For 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 duringWorld War II, the Korean War, and the Vietnam War to aid the pilot of a bomber aircraft in droppingbombs accurately.
An analog computer is a form of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically, as their numerical values change. As an analog computer does not use discrete values, but rather continuous values, processes cannot be reliably repeated with exact equivalence, as they can with Turing machines. Unlike digital signal processing, analog computers do not suffer from the quantization noise, but are limited by analog noise.
Analog computers were widely used in scientific and industrial applications where digital computers of the time lacked sufficient performance. Analog computers can have a very wide range of complexity. Slide rules and nomographs are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated.[1]Systems for process control and protective relays used analog computation to perform control and protective functions.
The advent of digital computing and its success made analog computers largely obsolete in 1950s and 1960s, though they remain in use in some specific applications, like the flight computer in aircraft, and for teaching control systems in universities.
Contents
Setup
Setting up an analog computer required scale factors to be chosen, along with initial
conditions—that is, starting values. Another essential was creating the required network
of interconnections between computing elements. Sometimes it was necessary to
re-think the structure of the problem so that the computer would function satisfactorily.
No variables could be allowed to exceed the computer's limits, and differentiation was
to be avoided, typically by rearranging the "network" of interconnects, using integrators
in a different sense.
conditions—that is, starting values. Another essential was creating the required network
of interconnections between computing elements. Sometimes it was necessary to
re-think the structure of the problem so that the computer would function satisfactorily.
No variables could be allowed to exceed the computer's limits, and differentiation was
to be avoided, typically by rearranging the "network" of interconnects, using integrators
in a different sense.
Running an electronic analog computer, assuming a satisfactory setup, started with the
computer held with some variables fixed at their initial values. Moving a switch released
the holds and permitted the problem to run. In some instances, the computer could, after
a certain running time interval, repeatedly return to the initial-conditions state to reset
the problem, and run it again.
computer held with some variables fixed at their initial values. Moving a switch released
the holds and permitted the problem to run. In some instances, the computer could, after
a certain running time interval, repeatedly return to the initial-conditions state to reset
the problem, and run it again.
Timeline of analog computers
See also: History of computing hardware
Precursors
This is a list of examples of early computation devices which are considered to be precursors
of the modern computers. Some of them may even have been dubbed as 'computers' by the
press, although they may fail to fit the modern definitions.
of the modern computers. Some of them may even have been dubbed as 'computers' by the
press, although they may fail to fit the modern definitions.
The south-pointing chariot can be considered the earliest analog computer. It was a
mechanical-geared wheeled vehicle used for to discern the southern cardinal direction.
mechanical-geared wheeled vehicle used for to discern the southern cardinal direction.
The ancient Greek-designedAntikythera mechanism, dating between 150 and 100 BC, is the world's oldest known analog computer.
The Antikythera mechanism was an orrery and is also claimed to be the earliest known mechanical analog computer, according to Derek J. de Solla Price.[2] 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 circa 100 BC. 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 a star chart invented by Abū Rayḥān al-Bīrūnī in the early 11th century.[3] 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] Abū Rayhān al-Bīrūnī 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] circa 1000 AD.
Persia in 1235.[6] Abū Rayhān al-Bīrūnī 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] circa 1000 AD.
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.
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.
over it with a mechanical linkage.
A slide rule
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.
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.
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.
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 Lord Kelvin 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.[10]
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.
equations by integration, used wheel-and-disc mechanisms to perform the integration.
In 1876 Lord Kelvin 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.[10]
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
Heathkit EC-1 educational analog computer
The Dumaresq was a mechanical calculating device invented around 1902 by LieutenantJohn Dumaresq of the Royal Navy. It was an analog computer which 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.
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 forfire-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.[11] 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.
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. 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.
analog computers. 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.
The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid
in his studies of neutron transport.[12] Project Cyclone was an analog computer developed
by Reeves in 1950 for the analysis and design of dynamic systems.[13] Project Typhoon
was an analog computer developed by RCA in 1952. It consisted of over 4000 electron
tubes and used 100 dials and 6000 plug-in connectors to program.[14] The MONIAC
Computer was a hydraulic model of a national economy first unveiled in 1949.
[citation needed]
in his studies of neutron transport.[12] Project Cyclone was an analog computer developed
by Reeves in 1950 for the analysis and design of dynamic systems.[13] Project Typhoon
was an analog computer developed by RCA in 1952. It consisted of over 4000 electron
tubes and used 100 dials and 6000 plug-in connectors to program.[14] The MONIAC
Computer was a hydraulic model of a national economy first unveiled in 1949.
[citation needed]
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.[15][16]
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.[15][16]
Educational analog computers illustrated the principles of analog calculation. The Heathkit
EC-1, a $199 educational analog computer, was made by the Heath Company, USA c.
1960.[17] It was programmed using patch cords that connected nine operational amplifiers
and other components.[18] General Electric also marketed an "educational" analog computer
kit of a simple design in the early 1960s consisting of a two transistor tone generator 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 considered
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.
EC-1, a $199 educational analog computer, was made by the Heath Company, USA c.
1960.[17] It was programmed using patch cords that connected nine operational amplifiers
and other components.[18] General Electric also marketed an "educational" analog computer
kit of a simple design in the early 1960s consisting of a two transistor tone generator 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 considered
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.
In industrial process control, thousands of 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.
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
The similarity between linear mechanical components, such as springs and dashpots(viscous-fluid dampers), and electrical components, such
as capacitors, inductors, andresistors is striking in terms of mathematics. They can be
modeled using equations of the same form.
Polish analog computer AKAT-1
as capacitors, inductors, andresistors is striking in terms of mathematics. They can be
modeled using equations of the same form.
Polish analog computer AKAT-1
If one considers a simple mass–spring system, constructing the physical system would
require making or modifying the springs and masses. This would be followed by attaching
them to each other and an appropriate anchor, collecting test equipment with the
appropriate input range, and finally, taking measurements. In more complicated cases,
such as suspensions for racing cars, experimental construction, modification, and
testing is both complicated and expensive.
The electrical equivalent can be constructed with a few operational amplifiers (op amps)
and some passive linear components; 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 a capacitor. The electrical system is an analogy
to the physical system, hence the name, but it is less expensive to construct, generally
safer, and typically much easier to modify.
and some passive linear components; 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 a capacitor. The electrical system is an analogy
to the physical system, hence the name, but it is less expensive to construct, generally
safer, and typically much easier to modify.
As well, an electronic circuit can typically operate at higher frequencies than the system
being simulated. This allows the simulation to run faster than real time (which could, in
some instances, be hours, weeks, or longer). Experienced users of electronic analog
computers said that they offered a comparatively intimate control and understanding
of the problem, relative to digital simulations.
being simulated. This allows the simulation to run faster than real time (which could, in
some instances, be hours, weeks, or longer). Experienced users of electronic analog
computers said that they offered a comparatively intimate control and understanding
of the problem, relative to digital simulations.
The drawback of the mechanical-electrical analogy is that electronics are limited by the
range over which the variables may vary. This is called dynamic range. They are also
limited by noise levels. Floating-point digital calculations have a comparatively huge
dynamic range.
range over which the variables may vary. This is called dynamic range. They are also
limited by noise levels. Floating-point digital calculations have a comparatively huge
dynamic range.
These electric circuits can also easily perform a wide variety of simulations. For example,
voltage can simulate water pressureand electric current can simulate rate of flow in
terms of cubic metres per second. An integrator can provide the total accumulated
volume of liquid, using an input current proportional to the (possibly varying) flow rate.
voltage can simulate water pressureand electric current can simulate rate of flow in
terms of cubic metres per second. An integrator can provide the total accumulated
volume of liquid, using an input current proportional to the (possibly varying) flow rate.
Analog computers are especially well-suited to representing situations described by
differential equations. Occasionally, they were used when a differential equation proved
very difficult to solve by traditional means.
differential equations. Occasionally, they were used when a differential equation proved
very difficult to solve by traditional means.
The accuracy of an analog computer is limited by its computing elements as well as
quality of the internal power and electrical interconnections. The precision of the
analog computer readout was limited chiefly by the precision of the readout equipment
used, generally three or four significant figures. The precision of a digital computer is
limited by the word size; arbitrary-precision arithmetic, while relatively slow, provides
any practical degree of precision that might be needed.
quality of the internal power and electrical interconnections. The precision of the
analog computer readout was limited chiefly by the precision of the readout equipment
used, generally three or four significant figures. The precision of a digital computer is
limited by the word size; arbitrary-precision arithmetic, while relatively slow, provides
any practical degree of precision that might be needed.
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.
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 8800
Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was
Applied Dynamics of Ann Arbor, Michigan.
, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its 8800
Analog Computer (solid state operational amplifiers, 64 integrators). 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 ANALACcomputer to use an alternative
technology: medium frequency carrier and non dissipative reversible circuits.
(also called "continuous current amplifiers" because they have no low frequency limitation),
in the 1960s an attempt was made in the French ANALACcomputer to use an alternative
technology: medium frequency carrier and non dissipative reversible circuits.
In the 1970s every big company and administration concerned with problems in dynamics
had a big analog computing center, for example:
had a big analog computing center, for example:
- In the USA: 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
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.
, 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.
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.[citation needed]
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.[citation needed]
Only one company was known as offering general commercial computing services on its
hybrid computers, CISI of France, in the 1970s.
hybrid computers, CISI of France, in the 1970s.
The best reference in this field is the 100 000 simulations runs for each certification of the
automatic landing systems of Airbusand Concorde aircraft.[citation needed]
automatic landing systems of Airbusand Concorde aircraft.[citation needed]
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.
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.
Implementations
Mechanical analog computers
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.
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 US 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.
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 US 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) that describes[19] the
fire control computer mechanisms. For adding and subtracting, precision miter-gear
differentials were in common use in some computers; the Ford InstrumentMark I
Fire Control Computer contained about 160 of them.
fire control computer mechanisms. For adding and subtracting, precision miter-gear
differentials were in common use in some computers; the Ford InstrumentMark 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 pickoff 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.)
Output came from a pickoff 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.
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.
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).
(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.
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.
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).
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.
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.
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.
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.
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.
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-pickoff rollers, quite similar to the mechanism of a
rolling-ball computer mouse (in this mechanism, the pickoff rollers were roughly the same
diameter as the ball). The pickoff roller axes were at right angles.
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-pickoff rollers, quite similar to the mechanism of a
rolling-ball computer mouse (in this mechanism, the pickoff rollers were roughly the same
diameter as the ball). The pickoff roller axes were at right angles.
A pair of rollers "above" and "below" the pickoff 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.
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.
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.
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 non-computational mechanisms included internal odometer-style counters with
interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.
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).
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
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 which 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 likely to be a zero-center analog pointer-type
meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide
known magnitudes.
sockets) that permit patch cords (flexible wires with plugs at both ends) to create the
interconnections which 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 likely to be 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.
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.
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.
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.
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.
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.
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.
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 which 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).
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
.
Analog computers often have a complicated framework, but they have, at their core, a set
of key components which perform the calculations, which the operator manipulates through the computer's framework.
of key components which perform the calculations, which the operator manipulates through the computer's framework.
Key hydraulic components might include pipes, valves and containers.
A 1960 Newmark analogue computer, made up of five units.
This computer was used
to solve differential
of Technology
Key mechanical components might include rotating shafts for carrying data within thecomputer, 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.
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.
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
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.
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
In 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 manufactures small analog
computers.[20] At Indiana University Bloomington,Jonathan Mills has developed the
Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard
Robotics Laboratory, 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]
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 manufactures small analog
computers.[20] At Indiana University Bloomington,Jonathan Mills has developed the
Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard
Robotics Laboratory, 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 in VLSI technology
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[21] in 2005[22] and an 4th-order hybrid computer (65 nm)
developed by Ning Guo[23] in 2015,[24] both targeting at energy-efficient ODE/PDEs
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.
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[21] in 2005[22] and an 4th-order hybrid computer (65 nm)
developed by Ning Guo[23] in 2015,[24] both targeting at energy-efficient ODE/PDEs
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.
Practical examples
These are examples of analog computers that have been constructed or practically used:
- Boeing B-29 Superfortress Central Fire Control System
- Deltar
- 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
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.
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 USA. 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.[25]
users in USA. 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.[25]
Real computers
Computer theorists often refer to idealized analog computers as real computers (because
they operate on the set of real numbers). Digital computers, by contrast, must first quantize
the signal into a finite number of values, and so can only work with the rational number set
(or, with an approximation of irrational numbers).
they operate on the set of real numbers). Digital computers, by contrast, must first quantize
the signal into a finite number of values, and so can only work with the rational number set
(or, with an approximation of irrational numbers).
These idealized analog computers may in theory solve problems that are intractable on
digital computers; however as mentioned, in reality, analog computers are far from attaining
this ideal, largely because of noise minimization problems. In theory, ambient noise is limited
by quantum noise (caused by the quantum movements of ions). Ambient noise may be
severely reduced – but never to zero – by using cryogenically cooled parametric amplifiers.
Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real
number problems.
digital computers; however as mentioned, in reality, analog computers are far from attaining
this ideal, largely because of noise minimization problems. In theory, ambient noise is limited
by quantum noise (caused by the quantum movements of ions). Ambient noise may be
severely reduced – but never to zero – by using cryogenically cooled parametric amplifiers.
Moreover, given unlimited time and memory, the (ideal) digital computer may also solve real
number problems.
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