#import "lib/unify.typ": qty

= Introduction <introduction>

== What is analog computing? <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 <short-history-of-analog-computing>

=== Mechanical and hydraulic analog computers
<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 <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
<golden-age-of-eletronic-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 <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 <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
<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 <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 <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 <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 <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 <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 <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
<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 <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 <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 <readers-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 <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."
