#import "@preview/unify:0.8.1": numrange, qty, qtyrange = Module design The preceding sections established what SAME is: its signal standards, precision tiers, power distribution, and mechanical format. This section addresses how SAME modules are designed to meet these specifications — particularly the demanding requirements of the Metrologic tier. The challenge is substantial. The Metrologic tier demands $qty(10, "ppm")$ precision, $qty(90, "dB")$ signal-to-noise ratio, and $qty(0.014, "ppm per hour")$ drift over a DC to $qty(20, "kHz")$ bandwidth. These specifications, taken together, require that a $qty(20, "V")$ signal range be resolved to $qty(200, "uV")$, that noise remain below $qty(632, "uV") upright("RMS")$, and that accumulated drift not exceed $qty(10, "ppm")$ over thirty days of continuous operation. Achieving this with commodity through-hole components — resistors, capacitors, and op-amps available from any electronics distributor — would appear to be impossible. The tolerances of standard components are measured in percent, not parts per million. The temperature coefficients of common resistors would exhaust the entire drift budget in minutes, not months. Yet it is possible. The gap between component specifications and system requirements is bridged not by exotic parts but by topology: the deliberate arrangement of ordinary components into configurations where their errors cancel, track, or become irrelevant to the computation. A resistor's absolute value may be uncertain to 1%, but its ratio to an adjacent resistor from the same batch, at the same temperature, can be stable to $qty(10, "ppm")$. An amplifier's offset voltage may drift by microvolts per degree, but a servo loop can continuously measure and nullify that drift faster than it accumulates. A multiplier's nonlinearity may be limited by transistor physics to $qty(0.1, "percent")$, but encoding the multiplication in the time domain rather than the amplitude domain sidesteps those physics entirely. These techniques are not novel. They are the accumulated wisdom of precision analog design, developed by metrologists and instrumentation engineers over seven decades. What SAME contributes is their systematic application within constraints that matter for sustainability and sovereignty: through-hole construction that can be assembled and repaired with basic equipment, open documentation that enables understanding rather than mere replication, and component choices that will remain available as specific part numbers inevitably become obsolete. This section proceeds in six parts. + #ref() establishes terminology. Precision analog design has a specialized vocabulary; ambiguous terms lead to ambiguous analysis. We define our terms once, carefully, and use them consistently throughout. + #ref() categorizes the three types of SAME modules — Interface, Compute, and Control — and specifies the requirements particular to each category. Not all modules face identical constraints; a control module generating voltages from a front-panel knob operates under different rules than a compute module performing four-quadrant multiplication. + #ref() develops the error budget framework. We enumerate every source of error in a precision analog signal path, quantify each source using commodity component specifications, and construct the naive error budget that results from conventional design. This budget exceeds our specifications by factors ranging from $11$ to $4000$. The purpose of this exercise is not despair but clarity: we must know precisely where the errors arise before we can systematically eliminate them. + #ref() presents the five fundamental compensation strategies that close the gap between naive and Metrologic performance. Each strategy is developed from physical principles, analyzed mathematically, and specified with design rules sufficient to implement it correctly. + #ref() extends these techniques for applications demanding performance beyond the base Metrologic specification. They can push precision into the 1-5ppm range for specialized applications. These techniques are optional — the base compensation strategies suffice for Metrologic tier — but they demonstrate that the approach has headroom. + #ref() introduces implicit computation, a design philosophy where mathematical operations emerge from feedback equilibrium rather than explicit signal processing. Division, for example, can be implemented explicitly using logarithms (with their associated nonlinearity) or implicitly using a multiplier in a feedback loop (where the loop forces the quotient to whatever value satisfies the multiplication). Implicit designs often achieve superior precision because the feedback loop continuously corrects errors that would accumulate in an explicit signal chain. The reader seeking to understand how the reference implementation in #ref() achieves its specifications, or to design new modules, will find the theoretical foundation here. We make no apology for the depth of what follows. Precision is not achieved by accident or by following recipes without understanding. It is achieved by understanding the physics deeply enough to make the physics work for you rather than against you. == Terminology == Module categories == Error budgeting and system-level compensation == Error compensation strategies == Advanced compensation topologies == Implicit computation