indicated at 83 to the position indicated at 85. 
The magnetic bubble domain approaches the right-hand repulsive boundary 64 
at the side 60 of the strip layer 18 at position 85. It is noted that the 
bubble domain diameter becomes smaller since the field Hd decreases toward 
zero during the second ninety degree quadrant and the D.C. bias field 
strength is opposed less. Although the intensity of the driving field 
gradient Hg at a given instant, will be greatest at the right-hand edge 60 
of the strip 18 as indicated by the length of the arrows in FIG. 2, to 
produce a domain velocity at an angle to the right, the strength of the 
control field Hg decreases to zero during the second ninety degree 
quadrant. Thus, at the position 83 the domain diameter returns to the 
neutral size and the velocity to the right is zero. At the maximum 
right-hand displacement of position 83 the domain also has progressed 
along the axis 36 or in a forward direction toward the end 21B. Further 
drift of the domain is opposed by repulsive boundary 64, as described 
further in connection with the description of FIG. 3, however, the 
propagating forces are negligible since the gradient is at zero strength. 
Upon phase reversal of the input signals Ig and Id and, therefore, the 
field gradient Hg and the diameter control field Hd, have the reverse 
directions from those indicated by the arrows 68 and 70 shown in FIG. 3. 
This occurs during the third ninety degree quadrant of field oscillations. 
The directional arrow 87 indicates the path of the bubble domain from the 
position 85 leftward toward the position 89 at the axis 36. The domain 
diameter control field Hd decreases the diameter of the magnetic bubble 
domain since it increases strength in the direction of the bias field Hb. 
The field gradient Hg effects movement of the bubble domain backward 
toward the end 21A and toward the left at an angle to the direction of the 
gradient control field coming out of the plane on the strip layer 18. The 
velocity reaches a maximum in the leftward direction at the position 89, 
however, the velocity is less than during the propagation indicated by the 
arrow 84 because of the smaller diameter of the domain. As the magnetic 
bubble domain moves to the position 89 it assumes the smallest diameter 
during its orbital motion. The slower domain velocity accounts for the 
less acute angle of the leftward movement of the domain along the arrow 
87. 
In the forth quadrant of the cycle of the oscillations of the propagation 
control fields Hd and Hg, the domain moves along the path indicated by the 
directional arrow 91 to the position 93 adjacent the repulsive boundary 
62. The strengths of the fields are decreasing to zero. Therefore, the 
diameter of the magnetic bubble domain becomes larger and again reaches 
its neutral size and the velocity is reduced to zero. Upon phase reversal 
of the field gradient and domain diameter control fields, the direction of 
the fields are again as shown in FIG. 3 and the hard magnetic bubble 
domain starts a new orbital propagation cycle along the directional arrow 
95 which is displaced from the corresponding directional arrow 80 by the 
amount of net displacement parallel to the axis 36. This net displacement 
produced by the complete orbit described is at a net velocity proportional 
to the product of the fields Hg and Hd. The domain then continues in an 
orbiting trajectory progressing with a net displacement along the 
propagating axis 36. The net displacement along the axis 37, for example 
between the positions 82 and 93, is a length of net movement which is 
proportional to the time integral of the product of the domain diameter 
control field Hd and the driving field gradient Hg. 
In the computating system 12, the time required for a domain to travel the 
predetermined distance between detectors 42 and 44 along the axis 36 is 
indicated by a detector pulse. The detector pulses 50 and 52 are then 
proportional to the time integral of the product of the two drive control 
fields Hd and Hg and the associated input signals. Effectively, each pulse 
50 and 52 produced in response to the net displacement of a domain 
traveling from one detector to the other is representative of a 
predetermined amount of electrical energy flow in the conductors 26 and 
27. Thus, the pulse counter 41 forms a computational output circuit where 
the pulses 54 are indicative of electrical energy flow in kilowatt hours. 
The upper portion of FIG. 4, within the strip layer 18 shows an alternative 
mode of propagating a hard magnetic bubble domain wherein the propagating 
channel 76 is formed between the repulsive boundary 62 adjacent the side 
edge 59 of the strip layer 18, as described hereinabove, and the boundary 
77 adjacent the axis 36 which is coincident with neutral center axis of 
the field gradient Hg and has found to form a repulsive boundary under 
carefully controlled field conditions. The directional arrows 102, 103, 
104 and 105 indicate one orbit of progressive propagation of a hard 
magnetic bubble domain between positions 107, 108, 109, 110 and 111. The 
arrows between the magnetic bubble domain positions 107, 108, 109, 110 and 
111 are similar to the description for the above-described propagation of 
the bubble domain beginning with the directional arrow 80 and ending with 
the directional arrow 91. The magnetic bubble domain is propagated with a 
net displacement along the axis 78. 
The net propagation axis 78 is parallel to the neutral axis of the driving 
field gradient Hg and the position of the axis is dependent upon the 
spacing between the center axis 36 and the side edge 50. By careful 
control of the strength of Hg, the spacing must be large enough not to 
force the bubble domain over the axis 36 and small enough not to allow the 
bubble net motion to drift such that bias field change due to the field 
gradient will exceed stability limits. It has been observed that the 
propagation incurs different amounts of the above-mentioned 
self-multiplication so that the net displacement along the axis 78 is in a 
somewhat non-linear relationship to the propagation control fields Hd and 
Hg. The net displacement of hard bubble domains in accordance with the 
embodiment just described, can provide a measure of the multiplication of 
the two A.C. input current signals Ig and Id. 
Referring now to FIG. 3, there is illustrated a cross-sectional view of the 
strip layer 18 for purposes of explanation of the domain repulsive effects 
produced by the side edges 59 and 60. The repulsive boundaries 62 and 64 
adjacent the side edges are representative of the magnetic repulsive 
effect on the hard bubble domain 20. It is an important aspect of this 
invention that repulsive boundaries extend parallel and substantially 
equidistant from the propagating axis 36 that extends in the plane of the 
neutral axis of the driving field gradient Hg. Non-linearities in domain 
movement transverse to the axis 36 are somewhat balanced out or cancelled. 
The edges are effective to define the repulsive boundaries 62 and 64 
because they each are a terminus of the magnetic material forming the 
layer 18. A change in the physical structure of material occurs on 
opposite sides of the side edges 59 and 60. 
The upwardly directed arrows 115 indicate the magnetization of the layer 18 
established by the D.C. bias field Hb and arrows 117 indicate the opposite 
magnetization of the hard bubble domain 20. The closed loop flux lines 119 
and 120 occur outside the layer 18 adjacent edges 59 and 60, respectively 
due to the magnetization of the layer 18 and absence of the domain 
magnetic material beyond the side edges. These flux lines are equivalent 
to an externally applied repulsive field since they occur externally of 
the layer 18. The direction of the field flux lines is opposite to the 
field associated with the bubble domain 20. As the domain reaches an area 
of the layer 18 close to one of the edges 59 or 60 indicated by the 
repulsive boundaries 62 and 64 it is subject to the fields indicated by 
the flux lines 119 and 120. These magnetically oppose the bubble domain 
such that a magnetic wall formed by a repulsive force acting on the domain 
20 to guide it. The repulsive boundaries help maintain the domain along an 
average parallel path along the axis when the driving field pushes the 
domain at an angle to the boundaries as indicated in FIG. 3. As noted 
further hereinbelow, the boundaries can be formed alternatively by a 
magnetic field source producing a repulsive magnetic field. The essential 
function of the boundaries is maintain the hard domain net displacement 
along the neutral axis of the field gradient Hg, in the one preferred 
embodiment shown in FIGS. 1 and 2. 
In FIG. 5 is illustrated an alternative embodiment of a hard bubble domain 
analog multiplier 114. A strip layer 116 of hard bubble domain magnetic 
material is provided corresponding to the layer 18 described above for 
movement of a hard bubble domain 118 therein. A D.C. bias field Hb and 
domain diameter control field for modulating the bias field Hb in response 
to the input signal Id is provided as described for the multiplier 14. 
An alternative source of the driving field gradient Hg is formed by the 
parallel conductors 120 and 121 carrying the input current signal Ig. With 
the current Ig applied in the same direction relative to common end 
portions of the conductors as shown in FIG. 5, the portion of the gradient 
field Hg associated with each conductor is directed into the layer 116 on 
opposite sides of a center propagating axis 124. The fields cancel each 
other along the axis 124 so that it is also the neutral axis of the 
driving field gradient Hg. The slopes of the strengths increase from the 
axis 124 in opposite directions toward the side edges 126 and 127 at the 
same value and in the same manner as described for the field gradient Hg 
described above and shown in FIG. 2. The field Hg is cyclically varying, 
also as previously described, to produce net domain displacement along the 
neutral field axis of the gradient field as an important feature of this 
invention as also previously noted. 
Repulsive boundaries 128 and 129 are formed at equal distance from the axis 
124 to guide the orbital trajectories of the domain 118 along the axis in 
a channel 130. The flux lines indicated by arrows 131 and 132 define 
domain repulsive magnetic fields generated by current Ir flowing in the 
conductors 134 and 135 extending along the side edges 126 and 127, 
respectively. The flux lines 131 and 132 oppose the hard bubble domain 118 
as it moves adjacent the boundaries 128 and 129 in an analogous manner 
that the flux lines 119 and 120, shown in FIG. 3, oppose the domain 20. 
The strength of the repulsive magnetic fields generated along the 
conductors 134 and 135 are related to the thickness of the layer 116, 
magnetization of the layer 116 and the bubble domain diameter. The hard 
bubble domain analog multiplier 114 can be utilized in the domain 
computing system 12 to perform multiplication of the A.C. current input 
signals Id and Ig and measurement of electrical energy flow as described 
in connection with the description of FIG. 1. 
It is contemplated that other alternative arrangements can provide the 
cyclical varying domain diameter control field Hd, the driving field 
gradient Hg and the repulsive magnetic field for forming repulsive 
boundaries at predetermined spacings from an axis of net displacement of 
hard bubble domain propagation. In accordance with the preferred form of 
this invention, the net displacement axis is to coincide with the neutral 
axis of a driving field gradient directed into the hard domain material in 
opposite field directions on opposite sides of the neutral axis. 
While preferred embodiments of this invention are disclosed hereinabove, it 
is to be understood that other embodiments may be made without departing 
from the spirit and scope of this invention.