Fullscreen HTML5Med Res (??MB)HTML4

Part 1 by Dr David Maddison, VK3DSM Analog Computers An analog computer at Lewis Flight Propulsion Laboratory in 1949 – https://w.wiki/HRcx These days, we are surrounded by digital computers, but computing wasn’t always performed with binary numbers. Analog computers were used extensively in the past, and possibly will also be in the future. T oday, what most people think of as a computer is a digital computer, like a laptop or smartphone. However, digital computers weren’t the first and aren’t the only kinds of computers. The first electronic digital computer was built in 1946. Called ENIAC, it filled a room – see Fig.1. One of its jobs was to compute artillery trajectories. The Moore School of Electrical Engineering at the University of Pennsylvania developed an alternative: a simple analog differential analyser, a type of mechanical analog computer (Fig.2). It performed the same task with gears and shafts in a much smaller space, foreshadowing a rivalry that has lasted nearly 100 years. Some analog computers are very ancient indeed. Originally, all analog computers were mechanical, but in the 1940s, electronic analog computers were developed. They are easier to develop than mechanical designs and more reliable. They have some advantages compared to digital computers. Unlike digital computers, which represent information using discrete 16 Silicon Chip binary states (0 or 1), or quantum computers, which use discrete qubits that can be in a superposition of the 0 and 1 states, an analog computer can represent and process a continuum of values, using something like a voltage or current. That gives it an almost infinite number of distinguishable states within the physical range. Analog computers started to become obsolete in the late 1950s with the rise of transistors and early digital machines, accelerating through the 1970s as microprocessors like the Intel 4004 (1971) made digital computers scalable and affordable. However, analog computers remained in some niches (eg, flight simulators) into the 1980s. By the 1970s, mechanical and electronic analog computers had become largely obsolete, replaced by faster, more precise digital systems. However, they are now making a comeback in various forms, where their ability to electronically represent a continuum can bypass digital computer bottlenecks. Australia's electronics magazine This article will concentrate on describing traditional analog computers, their uses, and covering their history. A follow-up article next month will look at the current and future uses of analog computers and state-of-theart technology. Differences between analog and digital computers An electronic analog computer cannot do everything a digital computer can do, but it can excel in certain realtime simulations of physical systems, where it can have superior speed and efficiency. Because an analog computer deals with continuous values, its accuracy and repeatability are inferior to a digital computer. Analog computers typically have a calculation error in the 0.1-1% range. Traditional electronic analog computers were programmed by physically rewiring a patch panel – see Fig.3. This same method was used on some of the earliest digital computers, such as ENIAC, the Harvard Mark I and the siliconchip.com.au Colossus computer for cryptographic key settings. In modern analog and mixed-signal systems, the physical patch panel has largely been replaced by digital configuration interfaces (SPI, I²C, USB etc) that program field-­programmable analog arrays (FPAAs), memristor crossbars, floating-gate arrays or switched-capacitor circuits, making it easier to change their configuration. Where analog computers excel Traditional analog computing excels at real-time simulations of continuous physical phenomena, such as the flight dynamics of aircraft. More recently, its ability to map physical variables directly onto continuously variable electrical signals (voltages, currents, or resistances) has made analog hardware extremely attractive for mimicking biological neural networks. They can perform the massive matrix-vector multiplications required in AI pattern recognition and sensory processing with far greater energy efficiency than conventional digital chips. This dramatic power consumption advantage, often by a factor of 1001000 times for similar workloads, is the primary driver behind the current resurgence of interest in analog and analog-inspired computing techniques. Figs.1: the ENIAC electronic digital computer circa 1947-1955. Like the one shown in Fig.2, it could compute artillery trajectories, but the analog computer was smaller and more efficient at the time. Source: https://penntoday.upenn. edu/news/worlds-first-general-purpose-computer-turns-75 Where digital computers excel Digital computing excels in precision, repeatability and accuracy, as intermediate and final values are represented by precise mathematical values, not analog properties, which cannot be precisely or reproducibly represented. Also, digital computers can run a huge array of software from word processing to video editors to databases and everything else imaginable; analog computers usually perform much more specific tasks. Digital computers can also store vast amounts of data and programs and with results reproducible between different computers, and are not subject to subtle hardware variations between platforms. The digital computer is a practical realisation of Alan Turing’s Universal Turing Machine (UTM) — a theoretical device capable of computing any function that is algorithmically computable. siliconchip.com.au Fig.2: a mechanical analog computer circa 1942-1945. Fig.3: a Comdyna GP-6 (user manual: siliconchip.au/link/acag) made for educational purposes. Its prominent patch panel is set up to solve the simple equation x’’ + x’ = 0 representing a certain case of pure viscous damping. Source: www.glennsmuseum.com Australia's electronics magazine May 2026  17 In contrast, real-world analog computers built in the 20th century were not universal in the Turing sense because they could only efficiently solve specific classes of problems (mainly differential equations) and lacked the ability to simulate arbitrary computation without exponential growth in hardware. However, Claude Shannon proved in 1941 that a theoretical model he called the General Purpose Analog Computer (GPAC), built from ideal integrators, adders, multipliers and constant units, is equivalent in computational power to a Universal Turing Machine and can therefore compute any computable real function (to arbitrary precision, given unlimited time and perfect components). While Shannon proved that a theoretically ideal GPAC is as powerful as a UTM, no physical GPAC can ever be implemented exactly because real electronics cannot provide infinite precision, infinite range or perfect components, making true analog universality practically unattainable. Despite this, special-purpose analog computers remain extremely useful. What analog computers do Traditional analog computers of the past could emulate physical systems, such as: • Aerospace and flight dynamics to model aerodynamic forces, pitch, roll, yaw and jet engine inlet control, such as on the SR-71, which used a hydraulic analog computer. • Aquifer simulation. • Astronomical or planetary motion Fig.4: a reproduction of the back of the Antikythera mechanism. Source: https://w.wiki/HRct 18 Silicon Chip (eg, the Antikythera mechanism and many later planetariums). • Automotive automatic transmissions; for more on this, see our article on “Fluid logic, Fluidics and Microfluidics” in August 2019 (siliconchip. au/Article/11762). • Ballistics and trajectory analysis. • Chemical reaction simulation. • Convective flow simulation. • Damped mechanical system simulation (eg, vehicle suspensions). • Economic modelling (as in the MONIAC hydraulic computer). • Electronic circuits. • Flight simulation. • Fluid dynamics simulation. • Heat transfer simulation. • Hydraulic and fluid networks, such as the flow of fluids through complex pipe networks in chemical plants, water supplies or sewerage systems. • Medical monitoring. • Nuclear reactor kinetics; modelling thermal and neutron flux. • Oscillating systems like massspring-dampers. • Power-grid analysis. • Radioactive decay simulation. • Tide prediction. • Temperature and industrial process control. Analog computer history The history of analog computers can be divided into two main eras, the ‘classic’ and ‘modern’ eras. The classic era is: • Up until the 1940s, mechanical and electro-mechanical computers dominated. They were expensive and slow to configure. Fig.5: a reproduction of the front of the Antikythera mechanism. Source: https://w.wiki/HRcs Australia's electronics magazine • During the 1940s and 1950s, valves and electronic analog computers appeared and began to dominate. The K2-W valve op amp module was introduced in 1953. • During the 1960s and 1970s, transistorised op-amp based computers became inexpensive and were used in engineering education and industry. This was the peak of analog computing in the classic era. • From the 70s onward, digital computers dominated, with analog computers continuing only in niche areas. In the modern ‘revival’ era, from around 2020 onward, the focus of analog computers is on energy-efficient AI inference engines and AI matrix-vector multiplications. Such analog or mixed-signal chips are being produced by companies like Imec (from 2020), Mythic (from 2021), Lightmatter (from 2022), Aspinity & SynSense (from 2023), ACCEL & IBM (from 2024), Anabrid (from 2025), as well as Encharge, Microsoft and Peking University. Mechanical analog computers Here is a list of some of the important mechanical analog computers: Antikythera mechanism (200BCE) The first known specialised mechanical analog computer was the Antikythera mechanism (Figs.4 & 5) made between 200BCE and 80BCE and discovered at the bottom of the Mediterranean Sea in 1901. It is a complex geared mechanism (the details of which can be seen at https://w. wiki/HRcu) that was used to predict Fig.6: Lord Kelvin’s tide predicting machine. Source: https://w.wiki/HRcv siliconchip.com.au Fig.7: a replica of the Difference Engine located at the Computer History Museum in Mountain View, California. The first complete one is located in London’s Science Museum. Source: www.flickr.com/photos/jitze1942/4305143894/ Fig.8: a Norden Bombsight. Source: https://w.wiki/HRcw astronomical positions and eclipses decades in advance. A neat interactive example of a partial reconstruction can be viewed at siliconchip.au/link/acaq It is a remarkable achievement of science and engineering that has been subject to intense study ever since its discovery. With X-ray tomography in 2005, it became possible to read its inscriptions and determine other details. It is estimated to have had at least 37 gears. An Australian YouTuber went through much of the manufacturing process using the same tools and materials the ancients would have had (see https://siliconchip.au/link/aca0). mechanical integrators (six in the initial version) driven by electric motors, shafts and gears to solve complex differential equations. It was originally built to model power transmission networks, but it quickly proved invaluable for problems in physics, ballistics, seismology and more, dramatically reducing calculation times from months to hours. Slide rule (1622) English clergyman William Oughtred invented the slide rule around 1622, shortly after John Napier introduced the logarithms on which it was based, in 1614. Slide rules were in use until around 1972, when they were replaced by calculators. Planimeter (1814, 1854) A planimeter is a form of specialised mechanical analog computer for measuring areas on a map or plan. It is a continuous mechanical integrator, hence an analog computer. A tracer is moved around the boundary enclosing an area, and the area is computed. siliconchip.com.au The first known planimeter was invented in 1814 by J. M. Hermann; the most popular design, still in use today, was invented by Jacob Amsler in 1854. The Difference Engine (1822) Charles Babbage completed his Difference Engine 0, a mechanical computer to produce mathematical tables, in 1822. This and Babbage’s subsequent work were brilliant, but suffered from enormous mechanical complexity and funding problems. Some of his designs were only completed in recent years (see Fig.7). Tide predictor (1872) Lord Kelvin developed a tide predicting analog computer (Fig.6). Machines based on this design and built by Arthur Doodson are credited with the accurate tide predictions that were vital for the D-Day Normandy landings in 1944. Differential Analyzer (1931) American engineer Vannevar Bush, along with Harold Hazen, unveiled their groundbreaking Differential Analyzer at MIT in 1931. It was a massive mechanical analog computer, often regarded as one of the first advanced computing devices of the modern era. It was a room-sized machine using interconnected wheel-and-disc Australia's electronics magazine Norden bombsight (1931) The Norden Mark XV bombsight (Fig.8) was a mechanical analog computer used during WW2 by the USAAF and US Navy, and into the Korean and Vietnam wars. Its purpose was to calculate when to drop bombs to hit a target on the ground. It was one of the most expensive programs of WW2, costing about half that of the Manhattan Project. E6-B flight computer (1940) This circular slide rule was used for flight planning. It has been replaced by electronic devices today, but is still in use for flight training, in aviation exams and for backup purposes in case electronic devices fail. Electronic and hydraulic analog computers We will now look at some significant early analog computers. Some hydraulic computers will be included among May 2026  19 Table 1: equivalent hydraulic and electrical concepts Concept Electrical Hydraulic Voltage Pressure Current Flow rate Electric charge Fluid quantity Path for ‘current’ flow Wire Pipe Impedance Resistor Constriction in pipe Energy storage Capacitor Bladder on diaphragm Inertia Inductor Turbine/paddle wheel Current flows in one direction Diode One-way valve Signal amplification Transistor Pressure-actuated valve Constant source Voltage or current source Pump w/ or w/o feedback control the electronic ones, as they operate on analogous principles – see Table 1. solving inhomogeneous differential equations. AC Network Analyzer (1929) This was an electronic or electromechanical analog computer first built by MIT’s Harold Locke Hazen under the leadership of Vannevar Bush. It was designed to study large-grid AC power systems and complex power flows in real time. The computer included components like phase-shifting transformers, inductors/gyrators, variable resistors, capacitors and adjustable loads. It was essentially a scale model of a large grid electrical system. It was programmed by physically wiring circuits on patch panels and reading results with meters. This type of machine was used extensively from 1929 to the 1960s. To reduce the size of transformers, these machines were run at a much higher frequency than the 50/60Hz of real-world networks. It was a special-purpose analog computer and a predecessor of the later general-purpose op-amp-based electronic analog computers of the 1950s. It does not seem to be regarded as an electronic analog computer by most commentators, but this author thinks it is. It is not to be confused with the 1931 Differential Analyzer, also built under Bush’s influence. V-2 Guidance Computer (1941) Despite the AC Network Analyzer above, the first generally-accepted electronic analog computer is considered to be the German Mischgerät V-2 guidance computer designed by Helmut Hölzer, used for rocket guidance. It was a single-purpose computer comprising resistors, capacitors and valve amplifiers. It differentiated voltages from yaw, roll and pitch gyroscopes to sense the rocket’s divergence from the original orientation of the gyroscopes, deriving the rate of divergence. This was converted to correcting voltages that controlled servos for the steering vanes located in the rocket exhaust. It was a much cheaper, lighter and better-performing solution than competing methods. It did not use op amps, but influenced later US analog computers, as the technology and Hölzer himself were brought to America after the war under Operation Paperclip. Water Integrator (1936) The Water Integrator (Fig.9) was a hydraulic computer invented by Russian Vladimir Lukyanov; versions of such hydraulic computers were in use in the USSR until the 1980s. In the 1930s, the original machine was the only one in the USSR capable of 20 Silicon Chip M9 Gun Director (1943) Bell Labs’ M9 Gun Director was a specialised electronic analog computer developed in the USA. It worked with the SCR-854 radar, which provided real-time range and direction data. It solved trigonometric equations, computed firing solutions and then transmitted aiming data such as azimuth, elevation and fusing time directly to gun servo motors. Apart from target speed, direction and range, it took into account wind, Australia's electronics magazine Fig.9: a version of the 1-IGL-1-3 Water Integrator hydraulic analog computer. Source: Polymus – siliconchip.au/ link/acar air pressure, shell velocity and gun parallax. It achieved a high success rate in England against German V-1 flying bombs and German aircraft, reducing the number of shells needed to shoot down a target from thousands to around 100. The M9 was the first electronic analog computer that contained circuits fulfilling the function of operational amplifiers, the foundation of later electronic analog computers, but which had not yet been named as such (see the PDF at siliconchip.au/link/aca1). The M9 laid the foundation for future integrated radar and fire control computers, including defensive weapons like the Phalanx CIWS still in use today, including by Australia. Project Cyclone (1946) A family of computers was developed by Reeves Instrument Corporation for the US Navy – see Fig.10. More than 60 REAC (Reeves Electronic Analog Computer) machines were built and placed in various institutions. Seven models were produced between 1947 and 1965. This family of computers is credited with proving that there was a viable commercial market for computers. ANACOM (1946, 1948) The Westinghouse ANACOM solved problems in grid-scale power systems, such as lightning surges on transmission lines, plus mechanical design problems, oil flow and many others (see Fig.11). It was in use until 1991. It was under constant development and, by the 1980s, it was under the control of a digital computer to set up the initial starting conditions for siliconchip.com.au Fig.10: a 1965 sales brochure for the REAC 600 from Reeves. Source: https://archive.org/details/TNM_REAC_600_ computer_system_-_Reeves_1965_20180302_0183/page/n1 problems being solved. It was probably the longest-lasting conventional analog computer used into the digital age. (like Philbrick’s K2-W) became widely used, and more advanced machines took over. model of the computer shown in the image; it may have been a REAC 100, released in 1947. The REAC 100 had 18 op amps, 10 integrators, 10 summers, 10 inverters, 25 potentiometers and five servo-multipliers. GEDA (1947) REAC (1949) The Goodyear Electronic DifferREAC (see the lead photo) was an ential Analyzer was developed for analog computer at Lewis Flight Prothe Goodyear Aircraft Corporation to pulsion Laboratory (now the John MONIAC (1949) solve differential equations for missile H. Glenn Research Center), in Ohio. The MONIAC was a hydraulic comguidance simulations. It was released NASA did not clearly identify the puter that used water and fluid logic commercially in 1949. instead of electricity and elecGEDA used valve-based tronic components for its calhigh-gain DC amplifiers staculations. It was invented by bilised by a unique commuNew Zealander Bill Phillips. tator system (a rotary switch Its purpose was to model the that periodically rebalanced national economic processes amplifier inputs to reduce of the United Kingdom. We drift), similar to the system described it in the August used in modern ‘chopper 2019 issue, on page 21. stabilised’ op amps. GEDA systems typically had 20-85 RCA Typhoon (1951-1952) amplifiers configured as inteThe RCA-designed Project grators, summers, multipliers Typhoon was one of the largetc, via patch panels. est electronic analog computThey were used for missile ers ever built (see Fig.14). It trajectory simulation, flight was designed for the US Navy dynamics, control systems to be used in solving complex and even early war-gaming. differential equations for the They were superseded by the Fig.11: the Westinghouse ANACOM (ANAlog COMputer). development of ships, submamid-1950s as true op amps rines, aircraft and missiles. It Source: www.researchgate.net/figure/fig1_220494419 siliconchip.com.au Australia's electronics magazine May 2026  21 Operational amplifiers An operational amplifier (op amp) is an extremely high-gain differential-voltagecontrolled amplifier. When negative feedback is added, typically via a few resistors and capacitors, it can be made to perform addition, subtraction, integration, voltage inversion or other mathematical operations with almost zero error. The op amp is the workhorse of the analog computer, with two inputs (+ and −) and one output. Its name comes from its original use, performing mathematical operations in electronic analog computers, but now it has many other uses. It was the basic computing element of all electronic analog computers of the 1950s to the 1970s. The term operational amplifier was coined in 1947 by John Ragazzini, but the first practical commercially available op amp was the Philbrick GAP/R K2-W, released in 1953 (Fig.12). The first truly ‘modern’ op amp was the μA741 IC, released in 1968 and still in production (see Fig.13). Other classic op amps that came later include the TL071/2/4, LM324/358, NE5532/4, LM833 and OP07. For more details, see our article on The History of the Op Amp in the August 2021 issue (siliconchip.au/Article/14987). required a staff of nine engineers and mathematicians, plus six technicians. It had 100 dials and 6,000 plug-in connections. Its output devices were two Electronic Associates Variplotters, 18 GE recording voltmeters and a 3D trajectory indicator. It had 4000 valves, 450 precision DC amplifiers, a bank of polystyrene capacitors for 80 simultaneous integrations, hybrid step multipliers and a power consumption of 46kW. Special circuitry was designed to achieve accuracies of 0.001%; the power supply was regulated to that tolerance as well. Convair Analog Computer (1953) It was used for stress analysis of aircraft, and flight simulation, including a cockpit simulator. It had 8500 valves, reportedly occupied several floors and was one of the largest analog computers ever made – see siliconchip.au/ link/acas K2-W (1953) The first commercially available, modular, standardised op amp was George A. Philbrick’s K2-W valve module, released in 1953 (some say 1952) – see Fig.12. It was manufactured until 1971. It is similar to an integrated circuit but based on valves, resistors and capacitors. It was a high-performance device designed for building electronic analog computers. Its design eased the implementation of functions like addition, subtraction, integration, Fig.14: the RCA Typhoon, possibly the largest electronic analog computer ever built. Note the rocket model in the foreground. Source: The Analogue Alternative, James S. Small, 2001 22 Silicon Chip Australia's electronics magazine Fig.12: the first commercially available op amp, the Philbrick K2-W. Source: https://w. wiki/HRd3 Fig.13: the first ‘modern’ IC op amp, the μA741. Source: https://w. wiki/3eHA differentiation, multiplication and division. A modular electronic analog computer for solving differential equations would use a few to dozens of op amps. Philbrick also made several ‘black box’ K3-series electronic analog computer components, which can be viewed at http://philbrickarchive.org/k3_series_ components.htm (see Fig.15). The K2-W was a significant step in the miniaturisation, modularisation and standardisation of electronic analog computers before the development of transistors. Central Air Data Computer (1956) The Bendix Central Air Data Computer was used in US military aircraft such as the F-101, F-111 and the B-58 Fig.15: a K3 Series component from GAP/R. This is an adding unit with four inputs, e1, e2, e3 & e4. Source: http://philbrickarchive.org/k3_series_ components.htm siliconchip.com.au Fig.16: a 1962 model of the Bendix Central Air Data Computer. Source: https://w.wiki/HRcy to compute altitude, airspeed, Mach number and other values from pressure and temperature inputs. It contains two pressure sensors and an analog computer built from gears and servos. It was a masterpiece of engineering, with 46 synchros (a device to convert rotation to electrical outputs), 511 gears, 820 ball bearings and 2781 major parts – see Fig.16 & siliconchip.au/link/aca2 Perceptron (1958) The Mark 1 Perceptron was an artificial neural network algorithm originally simulated by Frank Rosenblatt on an IBM 704 digital computer in 1957 before being built into hardware as the Mark 1 Perceptron electronic analog computer. It could distinguish between simple shapes like squares, circles, diamonds and the letters X, E and F with different orientations. In different experiments, it used between 500 and 1000 ‘neurons’ and was trained with up to 10,000 images. It had three main parts: 1. A set of sensory or S-units comprising a 20×20 array of photocells to receive optical inputs. 2. A set of 512 association or A-units, each of which fired based on inputs from multiple sensory units. 3. A set of 8 response or R-units, which fired based on inputs from multiple association units. The S-units were connected to the A-units via a plugboard (see Fig.17). The A-units were connected to the R-units with adjustable weights encoded in potentiometers, with weight updates adjusted during learning by electric motors. You can read an operator’s manual at https://apps.dtic.mil/sti/tr/pdf/ AD0236965.pdf This was an amazing machine for the time and the precursor to modern AI systems. PACE 231R (1958) This was Electronic Associates’ flagship computer and became the world’s most widely used electronic analog computer, even into the early 1980s – see Fig.18. It was used for simulations for Project Mercury, Project Gemini, HL-10 lifting bodies (famous from the Six Million Dollar Man) and the X-15 rocket plane. For X-15 simulations, NASA used three PACE 231R computers siliconchip.com.au Fig.17: the Mark I Perceptron showing the S-unit to A-unit plugboard. Source: www.researchgate.net/figure/ fig2_345813508 Fig.18: the Pace 231R computer. Fig.19: the AKAT-1 from Poland. A very interesting-looking machine! Source: https://w.wiki/HRcz containing a total of 380 op amps, 101 function generators, 32 servo amplifiers and five multipliers networked together. Simulations could be run between Mach 0.2 and Mach 7.0 at altitudes up to 321km. Landing simulations were not possible. AKAT-1 (1959) From Poland, it was one of the first differential equation analysers based on transistors. It was only ever built as a prototype – see Fig.19. Australia's electronics magazine May 2026  23 Heathkit EC-1 (1960) This was an educational electronic analog computer – see Fig.20. It contained nine op amps. MUDPAC (1961) The Melbourne University Dual Package Analogue Computer was built by Applied Dynamics in the USA, their first computer for export. It was used until 1986. It comprised two consoles, 64 op amps, 80 coefficient potentiometers, 16 multipliers, eight function generators and 20 diode networks. It had a 1632-hole patch panel – see Fig.21. Fig.22: the major components of the instrument unit of the Saturn V. Source: NASA – https://images.nasa.gov/details-0100984 Apollo (1961+) Analog computers played a critical role in the 1960s-1970s Apollo program, for ground simulations and in some on-board systems. Large-scale analog and hybrid analog-digital computers were used extensively on the ground for high-fidelity, real-time simulations of Saturn V rocket dynamics – see Fig.23. For example, the General Purpose Simulator (GPS) at NASA’s Marshall Space Flight Center ran 12-degree-offreedom models of the first stage that incorporated wind gusts, structural flexing and fuel sloshing, all in realtime, which was 3000 times faster than the digital computers of the era could achieve. The GPS comprised 50 integrators, 50 summers, 350 coefficient potentiometers, 20 quarter square multipliers and 15 function generators (which contained an additional 70 op amps). The Flight Control Computer (FCC) of the Saturn V instrument unit (Fig.22) was not purely analog; it was a hybrid analog/digital system (mostly analog for the guidance loops, with some digital logic), translating inertial measurement data into gimbal commands for the F-1 and J-2 engines. In contrast, the famous Apollo Guidance Computer (AGC) carried onboard the Command and Lunar Modules was entirely digital; it was the first real-time embedded digital computer flown in space. It handled navigation guidance and control of the spacecraft itself. At the time (in the 1960s), purely digital computers were too slow and memory-limited to perform the highspeed, continuous, multi-degree-offreedom simulations required for Saturn V development or the fast innerloop control of engine gimbals, which is why analog and hybrid solutions Australia's electronics magazine siliconchip.com.au Fig.20: a Heathkit EC-1 educational electronic analog computer. Source: https://w.wiki/HRc$ Fig.21: the MUDPAC computer used at the University of Melbourne in 1961. Photographer: David Demant, Museums Victoria, https://collections. museumsvictoria.com.au/items/399902 24 Silicon Chip remained indispensable on the ground and in some flight hardware. EAI PACE (1963) The EAI PACE/TR-20 transistor tabletop analog computer was designed for educational use and basic research, even as digital computing was growing in prominence. SR-71 (1964) The SR-71 Mach 3+ aircraft, first flown in 1964, used a hydraulic analog computer of cams, levers, pistons and valves to manage the complex engine inlet airflows and fuel mixtures. Digital computers of the time were not fast enough, small enough, robust enough or heat resistant enough to handle the task. Fig.23: a detailed view of NASA’s General Purpose Simulator, circa 1966. Source: www. joostrekveld. net/?p=1409 Moog synthesiser (1964) While it was a musical instrument, many sources call it an analog computer. It shares roots with electronic analog computers, using the same building blocks like voltage-controlled oscillators, filters, amplifiers and envelope generators derived from op amp circuits. It is arguably a specialised musical analog computer. Nebraska-Kansas dispute (~1966) Early in this dispute concerning the use of groundwater, which has run for decades, an analog computer was built to simulate groundwater flows. Water was pumped out of test wells to determine the land’s water storage capacity and resistance to flow. This was simulated with an analog computer made of a network of 30,400 resistors and an unspecified number of capacitors that took a month to build – see Fig.24. Land with coarse soil, a high storage capacity and low resistance to flow was represented by a high-value capacitor and low-value resistors, while land with fine soil, a low storage capacity and high resistance to flow was represented by low value-­ capacitors and high-value resistors. The output of the water table profile was read on an oscilloscope; future water levels could also be predicted. Fig.24: simulating groundwater flows with a resistor/capacitor network (top). The test well network is shown at bottom, with a high flow well on the left and low flow on the right. Source: Time Life Science Library “Water”, 1966 Fig.25: the Australianmade EAI 180 computer. Source: https:// artsandculture. google.com/ asset/eai-180analog-computerelectronicsassociatesincorporated-eai/ IgG4Y3h75wg07g EAI 180 (1972) An EAI 180 (Fig.25) was used at the University of Sydney, Department of Mechanical Engineering in the 1970s. It was designed by Electronic Associates Pty Ltd of Sydney and built by Hawker Siddeley. It was used in siliconchip.com.au Australia's electronics magazine May 2026  25 the 1970s for teaching engineering students. Prior to this, calculations were made on mainframe computers (if available) or slide rules. It was ultimately replaced for teaching purposes by inexpensive programmable calculators. The Powerhouse Museum notes that this was an Australian version of the EAI 180 from the US parent company; it sold very well in Europe, but was not allowed to be sold in the USA despite being considered a better machine than the one made in the USA. Its reference manual is available at siliconchip.au/link/aca3 Analog Thing (2025) The Analog Thing by anabrid (https://the-analog-thing.org) is an open-source analog computer – see Fig.26. It has five integrators, four summers, two comparators, eight coefficient potentiometers, two multipliers, a panel meter and a hybrid port for analog-digital hybrid programs. Multiple Things can be daisy-chained. It is available for about A$875 + shipping (we suspect our readers could build an equivalent for much less than that). Mechanical vs electronic computers Having looked at some representative mechanical and electronic analog computers, let’s compare them. Cost: mechanical computers are complicated and require expensive precision machining and extensive assembly. Electronic circuits also require high levels of precision, although that is achieved inexpensively by modern manufacturing methods. That makes them easier and cheaper to build, alter and program, unlike a complex mechanical device. Speed: mechanical computers rely on gears, shafts, cams, ball and disc Fig.27: an op-amp-based integrator circuit. 26 Silicon Chip Fig.26: the Analog Thing, an analog computer available for purchase today. mechanical integrators etc. They are limited in speed to a few cycles per second due to mechanical friction, inertia, balance etc. Electronic components such as valves or transistors can easily operate at thousands or millions of cycles per second. Ease of programming: reprogramming a mechanical computer can require complex gear, linkage and other changes, which could take a very long time. On an electronic analog computer, it is just a matter of changing some patch cables, rotating potentiometers, perhaps adding an electronic module with certain functions, etc. Digital and hybrid computers are even easier and quicker to reprogram. • Operational amplifiers (op amps) can be configured to perform addition, subtraction, integration, differentiation and signal amplification. • Diodes and transistors are used for signal conditioning, switching and more complex functions. • Potentiometers or variable resistors can be used for scaling values. • ICs are used for specialised functions in more modern machines. These components can be used to form basic circuit elements or modules of an electronic analog computer, with some examples as follows. Circuit elements & functions The following electronic components are used in an electronic analog computer. • Resistors and capacitors are used for scaling voltages (resistors), creating time delays (RC delay circuit) and forming filters (RC filter). An electronic analog computer comprises some or all of the following. • Amplifiers to boost weak signals. • Filters for processing signals in real-time, to attenuate high or low frequencies. • Function generators and comparators to create waveforms or compare signal levels. They can be built from transistors, diodes and capacitors or specialised ICs or modules. • Integrators and differentiators, as mentioned earlier, are usually built from op amps. • Circuit blocks to perform mathematical operations like addition, subtraction, multiplication, squaring, square rooting, division, exponentiation and logarithms. A differential equation is one that relates a function to one or more of its derivatives (rates of change); solving it involves finding the original function through the process of integration. An integrator circuit can be constructed using an op amp, resistor and capacitor whereby an output voltage Fig.28. an op-amp-based differentiator circuit. Fig.29: an op-amp-based summing circuit. Basic electronic components Australia's electronics magazine siliconchip.com.au is produced from the capacitor which is the integral of a voltage over time, a fundamental of simulating dynamic systems (Fig.27). Similarly, an op amp can be configured for differentiation, in which a voltage output is produced that is proportional to the input voltage’s rate-ofchange with respect to time (Fig.28). Another op amp based circuit is a summing amplifier (for addition) – see Fig.29. An op amp has multiple voltage inputs producing a weighted average of the input voltages. Other mathematical functions can be performed. The logarithm of an input signal can be determined by exploiting the inherent exponential relationship between the base-emitter voltage (Vbe) and collector current (Ic) of a bipolar junction transistor in the feedback loop of an op amp, as shown in Fig.30. The PDF at siliconchip.au/ link/aca4 has more specific details on this method. An analog electronic multiplier takes two analog input signals (usually voltages) and produces an output signal, typically a voltage or current that is proportional to the product of the inputs or, with feedback, their ratio. Beyond simple multiplication and division, analog multipliers can also perform squaring, square rooting, RMS-to-DC conversion and amplitude modulation by exploiting their inherent non-linear characteristics. One implementation of a modern analog multiplier is built around the Gilbert cell, invented in 1967, which is a clever arrangement of transistors whose currents multiply naturally because of the exponential relationship between a transistor’s base-­emitter voltage and its collector current. A modified version of a Gilbert cell is shown in Fig.31; this is Analog Devices’ implementation, as used in the classic but now discontinued Differential equations in computing A differential equation simply tells us how fast something is changing at any instant, for example, the rate at which a falling object accelerates due to the force of gravity acting on it, or the oscillatory acceleration of a mass on a spring due to spring tension. Integration is the reverse operation: it turns a rate of change into the total accumulated quantity, such as the speed of the object as it falls; velocity is the integral of acceleration, and position is the integral of velocity. In an electronic analog computer, differentiation and integration are calculated physically and continuously by the single most important building block, the integrator circuit. It uses just one operational amplifier, one resistor, and one capacitor (see Fig.27). The resistor converts the input voltage (representing the rate of change) into a current that steadily charges or discharges the capacitor; the voltage across the capacitor therefore becomes the running total, which is the mathematical integral of the input, all with virtually zero delay. As an analogy, think of the capacitor as a bucket collecting water (current) at a rate set by the input voltage (pressure); the water level at any moment is the integral, mirrored by the output voltage. Because this happens continuously and in real time, the falling object differential equation d2y/dt2 = -9.8m/s2 can be solved by feeding a constant -9.8V into the first integrator. Its output becomes a steadily rising voltage ramp (velocity), which can then be fed to a second integrator, producing a downward-opening parabolic voltage vs time curve (position). An oscilloscope or chart recorder connected to the output can visualise voltage (y-axis) over time (x-axis) to observe the parabolic trajectory. This is shown in a YouTube video at https://youtu.be/3tOA8Fo6b7A Another example is simple harmonic motion, x’’ + ω2x = 0. Two integrators integrate acceleration (x’’) to velocity (x’) and again to displacement (x) with one or two inverters to correct the signs. That is why analog computers were once called differential analysers: they almost instantly turned differential equations into voltage curves, providing an answer to many engineering problems. On a digital computer in the 1960s, this would have required pages of digital code and seconds or minutes of computation even on the fastest digital machines of the day. The same humble op amp based integrator principle that powered Apollo simulations and 1960s control systems is now reappearing with a different implementation in ultra-low-power-consumption AI chips, proving that for many continuous, real-world problems, analog integration remains unmatched in speed and energy efficiency. Fig.30: in this logarithm converter, Vy is a constant, while Is is a scaling parameter of the transistor. Fig.31: a modified Gilbert cell core, as used in Analog Devices’ AD534. The inputs are Vx and Vy, while the output is E0. Source: www.analog.com/ media/en/training-seminars/tutorials/MT-079.pdf siliconchip.com.au Australia's electronics magazine May 2026  27 Fig.32: a gyrator or synthetic inductor (far left) and its equivalent circuit. Fig.33: some mechanical and electrical analogies. AD534 multiplier chip. It was replaced by the AD633 and AD734, both still available. These chips were widely used in 1970s-1980s analog computing for multiplication, division, powering and root functions. Explaining how the Gilbert cell circuitry works is beyond the scope of this article; interested readers can visit siliconchip.au/link/aca5 and https://w. wiki/HHbV For multiplication, the circuit takes two input voltages Vx and Vy, converts them to currents, multiplies those currents in the transistor core, then converts the result back to an output voltage giving Vout = k × Vx × Vy (where k is a constant, usually about 1/10). By feeding the multiplier’s own output back into one of its inputs (often through an op amp), you get division (Vout = Vx ÷ Vy). Squaring simply involves connecting both inputs together. Square-rooting uses the multiplier in a feedback loop that forces Vout2 = Vin. The same building block, with a few extra resistors or capacitors, can also perform amplitude modulation, frequency doubling, RMS-to-DC conversion and even logarithmic/exponential functions. Another simple circuit that can form part of an electronic analog computer is the Wheatstone bridge. An unknown resistance is found by balancing known resistance values against the unknown. In essence, multiplication and division are performed using calibrated resistors to balance the bridge and find the unknown value. A modified Wheatstone bridge can also be used to compute the tangent of an angle or the hypotenuse Fig.34: the OME P2 is an electronic analog computer made by the Société d’électronique et d’automatisme (SEA) in 1952. It was used for simulations during the development of the Concorde. Source: https://w.wiki/HTe8 (CC-BY-SA 4.0) 28 Silicon Chip Australia's electronics magazine siliconchip.com.au of a right-angle triangle. A circuit to divide and multiply using a Wheatstone bridge was published in the June 1960 edition of Radio-Electronics (see siliconchip.au/link/aca6). As inductors are large for use at low frequencies and have other deficiencies, a gyrator circuit can act as a ‘synthetic inductor’, comprising an op amp, resistor and capacitor – see Fig.32. Electrical and mechanical equivalents One of the main uses of traditional analog computing was to simulate mechanical systems. There were two ways to do this with electronic analog computers: 1. The impedance analogy (force-­ voltage or Maxwell analogy), in which mechanical force corresponds to voltage and velocity to current. 2. The mobility analogy (force-­ current analogy or Firestone), in which force aligns with current and velocity with voltage. Other parameters equating physical and electrical quantities are shown in Table 2. The very name “analog computer” comes from the ability to generate analogies. Some examples are shown in Fig.33. To decide which analogy to apply, the following are considered: If a direct mapping of impedance values is desired, so mechanical impedances match electrical impedances numerically, the impedance analogy (also called the Maxwell analogy) is used. Mechanical impedance measures a system’s resistance to motion, while electrical impedance measures opposition to alternating current. This analogy allows direct quantitative correspondence, but has the disadvantage that the topology is inverted, that is, mechanical series connections become electrical parallel connections and vice versa – see Fig.35. Fig.35: a simple series LCR resonator, mechanical and electrical equivalents. This is the Maxwell analogy, in which mechanical parallel connections become series electrical connections. F = force, S = spring stiffness, M = mass and R = damper resistance. Fig.36: a simple series LCR resonator with mechanical and electrical equivalents. This is the Firestone analogy, in which mechanical parallel connections remain parallel electrical connections. If, instead, it is desired to preserve the physical topology of the system so that the electrical circuit mirrors the mechanical connections, the mobility analogy (also called the Firestone analogy) is chosen. Here, parallel mechanical elements are represented as parallel electrical elements, and series elements remain in series, making this arrangement more intuitive for complex systems. However, the impedances are inverted – see Fig.36. Figs.35 & 36 are electrically series or parallel LCR resonator circuits. Depending on the analogy used, both can be analogues of the same mechanical system, which could be an automotive suspension or engine mount system, a tuned mass damper in a tall building, the suspension of a washing machine drum or aircraft landing gear. The equivalent mechanical device comprises a damper (shock absorber; R or 1/R), a mass representing inertia (L or C) and a spring represented by its stiffness (C or L), all connected in parallel in both cases. As mentioned earlier, rather than using physical inductors for L, impedance inverters (gyrators) are usually used instead. Alternatively, real inductors could be used, but the circuit could be operated at a higher frequency than in reality (eg, 10× or 100×). Next month That’s all we have space for in this issue. As we have already discussed the history of analog computers, the second and final instalment next month will concentrate on their presSC ent and future. Table 2: mechanical and electrical equivalent quantities in analog computing. Quantity Impedance (force-voltage) analogy (Maxwell) Mobility (force-current) analogy (Firestone) Force (F) Voltage (V) Current (I) Velocity (v) Current (I) Voltage (V) Mass (m) Inductance (L) Capacitance (C) Damping (b) Resistance (R) Conductance (G) Spring constant (k) Reciprocal of capacitance (1/C) Reciprocal of inductance (1/L) Displacement (x) Magnetic flux linkage (λ) or charge in some contexts Charge (q) Impedance Preserved (Ze ∝ Zm) siliconchip.com.au Inverted (Ze ∝ 1/Zm) Australia's electronics magazine May 2026  29