#import "@preview/unify:0.8.1": qty = Introduction == What is analog computing? Analog computing is the action of leveraging the properties of physical phenomena to model mathematical principles. The actual phenomena can be as diverse as hydraulics, mechanics, or electrics. In an electronic analog computer, voltages represent variables and operational amplifier circuits perform mathematical operations on them. Modeling the mathematical principles being computed implies that the results are continuous in time and amplitude. This directly contrasts digital computing, where results are symbolic and discrete. == Short history of analog computing === Mechanical and hydraulic analog computers Analog computing traces its roots to ancient Greece, with the Antikythera mechanism. It re-emerged time and time again across the ages, notably with the invention of the Slide Rule for computation of multiplications and divisions in the 1620s, and Lord Kelvin's Tide-Predicting machine invented in 1872. Mechanical or hydraulic analog computers (sometimes electronically controlled) continued to be the standard until the late 1950s. === First electronic analog computers In 1941, Karl D. Swartzel Jr. of Bell Labs patented the first operational amplifier (op-amp). 1942 saw the birth of the first fully electronic analog computer for real-time computation by Helmut Hölzer, to calculate V-2 rocket trajectories. In 1950, Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi developed the "Direct Analogy Electric Analog Compute" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems" - James S. Small, "The Analogue Alternative: The Electronic Analogue Computer in Britain and the USA, 1930-1975" Routledge in 2001). In 1960, the first educational electronic analog computer, the Heathkit EC-1, was released. It was programmed with patch cords and featured nine operational amplifiers (op-amps). In the late 1960s, electronic analog computer designs were published in electronics magazines. This is notably the case for the PEAC (Practical Electronics Analog Computer), published in 1968 in Practical Electronics. === Golden age of electronic analog computers Starting with the EAI PACE TR-48, produced by Electronic Associates Inc. in 1961, hybrid computers became the industry standard for high-performance tasks. These machines combined the speed of analog computation for solving differential equations with the logical control and storage of digital computers. They were heavily utilized in the aerospace and automotive industries for real-time simulation — such as modeling the Space Shuttle's flight dynamics or nuclear power plant operations — tasks where purely digital computers of the era were still too slow. === Decline of analog computing The decline began in the late 1970s and accelerated swiftly throughout the 1980s, driven by the "Digital Revolution." While analog computers were fast, they suffered from physical limitations like noise floors and component aging (drift), which limited their precision compared to the perfect repeatability of digital machines. Furthermore, programming an analog computer required physically rewiring "patch cords," a laborious process compared to the rapidly evolving software-based programming of digital systems. === Current times A new rise of analog computing is currently underway, often referred to as "Neuromorphic Computing" or "In-Memory Computing". This generation uses the physical properties of memory devices (like resistance) to perform calculations, mimicking the neural structure of the human brain to process information. In 2021, startup Mythic introduced the M1076 Analog Matrix Processor, a chip that performs AI inference using the analog currents inside flash memory cells, delivering up to 25 TOPS (Trillion Operations Per Second) at incredibly low power. Mythic filed for bankruptcy in 2024, but managed to raise \$125 million in December 2025, showing that there is still turbulence in the neuromorphic startup space. The field is still very active, notably with the Innatera Pulsar or the Applied Brain Research TSP1, both released in 2025. == The case for modern general purpose analog computers We believe the time is ripe for a revival of the General Purpose Analog Computer. Reintroducing general-purpose analog computing is not an exercise in retro-computing; it is a solution to specific modern problems. By combining the transparency of "Golden Age" architectures with modern low-noise components, we can achieve a new standard of computing that is sustainable, secure, and strategically independent. === Theoretical capabilities Historically, the General Purpose Analog Computer (GPAC) was perceived as being limited to solving differential equations, distinct from the universal logic of Turing Machines. However, this distinction assumes a finite system. In a sufficiently large analog system (the same way a digital computer is a Turing Machine assuming sufficiently large memory), the combinatorial logic required for universal computation is inherent in the topology. We do not rely on discrete "extensions" like Sample & Hold to achieve Turing Completeness; we use them merely for convenience. The $I$$(I x = x)$, $K$$(K x y = x)$ and $S$$(S x y z = x z(y z))$ Combinators (which are sufficient for Turing Completeness) are not a special digital mode; they are a description of signal distribution and modulation that exists in every analog patch. With enough modules, the "patch" becomes a computational engine of unbounded complexity, capable of recursive structures defined purely by feedback loops rather than iterative loops. This argument will be fully developed in further sections. === Technological sovereignty In an era of chip shortages and trade restrictions, reliance on $qty(5, "nm")$ or $qty(3, "nm")$ silicon creates critical vulnerabilities. A computer built from standard through-hole operational amplifiers and passive components does not require a multi-billion dollar foundry. It can be assembled in a standard electronics lab anywhere in the world. With a 100% open-source design and macro-scale components, the hardware is fully auditable. There are no hidden "black box" intellectual property cores or potential hardware backdoors, ensuring high confidence in the computing substrate for sensitive modeling. === Cost and accessibility High-performance simulation usually requires expensive workstations or licensing fees for proprietary software. By utilizing off-the-shelf components (common op-amps, resistors, standard capacitors), the Bill of Materials (BOM) is a fraction of the cost of a modern FPGA or GPU-based accelerator. The "Through-Hole First" design philosophy means these machines can be produced, modified, and repaired by students, hobbyists, or labs in developing nations, without the need for robotic surface-mount assembly lines. === Energy efficiency While digital computers must toggle millions of transistors at gigahertz speeds to approximate a differential equation, an analog computer simply is the equation. Solving a complex set of coupled differential equations on this standard requires only the static power to bias the amplifiers. It avoids the massive dynamic power consumption associated with the high-frequency clock cycles of digital processors. Using an analog architecture delivers results with significantly lower total energy consumption per solution, aligning with global goals for reduced carbon footprints in data processing. This will be fully developed in further sections. === Sustainability through repairability A 100% through-hole and open-source design ensures that every component is human-accessible. There are no microscopic BGA chips; the machine can be maintained indefinitely, breaking the environmentally destructive cycle of planned obsolescence. It essentially enforces the right to repair while allowing a reduction of e-waste. == The SAME Analog Modular Ecosystem With this specification, we introduce a new analog computing ecosystem. We believe that with the right infrastructure, modern components and the advances in electronics research, we can now build analog computers that address the three main points that caused the decline of analog computing in the 1980s: cost, precision and drift. === Making analog computers reliable and sustainable Electronics components are cheaper than ever right now. Op-amps that once cost hundreds of euros now cost at most a few dozen euros. PCB manufacturing is democratized. The material conditions are here. New advances in electronics research have solved the two remaining issues: drift and precision: with a combination of laser-trimmed components and topological advancements (servo loops, automated gain control, pulse width amplitude modulation, etc.), it is now possible to design analog circuits that are able to reach 0.001% precision (10ppm), over a $qty(90, "dB")$ signal to noise ratio (SNR), in a bandwidth ranging from DC to more than $qty(20, "kHz")$. === What SAME is not SAME is not a modular synthesizer format. It is not Eurorack, Serge or Buchla. While those synthesizer formats are based on general purpose analog computers, they are not designed for precision computations or repeatability. While SAME can be used for sound design or experimental composition, it does not provide the abstractions and simplifications that make synthesizers powerful. SAME is not a digitally controlled or calibrated analog computer. It focuses on fully analog computer topologies. It advocates a "what you see is what you get" approach. It has no presets, no patch memory. But it is precise enough that a patch sheet and a pen and paper allow full patch repeatability. We believe this approach is needed as it is more educational, and eliminates black boxes in programming (patches) and design (topologies). It is also more sustainable, as a design doesn't depend on a microcontroller and code that might fail and be out of production in five years. SAME is not a system on a chip (SOC). The revival of analog computing in the 2020s has been mainly driven by SOCs. We do recognize the importance of this approach, and its many benefits, notably in energy consumption. However, SOCs require digital control. With SAME, we aim at creating an infrastructure for sustainable electronics. A unit built in 2026 should still work in 2076. Some parts will have been changed, but by focusing on through-hole parts in production at the time of designing, we ensure that a human with a soldering iron will be able to repair them. === The scope of this specification In this specification, we will provide full details and rationale behind the SAME format. We will provide schematics, gerber files, CAD files, as well as ngspice simulations of a reference implementation. We will provide a validation methodology for our precision claims, as well as the data to support them. Finally, we will propose a tiered approach to precision: we believe that a topology that manages 10ppm precision and $qty(90, "dB") upright("SNR")$ SNR over DC to $qty(20, "kHz")plus$ bandwidth is worth using and studying even with a lower precision target of $qty(100, "ppm")$ or $qty(1000, "ppm")$. While to achieve $qty(10, "ppm")$ some parts might get expensive due to their very high precision, someone could still achieve great reliability with lower precision parts. For this reason, while we will propose only one specification for the SAME chassis and power distribution, for each module in the reference implementation, we will propose three bills of material (BOM): Educational, aiming at $qty(1000, "ppm")$; Industrial, aiming at $qty(100, "ppm")$; and Metrologic aiming at $qty(10, "ppm")$. === Reader's guide We recommend a reader not familiar with the field to first read this specification sequentially. @electrical-specifications and @mechanical-specifications will develop the core specifications of the SAME ecosystem. @module-design will specify the module design principles that allows it to achieve its precision goals. @compliance-verification will explain how to verify conformity of a SAME product with this specification. @reference-implementation will present a reference implementation of the system. Finally, @theory-of-operation and @applications will show how and when to use a SAME Analog Computer. == Document conventions To ensure interoperability between modules, chassis backplanes, and signal routing standards within the SAME Analog Modular Ecosystem, this specification utilizes specific keywords to denote requirement levels. The key words MUST, MUST NOT, REQUIRED, SHALL, SHALL NOT, SHOULD, SHOULD NOT, RECOMMENDED, MAY, and OPTIONAL in this document are to be interpreted as described in IETF RFC 2119. / MUST / SHALL / REQUIRED: These terms indicate an absolute requirement of the specification. Hardware or documentation that fails to meet these criteria is non-compliant. Imperative statements (commands) that do not employ specific keywords are also considered to be in this default state. - Example: "The reference voltage rail MUST maintain stability within ±0.01% of the nominal 10V output." / MUST NOT / SHALL NOT: These terms indicate an absolute prohibition of the specification. - Example: "Signal ground MUST NOT be tied directly to the chassis earth at the module level." / SHOULD / RECOMMENDED: These terms indicate that there may exist valid reasons in particular circumstances to ignore a particular item, but the full implications must be understood and carefully weighed and documented before choosing a different course. - Example: "Input impedance for operational amplifiers SHOULD exceed 1MΩ to minimize loading effects." / SHOULD NOT / NOT RECOMMENDED: These terms indicate that there may exist valid reasons in particular circumstances when the particular behavior is acceptable or even useful, but the full implications should be understood and the case carefully weighed and documented before implementing any behavior described with this label. / MAY / OPTIONAL: These terms indicate that an item is truly optional. One vendor may choose to include the item because a particular marketplace requires it or because the vendor feels that it enhances the product while another vendor may omit the same item. - Example: "The integration module MAY include a digital overflow indicator LED."