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Analog computer
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Computer that uses continuously variable technology
For the Atari 8-bit computer magazine, see ANALOG Computing.
A page from the Bombardier's Information File (BIF) that describes the
components and controls of the Norden bombsight. The Norden bombsight
was a highly sophisticated optical/mechanical analog computer used by
the United States Army Air Force during World War II, the Korean War,
and the Vietnam War to aid the pilot of a bomber aircraft in dropping
bombs accurately.
TR-10 desktop analog computer of the late 1960s and early 70s
An analog computer or analogue computer is a type of computer that uses
the continuous variation aspect of physical phenomena such as
electrical, mechanical, or hydraulic quantities (analog signals) to
model the problem being solved. In contrast, digital computers
represent varying quantities symbolically and by discrete values of
both time and amplitude (digital signals).
Analog computers can have a very wide range of complexity. Slide rules
and nomograms are the simplest, while naval gunfire control computers
and large hybrid digital/analog computers were among the most
complicated.^[1] Complex mechanisms for process control and protective
relays used analog computation to perform control and protective
functions.
Analog computers were widely used in scientific and industrial
applications even after the advent of digital computers, because at the
time they were typically much faster, but they started to become
obsolete as early as the 1950s and 1960s, although they remained in use
in some specific applications, such as aircraft flight simulators, the
flight computer in aircraft, and for teaching control systems in
universities. Perhaps the most relatable example of analog computers
are mechanical watches where the continuous and periodic rotation of
interlinked gears drives the seconds, minutes and hours needles in the
clock. More complex applications, such as aircraft flight simulators
and synthetic-aperture radar, remained the domain of analog computing
(and hybrid computing) well into the 1980s, since digital computers
were insufficient for the task.^[2]
[ ]
Contents
* 1 Timeline of analog computers
+ 1.1 Precursors
+ 1.2 Modern era
* 2 Electronic analog computers
* 3 Analog-digital hybrids
* 4 Implementations
+ 4.1 Mechanical analog computers
+ 4.2 Electronic analog computers
* 5 Components
* 6 Limitations
* 7 Decline
* 8 Resurgence
* 9 Practical examples
* 10 See also
* 11 Notes
* 12 References
* 13 External links
Timeline of analog computers[edit]
See also: History of computing hardware S: Analog computers
Precursors[edit]
See also: Timeline of computing hardware before 1950
This is a list of examples of early computation devices considered
precursors of the modern computers. Some of them may even have been
dubbed 'computers' by the press, though they may fail to fit modern
definitions.
The Antikythera mechanism, dating between 150 and 100 BC, was an early
analog computer.
The Antikythera mechanism was an orrery and is considered an early
mechanical analog computer, according to Derek J. de Solla Price.^[3]
It was designed to calculate astronomical positions. It was discovered
in 1901 in the Antikythera wreck off the Greek island of Antikythera,
between Kythera and Crete, and has been dated to c. 100 BC during the
Hellenistic period of Greece. Devices of a level of complexity
comparable to that of the Antikythera mechanism would not reappear
until a thousand years later.
Many mechanical aids to calculation and measurement were constructed
for astronomical and navigation use. The planisphere was first
described by Ptolemy in the 2nd century AD. The astrolabe was invented
in the Hellenistic world in either the 1st or 2nd centuries BC and is
often attributed to Hipparchus. A combination of the planisphere and
dioptra, the astrolabe was effectively an analog computer capable of
working out several different kinds of problems in spherical astronomy.
An astrolabe incorporating a mechanical calendar computer^[4]^[5] and
gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235.^[6]
Abu Rayhan al-Biruni invented the first mechanical geared lunisolar
calendar astrolabe,^[7] an early fixed-wired knowledge processing
machine^[8] with a gear train and gear-wheels,^[9] c. AD 1000. The
castle clock, a hydropowered mechanical astronomical clock invented by
Al-Jazari in 1206, was the first programmable analog
computer.^[10]^[11]^[12]
The sector, a calculating instrument used for solving problems in
proportion, trigonometry, multiplication and division, and for various
functions, such as squares and cube roots, was developed in the late
16th century and found application in gunnery, surveying and
navigation.
The planimeter was a manual instrument to calculate the area of a
closed figure by tracing over it with a mechanical linkage.
A slide rule. The sliding central slip is set to 1.3, the cursor to 2.0
and points to the multiplied result of 2.6.
The slide rule was invented around 1620-1630, shortly after the
publication of the concept of the logarithm. It is a hand-operated
analog computer for doing multiplication and division. As slide rule
development progressed, added scales provided reciprocals, squares and
square roots, cubes and cube roots, as well as transcendental functions
such as logarithms and exponentials, circular and hyperbolic
trigonometry and other functions. Aviation is one of the few fields
where slide rules are still in widespread use, particularly for solving
time-distance problems in light aircraft.
In 1831-1835, mathematician and engineer Giovanni Plana devised a
perpetual-calendar machine, which, through a system of pulleys and
cylinders, could predict the perpetual calendar for every year from
AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and
varying day length.^[13]
The tide-predicting machine invented by Sir William Thomson in 1872 was
of great utility to navigation in shallow waters. It used a system of
pulleys and wires to automatically calculate predicted tide levels for
a set period at a particular location.
The differential analyser, a mechanical analog computer designed to
solve differential equations by integration, used wheel-and-disc
mechanisms to perform the integration. In 1876 James Thomson had
already discussed the possible construction of such calculators, but he
had been stymied by the limited output torque of the ball-and-disk
integrators. A number of similar systems followed, notably those of the
Spanish engineer Leonardo Torres y Quevedo, who built several machines
for solving real and complex roots of polynomials; and Michelson and
Stratton, whose Harmonic Analyser performed Fourier analysis, but using
an array of 80 springs rather than Kelvin integrators. This work led to
the mathematical understanding of the Gibbs phenomenon of overshoot in
Fourier representation near discontinuities.^[14] In a differential
analyzer, the output of one integrator drove the input of the next
integrator, or a graphing output. The torque amplifier was the advance
that allowed these machines to work. Starting in the 1920s, Vannevar
Bush and others developed mechanical differential analyzers.
Modern era[edit]
Analog computing machine at the Lewis Flight Propulsion Laboratory
circa 1949.
Heathkit EC-1 educational analog computer
The Dumaresq was a mechanical calculating device invented around 1902
by Lieutenant John Dumaresq of the Royal Navy. It was an analog
computer that related vital variables of the fire control problem to
the movement of one's own ship and that of a target ship. It was often
used with other devices, such as a Vickers range clock to generate
range and deflection data so the gun sights of the ship could be
continuously set. A number of versions of the Dumaresq were produced of
increasing complexity as development proceeded.
By 1912, Arthur Pollen had developed an electrically driven mechanical
analog computer for fire-control systems, based on the differential
analyser. It was used by the Imperial Russian Navy in World War
I.^[citation needed]
Starting in 1929, AC network analyzers were constructed to solve
calculation problems related to electrical power systems that were too
large to solve with numerical methods at the time.^[15] These were
essentially scale models of the electrical properties of the full-size
system. Since network analyzers could handle problems too large for
analytic methods or hand computation, they were also used to solve
problems in nuclear physics and in the design of structures. More than
50 large network analyzers were built by the end of the 1950s.
World War II era gun directors, gun data computers, and bomb sights
used mechanical analog computers. In 1942 Helmut Hoelzer built a fully
electronic analog computer at Peenemuende Army Research
Center^[16]^[17]^[18] as an embedded control system (mixing device) to
calculate V-2 rocket trajectories from the accelerations and
orientations (measured by gyroscopes) and to stabilize and guide the
missile.^[19]^[20] Mechanical analog computers were very important in
gun fire control in World War II, The Korean War and well past the
Vietnam War; they were made in significant numbers.
In the period 1930-1945 in the Netherlands, Johan van Veen developed an
analogue computer to calculate and predict tidal currents when the
geometry of the channels are changed. Around 1950, this idea was
developed into the Deltar, a hydraulic analogy computer supporting the
closure of estuaries in the southwest of the Netherlands (the Delta
Works).
The FERMIAC was an analog computer invented by physicist Enrico Fermi
in 1947 to aid in his studies of neutron transport.^[21] Project
Cyclone was an analog computer developed by Reeves in 1950 for the
analysis and design of dynamic systems.^[22] Project Typhoon was an
analog computer developed by RCA in 1952. It consisted of over 4,000
electron tubes and used 100 dials and 6,000 plug-in connectors to
program.^[23] The MONIAC Computer was a hydraulic analogy of a national
economy first unveiled in 1949.^[24]
Computer Engineering Associates was spun out of Caltech in 1950 to
provide commercial services using the "Direct Analogy Electric Analog
Computer" ("the largest and most impressive general-purpose analyzer
facility for the solution of field problems") developed there by
Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi.^[25]^[26]
Educational analog computers illustrated the principles of analog
calculation. The Heathkit EC-1, a $199 educational analog computer, was
made by the Heath Company, US c. 1960.^[27] It was programmed using
patch cords that connected nine operational amplifiers and other
components.^[28] General Electric also marketed an "educational" analog
computer kit of a simple design in the early 1960s consisting of a two
transistor tone generators and three potentiometers wired such that the
frequency of the oscillator was nulled when the potentiometer dials
were positioned by hand to satisfy an equation. The relative resistance
of the potentiometer was then equivalent to the formula of the equation
being solved. Multiplication or division could be performed, depending
on which dials were inputs and which was the output. Accuracy and
resolution was limited and a simple slide rule was more accurate.
However, the unit did demonstrate the basic principle.
Analog computer designs were published in electronics magazines. One
example is the PEAC (Practical Electronics analogue computer),
published in Practical Electronics in the January 1968 edition.^[29]
Another more modern hybrid computer design was published in Everyday
Practical Electronics in 2002.^[30] An example described in the EPE
hybrid computer was the flight of a VTOL aircraft such as the Harrier
jump jet.^[30] The altitude and speed of the aircraft were calculated
by the analog part of the computer and sent to a PC via a digital
microprocessor and displayed on the PC screen.
In industrial process control, analog loop controllers were used to
automatically regulate temperature, flow, pressure, or other process
conditions. The technology of these controllers ranged from purely
mechanical integrators, through vacuum-tube and solid-state devices, to
emulation of analog controllers by microprocessors.
Electronic analog computers[edit]
Polish analog computer AKAT-1 (1959)
EAI 8800 Analog computing system used for hardware-in-the-loop
simulation of a Claas tractor (1986)
The similarity between linear mechanical components, such as springs
and dashpots (viscous-fluid dampers), and electrical components, such
as capacitors, inductors, and resistors is striking in terms of
mathematics. They can be modeled using equations of the same form.
However, the difference between these systems is what makes analog
computing useful. Complex systems often are not amenable to
pen-and-paper analysis, and require some form of testing or simulation.
Complex mechanical systems, such as suspensions for racing cars, are
expensive to fabricate and hard to modify. And taking precise
mechanical measurements during high-speed tests adds further
difficulty.
By contrast, it is very inexpensive to build an electrical equivalent
of a complex mechanical system, to simulate its behavior. Engineers
arrange a few operational amplifiers (op amps) and some passive linear
components to form a circuit that follows the same equations as the
mechanical system being simulated. All measurements can be taken
directly with an oscilloscope. In the circuit, the (simulated)
stiffness of the spring, for instance, can be changed by adjusting the
parameters of an integrator. The electrical system is an analogy to the
physical system, hence the name, but it is much less expensive than a
mechanical prototype, much easier to modify, and generally safer.
The electronic circuit can also be made to run faster or slower than
the physical system being simulated. Experienced users of electronic
analog computers said that they offered a comparatively intimate
control and understanding of the problem, relative to digital
simulations.
Electronic analog computers are especially well-suited to representing
situations described by differential equations. Historically, they were
often used when a system of differential equations proved very
difficult to solve by traditional means. As a simple example, the
dynamics of a spring-mass system can be described by the equation
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<annotation encoding="application/x-tex">{\displaystyle m{\ddot
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{\displaystyle m{\ddot {y}}+d{\dot {y}}+cy=mg} , with
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y as the vertical position of a mass
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m ,
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d the damping coefficient,
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c the spring constant and
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g the gravity of Earth. For analog computing, the equation is
programmed as
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{\displaystyle {\ddot {y}}=-{\tfrac {d}{m}}{\dot {y}}-{\tfrac
{c}{m}}y-g} . The equivalent analog circuit consists of two integrators
for the state variables
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{\displaystyle -{\dot {y}}} (speed) and
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y (position), one inverter, and three potentiometers.
Electronic analog computers have drawbacks: the value of the circuit's
supply voltage limits the range over which the variables may vary
(since the value of a variable is represented by a voltage on a
particular wire). Therefore, each problem must be scaled so its
parameters and dimensions can be represented using voltages that the
circuit can supply --e.g., the expected magnitudes of the velocity and
the position of a spring pendulum. Improperly scaled variables can have
their values "clamped" by the limits of the supply voltage. Or if
scaled too small, they can suffer from higher noise levels. Either
problem can cause the circuit to produce an incorrect simulation of the
physical system. (Modern digital simulations are much more robust to
widely varying values of their variables, but are still not entirely
immune to these concerns: floating-point digital calculations support a
huge dynamic range, but can suffer from imprecision if tiny differences
of huge values lead to numerical instability.)
Analog circuit for the dynamics of a spring-mass system (without
scaling factors)
Damped motion of a spring-mass system
The precision of the analog computer readout was limited chiefly by the
precision of the readout equipment used, generally three or four
significant figures. (Modern digital simulations are much better in
this area. Digital arbitrary-precision arithmetic can provide any
desired degree of precision.) However, in most cases the precision of
an analog computer is absolutely sufficient given the uncertainty of
the model characteristics and its technical parameters.
Many small computers dedicated to specific computations are still part
of industrial regulation equipment, but from the 1950s to the 1970s,
general-purpose analog computers were the only systems fast enough for
real time simulation of dynamic systems, especially in the aircraft,
military and aerospace field.
In the 1960s, the major manufacturer was Electronic Associates of
Princeton, New Jersey, with its 231R Analog Computer (vacuum tubes, 20
integrators) and subsequently its EAI 8800 Analog Computer (solid state
operational amplifiers, 64 integrators).^[31] Its challenger was
Applied Dynamics of Ann Arbor, Michigan.
Although the basic technology for analog computers is usually
operational amplifiers (also called "continuous current amplifiers"
because they have no low frequency limitation), in the 1960s an attempt
was made in the French ANALAC computer to use an alternative
technology: medium frequency carrier and non dissipative reversible
circuits.
In the 1970s, every large company and administration concerned with
problems in dynamics had an analog computing center, such as:
* In the US: NASA (Huntsville, Houston), Martin Marietta (Orlando),
Lockheed, Westinghouse, Hughes Aircraft
* In Europe: CEA (French Atomic Energy Commission), MATRA,
Aerospatiale, BAC (British Aircraft Corporation).
Analog-digital hybrids[edit]
Analog computing devices are fast, digital computing devices are more
versatile and accurate, so the idea is to combine the two processes for
the best efficiency. An example of such hybrid elementary device is the
hybrid multiplier where one input is an analog signal, the other input
is a digital signal and the output is analog. It acts as an analog
potentiometer upgradable digitally. This kind of hybrid technique is
mainly used for fast dedicated real time computation when computing
time is very critical as signal processing for radars and generally for
controllers in embedded systems.
In the early 1970s, analog computer manufacturers tried to tie together
their analog computer with a digital computer to get the advantages of
the two techniques. In such systems, the digital computer controlled
the analog computer, providing initial set-up, initiating multiple
analog runs, and automatically feeding and collecting data. The digital
computer may also participate to the calculation itself using
analog-to-digital and digital-to-analog converters.
The largest manufacturer of hybrid computers was Electronics
Associates. Their hybrid computer model 8900 was made of a digital
computer and one or more analog consoles. These systems were mainly
dedicated to large projects such as the Apollo program and Space
Shuttle at NASA, or Ariane in Europe, especially during the integration
step where at the beginning everything is simulated, and progressively
real components replace their simulated part.^[32]
Only one company was known as offering general commercial computing
services on its hybrid computers, CISI of France, in the 1970s.
The best reference in this field is the 100,000 simulation runs for
each certification of the automatic landing systems of Airbus and
Concorde aircraft.^[33]
After 1980, purely digital computers progressed more and more rapidly
and were fast enough to compete with analog computers. One key to the
speed of analog computers was their fully parallel computation, but
this was also a limitation. The more equations required for a problem,
the more analog components were needed, even when the problem wasn't
time critical. "Programming" a problem meant interconnecting the analog
operators; even with a removable wiring panel this was not very
versatile. Today there are no more big hybrid computers, but only
hybrid components.^[citation needed]
Implementations[edit]
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Mechanical analog computers[edit]
Main article: Mechanical computer
William Ferrel's tide-predicting machine of 1881-1882
While a wide variety of mechanisms have been developed throughout
history, some stand out because of their theoretical importance, or
because they were manufactured in significant quantities.
Most practical mechanical analog computers of any significant
complexity used rotating shafts to carry variables from one mechanism
to another. Cables and pulleys were used in a Fourier synthesizer, a
tide-predicting machine, which summed the individual harmonic
components. Another category, not nearly as well known, used rotating
shafts only for input and output, with precision racks and pinions. The
racks were connected to linkages that performed the computation. At
least one U.S. Naval sonar fire control computer of the later 1950s,
made by Librascope, was of this type, as was the principal computer in
the Mk. 56 Gun Fire Control System.
Online, there is a remarkably clear illustrated reference
(OP 1140)^[34] that describes the fire control computer
mechanisms.^[34] For adding and subtracting, precision miter-gear
differentials were in common use in some computers; the Ford Instrument
Mark I Fire Control Computer contained about 160 of them.
Integration with respect to another variable was done by a rotating
disc driven by one variable. Output came from a pick-off device (such
as a wheel) positioned at a radius on the disc proportional to the
second variable. (A carrier with a pair of steel balls supported by
small rollers worked especially well. A roller, its axis parallel to
the disc's surface, provided the output. It was held against the pair
of balls by a spring.)
Arbitrary functions of one variable were provided by cams, with gearing
to convert follower movement to shaft rotation.
Functions of two variables were provided by three-dimensional cams. In
one good design, one of the variables rotated the cam. A hemispherical
follower moved its carrier on a pivot axis parallel to that of the
cam's rotating axis. Pivoting motion was the output. The second
variable moved the follower along the axis of the cam. One practical
application was ballistics in gunnery.
Coordinate conversion from polar to rectangular was done by a
mechanical resolver (called a "component solver" in US Navy fire
control computers). Two discs on a common axis positioned a sliding
block with pin (stubby shaft) on it. One disc was a face cam, and a
follower on the block in the face cam's groove set the radius. The
other disc, closer to the pin, contained a straight slot in which the
block moved. The input angle rotated the latter disc (the face cam
disc, for an unchanging radius, rotated with the other (angle) disc; a
differential and a few gears did this correction).
Referring to the mechanism's frame, the location of the pin
corresponded to the tip of the vector represented by the angle and
magnitude inputs. Mounted on that pin was a square block.
Rectilinear-coordinate outputs (both sine and cosine, typically) came
from two slotted plates, each slot fitting on the block just mentioned.
The plates moved in straight lines, the movement of one plate at right
angles to that of the other. The slots were at right angles to the
direction of movement. Each plate, by itself, was like a Scotch yoke,
known to steam engine enthusiasts.
During World War II, a similar mechanism converted rectilinear to polar
coordinates, but it was not particularly successful and was eliminated
in a significant redesign (USN, Mk. 1 to Mk. 1A).
Multiplication was done by mechanisms based on the geometry of similar
right triangles. Using the trigonometric terms for a right triangle,
specifically opposite, adjacent, and hypotenuse, the adjacent side was
fixed by construction. One variable changed the magnitude of the
opposite side. In many cases, this variable changed sign; the
hypotenuse could coincide with the adjacent side (a zero input), or
move beyond the adjacent side, representing a sign change.
Typically, a pinion-operated rack moving parallel to the
(trig.-defined) opposite side would position a slide with a slot
coincident with the hypotenuse. A pivot on the rack let the slide's
angle change freely. At the other end of the slide (the angle, in trig.
terms), a block on a pin fixed to the frame defined the vertex between
the hypotenuse and the adjacent side.
At any distance along the adjacent side, a line perpendicular to it
intersects the hypotenuse at a particular point. The distance between
that point and the adjacent side is some fraction that is the product
of 1 the distance from the vertex, and 2 the magnitude of the opposite
side.
The second input variable in this type of multiplier positions a
slotted plate perpendicular to the adjacent side. That slot contains a
block, and that block's position in its slot is determined by another
block right next to it. The latter slides along the hypotenuse, so the
two blocks are positioned at a distance from the (trig.) adjacent side
by an amount proportional to the product.
To provide the product as an output, a third element, another slotted
plate, also moves parallel to the (trig.) opposite side of the
theoretical triangle. As usual, the slot is perpendicular to the
direction of movement. A block in its slot, pivoted to the hypotenuse
block positions it.
A special type of integrator, used at a point where only moderate
accuracy was needed, was based on a steel ball, instead of a disc. It
had two inputs, one to rotate the ball, and the other to define the
angle of the ball's rotating axis. That axis was always in a plane that
contained the axes of two movement pick-off rollers, quite similar to
the mechanism of a rolling-ball computer mouse (in that mechanism, the
pick-off rollers were roughly the same diameter as the ball). The
pick-off roller axes were at right angles.
A pair of rollers "above" and "below" the pick-off plane were mounted
in rotating holders that were geared together. That gearing was driven
by the angle input, and established the rotating axis of the ball. The
other input rotated the "bottom" roller to make the ball rotate.
Essentially, the whole mechanism, called a component integrator, was a
variable-speed drive with one motion input and two outputs, as well as
an angle input. The angle input varied the ratio (and direction) of
coupling between the "motion" input and the outputs according to the
sine and cosine of the input angle.
Although they did not accomplish any computation, electromechanical
position servos were essential in mechanical analog computers of the
"rotating-shaft" type for providing operating torque to the inputs of
subsequent computing mechanisms, as well as driving output
data-transmission devices such as large torque-transmitter synchros in
naval computers.
Other readout mechanisms, not directly part of the computation,
included internal odometer-like counters with interpolating drum dials
for indicating internal variables, and mechanical multi-turn limit
stops.
Considering that accurately controlled rotational speed in analog
fire-control computers was a basic element of their accuracy, there was
a motor with its average speed controlled by a balance wheel,
hairspring, jeweled-bearing differential, a twin-lobe cam, and
spring-loaded contacts (ship's AC power frequency was not necessarily
accurate, nor dependable enough, when these computers were designed).
Electronic analog computers[edit]
Switching board of EAI 8800 analog computer (front view)
Electronic analog computers typically have front panels with numerous
jacks (single-contact sockets) that permit patch cords (flexible wires
with plugs at both ends) to create the interconnections that define the
problem setup. In addition, there are precision high-resolution
potentiometers (variable resistors) for setting up (and, when needed,
varying) scale factors. In addition, there is usually a zero-center
analog pointer-type meter for modest-accuracy voltage measurement.
Stable, accurate voltage sources provide known magnitudes.
Typical electronic analog computers contain anywhere from a few to a
hundred or more operational amplifiers ("op amps"), named because they
perform mathematical operations. Op amps are a particular type of
feedback amplifier with very high gain and stable input (low and stable
offset). They are always used with precision feedback components that,
in operation, all but cancel out the currents arriving from input
components. The majority of op amps in a representative setup are
summing amplifiers, which add and subtract analog voltages, providing
the result at their output jacks. As well, op amps with capacitor
feedback are usually included in a setup; they integrate the sum of
their inputs with respect to time.
Integrating with respect to another variable is the nearly exclusive
province of mechanical analog integrators; it is almost never done in
electronic analog computers. However, given that a problem solution
does not change with time, time can serve as one of the variables.
Other computing elements include analog multipliers, nonlinear function
generators, and analog comparators.
Electrical elements such as inductors and capacitors used in electrical
analog computers had to be carefully manufactured to reduce non-ideal
effects. For example, in the construction of AC power network
analyzers, one motive for using higher frequencies for the calculator
(instead of the actual power frequency) was that higher-quality
inductors could be more easily made. Many general-purpose analog
computers avoided the use of inductors entirely, re-casting the problem
in a form that could be solved using only resistive and capacitive
elements, since high-quality capacitors are relatively easy to make.
The use of electrical properties in analog computers means that
calculations are normally performed in real time (or faster), at a
speed determined mostly by the frequency response of the operational
amplifiers and other computing elements. In the history of electronic
analog computers, there were some special high-speed types.
Nonlinear functions and calculations can be constructed to a limited
precision (three or four digits) by designing function
generators--special circuits of various combinations of resistors and
diodes to provide the nonlinearity. Typically, as the input voltage
increases, progressively more diodes conduct.
When compensated for temperature, the forward voltage drop of a
transistor's base-emitter junction can provide a usably accurate
logarithmic or exponential function. Op amps scale the output voltage
so that it is usable with the rest of the computer.
Any physical process that models some computation can be interpreted as
an analog computer. Some examples, invented for the purpose of
illustrating the concept of analog computation, include using a bundle
of spaghetti as a model of sorting numbers; a board, a set of nails,
and a rubber band as a model of finding the convex hull of a set of
points; and strings tied together as a model of finding the shortest
path in a network. These are all described in Dewdney (1984).
Components[edit]
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section by adding citations to reliable sources. Unsourced material may
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this template message)
A 1960 Newmark analogue computer, made up of five units. This computer
was used to solve differential equations and is currently housed at the
Cambridge Museum of Technology.
Analog computers often have a complicated framework, but they have, at
their core, a set of key components that perform the calculations. The
operator manipulates these through the computer's framework.
Key hydraulic components might include pipes, valves and containers.
Key mechanical components might include rotating shafts for carrying
data within the computer, miter gear differentials, disc/ball/roller
integrators, cams (2-D and 3-D), mechanical resolvers and multipliers,
and torque servos.
Key electrical/electronic components might include:
* precision resistors and capacitors
* operational amplifiers
* multipliers
* potentiometers
* fixed-function generators
The core mathematical operations used in an electric analog computer
are:
* addition
* integration with respect to time
* inversion
* multiplication
* exponentiation
* logarithm
* division
In some analog computer designs, multiplication is much preferred to
division. Division is carried out with a multiplier in the feedback
path of an Operational Amplifier.
Differentiation with respect to time is not frequently used, and in
practice is avoided by redefining the problem when possible. It
corresponds in the frequency domain to a high-pass filter, which means
that high-frequency noise is amplified; differentiation also risks
instability.
Limitations[edit]
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section by adding citations to reliable sources. Unsourced material may
be challenged and removed. (April 2012) (Learn how and when to remove
this template message)
In general, analog computers are limited by non-ideal effects. An
analog signal is composed of four basic components: DC and AC
magnitudes, frequency, and phase. The real limits of range on these
characteristics limit analog computers. Some of these limits include
the operational amplifier offset, finite gain, and frequency response,
noise floor, non-linearities, temperature coefficient, and parasitic
effects within semiconductor devices. For commercially available
electronic components, ranges of these aspects of input and output
signals are always figures of merit.
Decline[edit]
In the 1950s to 1970s, digital computers based on first vacuum tubes,
transistors, integrated circuits and then micro-processors became more
economical and precise. This led digital computers to largely replace
analog computers. Even so, some research in analog computation is still
being done. A few universities still use analog computers to teach
control system theory. The American company Comdyna manufactured small
analog computers.^[35] At Indiana University Bloomington, Jonathan
Mills has developed the Extended Analog Computer based on sampling
voltages in a foam sheet.^[36] At the Harvard Robotics Laboratory,^[37]
analog computation is a research topic. Lyric Semiconductor's error
correction circuits use analog probabilistic signals. Slide rules are
still popular among aircraft personnel.^[citation needed]
Resurgence[edit]
With the development of very-large-scale integration (VLSI) technology,
Yannis Tsividis' group at Columbia University has been revisiting
analog/hybrid computers design in standard CMOS process. Two VLSI chips
have been developed, an 80th-order analog computer (250 nm) by Glenn
Cowan^[38] in 2005^[39] and a 4th-order hybrid computer (65 nm)
developed by Ning Guo in 2015,^[40] both targeting at energy-efficient
ODE/PDE applications. Glenn's chip contains 16 macros, in which there
are 25 analog computing blocks, namely integrators, multipliers,
fanouts, few nonlinear blocks. Ning's chip contains one macro block, in
which there are 26 computing blocks including integrators, multipliers,
fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation
is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores
the nonlinear function data. The experiments from the related
publications revealed that VLSI analog/hybrid computers demonstrated
about 1-2 orders magnitude of advantage in both solution time and
energy while achieving accuracy within 5%, which points to the promise
of using analog/hybrid computing techniques in the area of
energy-efficient approximate computing.^[citation needed] In 2016, a
team of researchers developed a compiler to solve differential
equations using analog circuits.^[41]
Analog computers are also used in neuromorphic computing, and in 2021 a
group of researchers have shown that a specific type of artificial
neural network called a spiking neural network was able to work with
analog neuromorphic computers.^[42]
Practical examples[edit]
X-15 simulator analog computer
These are examples of analog computers that have been constructed or
practically used:
* Boeing B-29 Superfortress Central Fire Control System
* Deltar
* E6B flight computer
* Kerrison Predictor
* Leonardo Torres y Quevedo's Analogue Calculating Machines based on
"fusee sans fin"
* Librascope, aircraft weight and balance computer
* Mechanical computer
* Mechanical integrators, for example, the planimeter
* Nomogram
* Norden bombsight
* Rangekeeper, and related fire control computers
* Scanimate
* Torpedo Data Computer
* Torquetum
* Water integrator
* MONIAC, economic modelling
* Ishiguro Storm Surge Computer
Analog (audio) synthesizers can also be viewed as a form of analog
computer, and their technology was originally based in part on
electronic analog computer technology. The ARP 2600's Ring Modulator
was actually a moderate-accuracy analog multiplier.
The Simulation Council (or Simulations Council) was an association of
analog computer users in US. It is now known as The Society for
Modeling and Simulation International. The Simulation Council
newsletters from 1952 to 1963 are available online and show the
concerns and technologies at the time, and the common use of analog
computers for missilry.^[43]
See also[edit]
Wikimedia Commons has media related to Analog computers.
* Analog neural network
* Analogical models
* Chaos theory
* Differential equation
* Dynamical system
* Field-programmable analog array
* General purpose analog computer
* Lotfernrohr 7 series of WW II German bombsights
* Signal (electrical engineering)
* Voskhod Spacecraft "Globus" IMP navigation instrument
* XY-writer
Notes[edit]
1. ^ "Gears of war: When mechanical analog computers ruled the waves".
18 March 2014. Archived from the original on 8 September 2018.
Retrieved 14 June 2017.
2. ^ Johnston, Sean F. (2006). Holographic Visions: A History of New
Science. OUP Oxford. p. 90. ISBN 978-0191513886.
3. ^ The Antikythera Mechanism Research Project Archived 2008-04-28 at
the Wayback Machine, The Antikythera Mechanism Research Project.
Retrieved 1 July 2007.
4. ^ Fuat Sezgin "Catalogue of the Exhibition of the Institute for the
History of Arabic-Islamic Science (at the Johann Wolfgang Goethe
University", Frankfurt, Germany) Frankfurt Book Fair 2004, pp. 35 &
38.
5. ^ Franc,ois Charette, Archaeology: High tech from Ancient Greece,
Nature 444, 551-552(30 November 2006), doi:10.1038/444551a
6. ^ Silvio A. Bedini, Francis R. Maddison (1966). "Mechanical
Universe: The Astrarium of Giovanni de' Dondi", Transactions of the
American Philosophical Society 56 (5), pp. 1-69.
7. ^ D. De S. Price (1984). "A History of Calculating Machines", IEEE
Micro 4 (1), pp. 22-52.
8. ^ Tuncer O"ren (2001). "Advances in Computer and Information
Sciences: From Abacus to Holonic Agents", Turk J Elec Engin 9 (1),
pp. 63-70 [64].
9. ^ Donald Routledge Hill (1985). "Al-Biruni's mechanical calendar",
Annals of Science 42, pp. 139-163.
10. ^ "Episode 11: Ancient Robots", Ancient Discoveries, History
Channel, archived from the original on 1 March 2014, retrieved 6
September 2008
11. ^ Howard R. Turner (1997), Science in Medieval Islam: An
Illustrated Introduction, p. 184, University of Texas Press,
ISBN 0-292-78149-0
12. ^ Donald Routledge Hill, "Mechanical Engineering in the Medieval
Near East", Scientific American, May 1991, pp. 64-69 (cf. Donald
Routledge Hill, Mechanical Engineering Archived 25 December 2007 at
the Wayback Machine)
13. ^ "An Amazing Perpetual Calendar, Hidden in an Italian Chapel".
Atlas Obscura. Retrieved 7 September 2020.
14. ^ Ray Girvan, "The revealed grace of the mechanism: computing after
Babbage" Archived November 3, 2012, at the Wayback Machine,
Scientific Computing World, May/June 2003
15. ^ Thomas Parke Hughes Networks of power: electrification in Western
society, 1880-1930 JHU Press, 1993 ISBN 0-8018-4614-5 page 376
16. ^ James E. Tomayko, Helmut Hoelzer's Fully Electronic Analog
Computer; In: IEEE Annals of the History of Computing, Vol. 7, No.
3, pp. 227-240, July-Sept. 1985, doi:10.1109/MAHC.1985.10025
17. ^ Neufeld, Michael J. (2013). The Rocket and the Reich: Peenemunde
and the Coming of the Ballistic Missile Era. Smithsonian
Institution. p. 138. ISBN 9781588344663.
18. ^ Ulmann, Bernd (22 July 2013). Analog Computing. Walter de
Gruyter. p. 38. ISBN 9783486755183.
19. ^ Neufeld (2013), p. 106.
20. ^ Tomayko, James E. (1 July 1985). "Helmut Hoelzer". IEEE Annals of
the History of Computing. 7 (3): 227-240.
doi:10.1109/MAHC.1985.10025. S2CID 15986944.
21. ^ Metropolis, N. "The Beginning of the Monte Carlo Method." Los
Alamos Science, No. 15, p. 125
22. ^ Small, J. S. "The analogue alternative: The electronic analogue
computer in Britain and the USA, 1930-1975" Psychology Press, 2001,
p. 90
23. ^ Small, J. S. "The analogue alternative: The electronic analogue
computer in Britain and the USA, 1930-1975" Psychology Press, 2001,
p. 93
24. ^ Bissell, C. (1 February 2007). "Historical perspectives - The
Moniac A Hydromechanical Analog Computer of the 1950s" (PDF). IEEE
Control Systems Magazine. 27 (1): 69-74.
doi:10.1109/MCS.2007.284511. ISSN 1066-033X. S2CID 37510407.
Archived (PDF) from the original on 9 October 2022.
25. ^ "History - Accounts". me100.caltech.edu.
26. ^ Karplus, Walter J. (29 November 2017). "Analog simulation:
solution of field problems". McGraw-Hill - via Google Books.
27. ^ Petersen, Julie K. (2003). Fiber optics illustrated dictionary.
CRC Press. p. 441. ISBN 978-0-8493-1349-3.
28. ^ "Heathkit EC - 1 Educational Analog Computer". Computer History
Museum. Archived from the original on 20 May 2010. Retrieved 9 May
2010.
29. ^ [1]Practical Electronics, January 1968
30. ^ ^a ^b EPE Hybrid Computer - Part 1 (November 2002), Part 2
(December 2002), Everyday Practical Electronics
31. ^ "System Description EAI 8800 Scientific Computing System" (PDF).
1 May 1965. Archived (PDF) from the original on 9 October 2022.
Retrieved 17 September 2019.
32. ^ Small, James S. (2001). The Analogue Alternative. The Electronic
Analogue Computer in Britain and USA, 1930-1975. London: Routledge.
pp. 119-178.
33. ^ Havranek, Bill (1 August 1966). The role of a hybrid computer in
supersonic transport simulation. SIMULATION. Vol. 7. pp. 91-99.
34. ^ ^a ^b "Basic Fire Control Mechanisms". maritime.org.
35. ^ "Analog Computers". Comdyna. Archived from the original on 1
December 2017. Retrieved 6 October 2008.
36. ^ "Kirchhoff-Lukasiewicz Machines".
37. ^ "Harvard Robotics Laboratory".
38. ^ "Glenn Cowan". Concordia.ca. Retrieved 5 February 2016.
39. ^ Cowan, G.E.R.; Melville, R.C.; Tsividis, Y. (1 February 2005). "A
VLSI analog computer/math co-processor for a digital computer".
Solid-State Circuits Conference, 2005. Digest of Technical Papers.
ISSCC. 2005 IEEE International. 1: 82-586.
doi:10.1109/ISSCC.2005.1493879. ISBN 978-0-7803-8904-5.
S2CID 38664036.
40. ^ Guo, Ning; Huang, Yipeng; Mai, Tao; Patil, S.; Cao, Chi; Seok,
Mingoo; Sethumadhavan, S.; Tsividis, Y. (1 September 2015).
"Continuous-time hybrid computation with programmable
nonlinearities". European Solid-State Circuits Conference
(ESSCIRC), ESSCIRC 2015 - 41st: 279-282.
doi:10.1109/ESSCIRC.2015.7313881. ISBN 978-1-4673-7470-5.
S2CID 16523767.
41. ^ "Analog computing returns".
42. ^ Benjamin Cramer; Sebastian Billaudelle; Simeon Kanya; Aron
Leibfried; Andreas Gruebl; Vitali Karasenko; Christian Pehle;
Korbinian Schreiber; Yannik Stradmann; Johannes Weis; Johannes
Schemmel; View ORCID ProfileFriedemann Zenke (25 January 2022).
"Surrogate gradients for analog neuromorphic computing". PNAS. 119
(4). Bibcode:2022PNAS..11909194C. doi:10.1073/pnas.2109194119.
PMC 8794842. PMID 35042792.
43. ^ "Simulation Council newsletter". Archived from the original on 28
May 2013.
References[edit]
* A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets
for Problem Solving", Scientific American, 250(6):19-26, June 1984.
Reprinted in The Armchair Universe, by A.K. Dewdney, published by
W.H. Freeman & Company (1988),
ISBN 0-7167-1939-8.
Universiteit van Amsterdam Computer Museum. (2007). Analog Computers.
Jackson, Albert S., "Analog Computation". London & New York:
McGraw-Hill, 1960. OCLC 230146450
External links[edit]
* Biruni's eight-geared lunisolar calendar in "Archaeology: High tech
from Ancient Greece", Franc,ois Charette, Nature 444, 551-552(30
November 2006),
doi:10.1038/444551a
The first computers
Large collection of electronic analog computers with lots of
pictures, documentation and samples of implementations (some in German)
Large collection of old analog and digital computers at Old Computer
Museum
A great disappearing act: the electronic analogue computer Chris
Bissell, The Open University, Milton Keynes, UK Accessed February 2007
German computer museum with still runnable analog computers
Analog computer basics Archived 6 August 2009 at the Wayback Machine
Analog computer trumps Turing model
Harvard Robotics Laboratory Analog Computation
The Enns Power Network Computer - an analog computer for the analysis
of electric power systems (advertisement from 1955)
Librascope Development Company - Type LC-1 WWII Navy PV-1 "Balance
Computor"
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