path: root/module-design.typ

#import "@preview/unify:0.8.1": numrange, qty, qtyrange, unit
#import "@preview/diverential:0.3.0": *

= Module design <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(<module-design-terminology>) 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(<module-design-modules-categories>) 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(<error-budgeting-and-system-level-compensation>) 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(<error-compensation-strategies>) 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(<advanced-compensation-topologies>) 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(<implicit-computation>) 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(<reference-implementation>) 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-design-terminology>

This section defines the specialized terminology used throughout
#ref(<module-design>). These definitions establish a consistent vocabulary for
discussing precision analog circuit design within the SAME ecosystem. Terms are
organized into logical categories for ease of reference. Terms defined here may
have already appeared in earlier sections but are formally defined here for the
Module Design context.

=== Mathematical symbols <mathematical-symbols>

This section defines the mathematical symbols and notational conventions used
throughout #ref(<module-design>). Symbols are organized by category: fundamental
constants, electrical quantities, circuit parameters, error quantities, and
operators.

==== Fundamental constants <fundamental-constants>

#figure(
  table(
    columns: 4,
    table.header([Symbol], [Definition], [Value], [Unit]),
    [$k_B$], [Boltzmann constant], [$1.381 times 10^(-23)$], [$unit("joule per kelvin")$],

    [$upright(T)$], [Absolute temperature], [N/A], [$unit(K)$],
    [$upright(e)$], [Elementary charge], [$1.603 times 10^(-19)$], [$unit(C)$],
  ),
  caption: [Fundamental constants],
) <table-fundamental-constants>

==== Electrical quantities <electrical-quantities>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$upright(V)$], [Voltage (general)], [$unit(V)$],
    [$upright(I)$], [Current (general)], [$unit(A)$],
    [$upright(R)$], [Resistance], [$unit("ohm")$],
    [$upright(C)$], [Capacitance], [$unit(F)$],
    [$upright(L)$], [Inductance], [$unit(H)$],
    [$upright(P)$], [Power], [$unit(W)$],
    [$upright(f)$], [Frequency], [$unit("Hz")$],
    [$omega$], [Angular frequency ($omega = 2 pi upright(f)$)], [$unit("radian per second")$],

    [$tau$], [Time constant ($tau = upright("RC") "or" upright("L/R")$)], [$unit(s)$],

    [$upright("BW")$], [Bandwidth], [$unit("Hz")$],
  ),
)

==== Voltage and current subscript conventions
<voltage-and-current-subscript-conventions>

#figure(
  table(
    columns: 3,
    table.header([Subscript], [Meaning], [Example]),
    [in], [Input], [$V_"in", I_"in"$],
    [out], [Output], [$V_"out", I_"out"$],
    [ref], [Reference], [$V_"ref"$],
    [pp], [Peak-to-peak], [$V_"pp"$],
    [rms], [Root-mean-square], [$V_"rms"$],
    [n, noise], [Noise], [$V_n, upright(e)_n, i_n$],
    [OS], [Offset], [$V_"OS"$],
    [leak], [Leakage], [$I_"leak"$],
    [supply], [Power supply], [$V_"supply"$],
    [$plus$, $minus$], [Positive / negative input or rail], [$V_plus, V_minus$],

    [CM], [Common-mode], [$V_"CM"$],
    [diff], [Differential], [$V_"diff"$],
    [CR], [Coefficient of resistance], [$V_"CR"$],
    [CC], [Coefficient of capacitance], [$V_"CC"$],
  ),
  caption: [Voltage and current subscript conventions],
) <table-voltage-and-current-subscript-conventions>

==== Circuit and component parameters <circuit-and-component-parameters>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$upright(G)$], [Gain (closed-loop)], [dimensionless or $unit("dB")$],
    [$upright(A)$], [Gain (open-loop)], [dimensionless or $unit("dB")$],
    [$upright(A)_"OL"$], [Open-loop gain (explicit)], [dimensionless],
    [$beta$], [Feedback factor], [dimensionless],
    [$upright(A) beta$], [Loop gain], [dimensionless],
    [$upright(H)$], [Transfer function], [dimensionless],
    [$R_f$], [Feedback resistor], [$unit("ohm")$],
    [$R_"in"$], [Input resistor], [$unit("ohm")$],
    [$Z_"in"$], [Input impedance], [$unit("ohm")$],
    [$Z_"out"$], [Output impedance], [$unit("ohm")$],
    [$upright("GBW")$], [Gain-bandwidth product], [$unit("Hz")$],
    [$upright("SR")$], [Slew rate], [$unit("volt per micro second")$],
    [$upright("CMRR")$], [Common-mode rejection ration], [$unit("dB")$],
    [$upright("PSRR")$], [Power supply rejection ratio], [$unit("dB")$],
    [$upright("TC")$], [Temperature coefficient], [$unit("ppm per celsius")$],
    [$V_"CR"$], [Voltage coefficient of resistance], [$unit("ppm per volt")$],
    [$V_"CC"$], [Voltage coefficient of capacitance], [$unit("ppm per volt")$],
    [$upright("DA")$], [Dielectric absorption], [$unit("percent")$],
    [$S$], [Seebeck coefficient], [$unit("micro volt per celsius")$],
    [$theta$], [Thermal resistance], [$unit("celsius per watt")$],
  ),
  caption: [Circuit and component parameters],
) <table-circuit-and-component-parameters>

==== Error and precision quantities <error-and-precision-quantities>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$epsilon$], [Error (general)], [$unit("ppm")$ or $unit("uV")$],
    [$epsilon_"max"$], [Maximum allowable error], [$unit("ppm")$ or $unit("uV")$],

    [$epsilon_"total"$], [Total combined error], [$unit("ppm")$ or $unit("uV")$],

    [$epsilon_"systematic"$], [Systematic error component], [$unit("ppm")$],
    [$epsilon_"random"$], [Random error component], [$unit("uV") upright("RMS")$],

    [$epsilon_"offset"$], [Offset error], [$unit("uV")$],
    [$epsilon_"gain"$], [Gain error], [$unit("ppm")$],
    [$epsilon_"ratio"$], [Ratio error for matched components], [$unit("ppm")$],
    [$epsilon_"thermal"$], [Thermally-induced error], [$unit("ppm")$],
    [$dv(epsilon, t)$], [Drift rate], [$unit("ppm per hour")$],
    [$S_y^p$], [Sensitivity of $y$ to parameter $p$], [dimensionless],
    [$upright("SNR")$], [Signal-to-noise ratio], [$unit("dB")$],
    [$upright("RTI")$], [Referred-to-input], [$unit("uV")$],
    [$upright("RTO")$], [Referred-to-output], [$unit("uV")$],
    [$upright("FS")$], [Full scale], [$unit("V")$],
  ),
  caption: [Error and precision quantities],
) <table-error-and-precision-quantities>

==== Noise quantities <noise-quantities>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$upright(e)_n$], [Voltage noise spectral density], [$unit("nV")/sqrt(unit("Hz"))$],

    [$upright(i)_n$],
    [Current noise spectral density],
    [$unit("pA")/sqrt(unit("Hz"))$ or $unit("fA")/sqrt(unit("Hz"))$],

    [$upright(e)_(n,"white")$], [White noise component], [$unit("nV")/sqrt(unit("Hz"))$],

    [$upright(e)_(n,1/upright(f))$],
    [$1/upright(f)$ noise component],
    [$unit("nV")/sqrt(unit("Hz"))$ at $qty(1, "Hz")$],

    [$upright(f)_c$], [Noise corner frequency ($1/upright(f)$ to white)], [$unit("Hz")$],

    [$upright(V)_n$], [Total noise voltage], [$unit("V") upright("RMS")$],
    [$upright("CNI")$], [Current noise index (potentiometers)], [$unit("dB")$],
  ),
  caption: [Noise quantities],
) <table-noise-quantities>

==== Time domain and modulation quantities
<time-domain-and-modulation-quantities>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$upright(D)$], [Duty cycle], [$unit("percent")$ or dimensionless],
    [$upright(f)_"carrier"$], [Carrier frequency], [$unit("Hz")$],
    [$upright(f)_0$], [Resonant or center frequency], [$unit("Hz")$],
    [$phi$], [Phase], [$unit("radian")$ or $unit("degree")$],
    [$Delta phi$], [Phase error or shift], [$unit("radian")$ or $unit("degree")$],

    [$upright(t)_"settle"$], [Settling time], [$unit("s")$],
    [$upright(t)_h$], [Timing jitter], [$unit("ps")$ or $unit("ns")$],
  ),
  caption: [Time domain and modulation quantities],
) <table-time-domain-and-modulation-quantities>

==== Thermal quantities <thermal-quantites>

#figure(
  table(
    columns: 3,
    table.header([Symbol], [Definition], [Typical unit]),
    [$upright(T)$], [Temperature (absolute)], [$unit("K")$],
    [$delta upright(T)$], [Temperature difference], [$unit("celsius")$ or $unit("K")$],

    [$(Delta upright(T))/(upright(d) y)$], [Vertical temperature gradient], [$unit("celsius per centimeter")$],

    [$theta_"conv"$], [Convective thermal resistance], [$unit("celsius per watt")$],

    [$theta_"cond"$], [Conductive thermal resistance], [$unit("celsius per watt")$],

    [$accent(Q, dot)$], [Heat flux], [$unit("W")$],
    [$accent(upright(m), dot)$], [Mass flow rate], [$unit("kilo gram per second")$],

    [$upright(c)_p$], [Specific heat capacity], [$unit("J")/(unit("kg") unit("K"))$],
  ),
  caption: [Thermal quantities],
) <table-thermal-quantities>

==== Mathematical operators and functions <mathematical-operators-and-functions>

#figure(
  table(
    columns: 2,
    table.header([Notation], [Meaning]),
    [$sum$], [Summation],
    [$product$], [Product],
    [$sqrt("")$], [Square root],
    [$dvp(y, x)$], [Partial derivative of $y$ with respect to $x$],
    [$dv(y, x)$], [Total derivative of $y$ with respect to $x$],
    [$integral$], [Integral],
    [$log_10$], [Common logarithm (base $10$)],
    [$ln$], [Natural logarithm (base $e$)],
    [$exp$], [Exponential function],
    [$abs(x)$], [Absolute value of $x$],
    [$x mod y$], [Modulo operation (remainder of $x$ divided by $y$)],
    [$in$], [Element of a set],
    [$upright("RSS")$], [Root-sum-square: $sqrt(x_1^2 + x_2^2 + ... + x_n^2)$],
  ),
  caption: [Mathematical operators and functions],
) <table-mathematical-operators-and-functions>

==== Unit prefixes <unit-prefixes>

Standard SI prefixes are used throughout:

#figure(
  table(
    columns: 3,
    table.header([Prefix], [Symbol], [Factor]),
    [tera], [$upright(T)$], [$10^12$],
    [giga], [$upright(G)$], [$10^9$],
    [mega], [$upright(M)$], [$10^6$],
    [kilo], [$upright(k)$], [$10^3$],
    [], [], [$10^0$],
    [milli], [$upright(m)$], [$10^(-3)$],
    [micro], [$upright(mu)$], [$10^(-6)$],
    [nano], [$upright(n)$], [$10^(-9)$],
    [pico], [$upright(p)$], [$10^(-12)$],
    [femto], [$upright(f)$], [$10^(-15)$],
  ),
  caption: [Unit prefixes],
) <table-unit-prefixes>

==== Special notation conventions <special-notation-conventions>

/ Parts per million ($unit("ppm")$): Dimensionless ratio equal to $10^(-6)$.
  Used for expressing small fractional errors.
  / Example: $qty(10, "ppm") "of" qty(20, "V") = qty(200, "uV")$.
/ Parts per billion ($unit("ppb")$): Dimensionless ratio equal to $10^(-9)$.
  Used for expressing frequency stability of precision oscillators.
/ Decibels ($unit("dB")$): Logarithmic ratio.
  / For voltage or amplitude ratios:
    $unit("dB") = 20 log_10(upright(V)_1/upright(V)_2)$.
  / For power ratios: $unit("dB") = 10 log_10(upright(P)_1/upright(P)_2)$.
/ $unit("dBc")/unit("Hz")$: Phase noise specification. Power spectral density of
  phase fluctuations relative to carrier power, per hertz of bandwidth.
/ Subscript conventions for matched pairs: When two components are matched,
  subscripts 1 and 2 (or A and B) denote individual components, while the ratio
  $upright(R)_1/upright(R)_2$ denotes the matched ratio whose tolerance is
  tighter than either individual tolerance.
/ Temperature in calculations: Noise calculations use absolute temperature
  (Kelvin). Temperature coefficients use Celsius ($unit("celsius")$), since only
  temperature differences matter and $Delta upright(T)$ in Kelvin equals
  $Delta upright(T)$ in Celsius.
/ Frequency-domain notation: Transfer functions are expressed in the Laplace
  domain with the complex frequency variable $s = sigma + j omega$, where
  $j = sqrt(−1)$. For sinusoidal steady-state analysis, $s = j omega$.

=== Error and precision terminology <error-and-precision-terminology>

/ Error: Any deviation of an actual output from its ideal mathematical value.
  Errors are classified by their time dependence (static vs. drift), signal
  dependence (offset, gain, nonlinearity), and statistical character (systematic
  vs. random).
/ Systematic Error: A deterministic deviation that could, in principle, be
  predicted and corrected if all influence quantities were known. Systematic
  errors contribute to the precision budget. Examples include resistor
  temperature coefficients and op-amp offset voltage.
/ Random Error: A fundamentally unpredictable deviation arising from thermal
  agitation, quantum fluctuations, or chaotic dynamics. Random errors contribute
  to the noise budget. Examples include thermal noise and shot noise.
/ Offset Error: A constant additive error independent of signal amplitude. An
  offset error adds a fixed voltage to the output regardless of input level.
/ Gain Error: An error proportional to signal amplitude. A gain error multiplies
  the output by a factor deviating from the ideal unity or specified gain.
/ Nonlinearity Error: An error that depends on signal amplitude in a complex,
  non-proportional way. Nonlinearity errors introduce harmonic distortion and
  intermodulation products.
/ Static Error: An error that is constant over the timescale of a measurement or
  computation. Static errors can be calibrated out at a single point in time.
/ Drift: A time-varying systematic error that changes either deterministically
  (as with temperature-driven parameter changes) or stochastically (as with
  flicker noise). Drift errors require continuous compensation or periodic
  recalibration.
/ Drift Rate: The rate at which a parameter changes over time, typically
  specified in $unit("ppm per hour")$. The SAME Metrologic tier specifies a
  maximum drift rate of $qty(0.014, "ppm per hour")$.
/ Precision: A measure of how closely repeated measurements or computations
  agree with each other, expressed as the maximum acceptable deviation from the
  ideal value. The SAME Metrologic tier specifies $qty(10, "ppm")$
  ($qty(0.001, "percent")$) precision.
/ Accuracy: A measure of how closely a measurement or computation agrees with
  the true value. In SAME, accuracy is defined relative to the
  $plus.minus qty(10.0000, "V")$ system reference.
/ Signal-to-Noise Ratio ($upright("SNR")$): The ratio of signal power to noise
  power, typically expressed in decibels. The SAME Metrologic tier specifies
  $qty(90, "dB") upright("SNR")$, corresponding to approximately
  $qty(632, "uV") upright("RMS")$ noise referred to the $qty(20, "Vpp")$ signal
  range.
/ Referred-to-Input ($upright("RTI")$): An error specification expressed as an
  equivalent error at the circuit input. $upright("RTI")$ allows comparison of
  errors across stages with different gains.
/ Referred-to-Output ($upright("RTO")$): An error specification expressed at the
  circuit output. $upright("RTO")$ is the natural choice for specifications that
  must be met at the output.
/ Noise Gain: The gain seen by error sources at the amplifier input, which
  differs from signal gain in inverting configurations. For an inverting
  amplifier with feedback resistor $upright(R)_upright(f)$ and input resistor
  $upright(R)_"in"$, noise gain equals
  $1 + upright(R)_upright(f)/upright(R)_"in"$.
/ Error Budget: A systematic accounting of all error sources and their
  contributions to total system error. Errors are typically combined by
  root-sum-square ($upright("RSS")$) for independent sources or algebraic sum
  for correlated sources.

=== Component terminology <component-terminology>

/ Temperature Coefficient (Tempco): The rate at which a component parameter
  changes with temperature, typically specified in $unit("ppm per celsius")$.
  Lower tempco indicates greater temperature stability.
/ Voltage Coefficient of Resistance ($upright(V)_"CR"$): The rate at which
  resistance changes with applied voltage, specified in $unit("ppm")/unit("V")$
  or $unit("ppm")/unit("V")_2$. $upright(V)_"CR"$ creates nonlinearity in
  circuits with signal-dependent voltage across resistors.
/ Voltage Coefficient of Capacitance ($upright(V)_"CC"$): The rate at which
  capacitance changes with applied voltage. Class 2 ceramic capacitors (X7R,
  X5R) can exhibit $upright(V)_"CC"$ of
  $qtyrange(-30, -80, "percent", delimiter: "\"to\"")$ at rated voltage, making
  them unsuitable for signal paths.
/ Dielectric Absorption ($upright("DA")$): A memory effect in capacitors where
  rapid charge/discharge cycles leave residual polarization that manifests as
  unpredictable voltage contributions. Film capacitors (polypropylene,
  polystyrene) have $upright("DA")$ below $qty(0.05, "percent")$.
/ Seebeck Effect: The thermoelectric effect where a temperature difference
  across a junction of dissimilar metals produces a voltage. Seebeck voltages at
  solder joints can contribute significant offset errors if thermal gradients
  exist.
/ Seebeck Coefficient: The voltage generated per degree of temperature
  difference at a thermocouple junction, specified in
  $unit("micro volt per celsius")$. Copper-to-Kovar junctions have coefficients
  around $qty(40, "micro volt per celsius")$.
/ Matched Components: Components fabricated together on a common substrate or
  selected to have closely tracking parameter values. Matching reduces ratio
  errors even when absolute tolerances are significant.
/ Ratio Tolerance: The tolerance on the ratio of two matched component values,
  which is typically much tighter than individual absolute tolerances. Thin-film
  resistor networks achieve ratio tolerances of $qty(0.01, "percent")$
  ($qty(100, "ppm")$) or better.
/ Tracking Temperature Coefficient: The difference in temperature coefficients
  between matched components. Well-matched components have tracking tempcos
  below $qty(2, "ppm per celsius")$ even when individual tempcos are
  $qty(25, "ppm per celsius")$.

=== Amplifier and circuit terminology <amplifier-and-circuit-terminology>

/ Input Offset Voltage ($upright(V)_"OS"$): The DC voltage that must be applied
  between an op-amp's inputs to force the output to zero. $upright(V)_"OS"$
  appears as an error at the input that is multiplied by the noise gain.
/ Input Bias Current ($upright(I)_upright(B)$): The DC current flowing into or
  out of an op-amp's input terminals required to bias the input stage. Bias
  current through source impedances creates voltage errors.
/ Input Offset Current ($upright(I)_"OS"$): The difference between the bias
  currents at an op-amp's two input terminals. Balancing source impedances can
  reduce bias current error to offset current error.
/ Common-Mode Rejection Ratio ($upright("CMRR")$): The ratio of differential
  gain to common-mode gain, expressing an amplifier's ability to reject signals
  that appear equally on both inputs. High $upright("CMRR")$
  ($gt qty(120, "dB")$) is essential for precision differential measurements.
/ Power Supply Rejection Ratio ($upright("PSRR")$): The ratio of differential
  gain to power supply gain, expressing an amplifier's immunity to supply
  voltage variations. $upright("PSRR")$ degrades with frequency, making
  high-frequency supply noise more problematic.
/ Open-Loop Gain ($upright(A)_"OL"$): The gain of an amplifier without feedback,
  typically $106$ to $108$ ($qtyrange(120, 160, "dB")$) for precision op-amps.
  Finite open-loop gain creates closed-loop gain error proportional to
  $upright(G)_"ideal"/upright(A)_"OL"$.
/ Gain-Bandwidth Product ($upright("GBW")$): The product of an op-amp's DC
  open-loop gain and the frequency at which open-loop gain falls to unity. For a
  single-pole op-amp, $upright("GBW")$ is constant and determines gain error at
  frequency.
/ Slew Rate: The maximum rate of change of an op-amp's output voltage, typically
  specified in $unit("volt per micro second")$. Insufficient slew rate causes
  distortion for large, fast signals.
/ Settling Time: The time required for an amplifier output to settle within a
  specified error band after a step input. Settling to $qty(10, "ppm")$
  typically requires $10$-$20$ time constants.
/ Chopper Stabilization: A technique that eliminates low-frequency errors by
  periodically reversing signal polarity and correcting for the resulting
  offset. Chopper-stabilized amplifiers achieve offset drifts below
  $qty(0.05, "micro volt per celsius")$.
/ Loop Gain: The product of forward gain $upright(A)$ and feedback factor $beta$ in a
  feedback system. Loop gain determines error suppression: errors in the forward
  path are divided by $(1 + upright(A) beta)$.

=== Computation terminology <computation-terminology>

/ Ratiometric Design: A design methodology where computations depend on
  component ratios rather than absolute values. Ratiometric designs achieve
  precision far exceeding individual component tolerances.
/ Implicit Computation: A design methodology where results emerge from the
  equilibrium condition of a feedback system rather than from explicit
  calculation. Implicit computation exploits high loop gain to achieve precision
  exceeding that of explicit approaches.
/ Explicit Computation: A design methodology where results are calculated by
  applying known operations sequentially. Errors accumulate through the
  computation chain.
/ Summing Divider: An implicit computation topology that computes the ratio of
  two current sums, implementing division through feedback equilibrium rather
  than explicit divider circuitry.
/ Virtual Ground: A circuit node maintained at ground potential by op-amp
  feedback, despite signal currents flowing through it. The accuracy of a
  virtual ground depends on the op-amp's open-loop gain.
/ Summing Junction: The node at an op-amp's inverting input in a summing
  amplifier configuration, where input currents sum to zero (Kirchhoff's current
  law). Also called a summing node.

=== Time-domain and modulation terminology
<time-domain-and-modulation-terminology>

/ Pulse-Width Amplitude Modulation (PWAM): A modulation technique where one
  multiplicand is encoded as the duty cycle of a pulse train, enabling
  multiplication through time-domain encoding rather than amplitude-domain
  multiplication.
/ Duty Cycle: The fraction of a period during which a pulse signal is high. In
  PWAM, the duty cycle encodes signal amplitude: $qty(50, "percent")$
  corresponds to zero, $qty(0, "percent")$ to $minus upright(V)_"ref"$, and
  $qty(100, "percent")$ to $plus upright(V)_"ref"$.
/ Carrier Frequency: The frequency of the triangle wave or pulse train used in
  PWAM modulation. The SAME specification uses a $qty(500, "kHz")$ carrier
  derived from the $qty(10, "MHz")$ Master Oscillator.
/ Master Oscillator: The system-wide $qty(10, "MHz")$ sine wave reference
  distributed to all modules for time-domain computations. The Master Oscillator
  provides frequency stability of $plus.minus qty(10, "ppb")$ using an
  oven-controlled crystal oscillator (OCXO).
/ Stagger: The phase offset applied to PWAM carriers in adjacent modules to
  prevent intermodulation between neighboring switching frequencies. The Stagger
  rail indicates whether a module should operate at $qty(0, "degree")$ or
  $qty(90, "degree")$ phase relative to the Master Oscillator.
/ Phase Noise: Random fluctuations in the phase of an oscillator signal, which
  manifest as timing jitter. Low phase noise ($lt.eq qty(-140, "dBc per hertz")$
  at $qty(1, "kHz")$ offset) is essential for high-precision PWAM.
/ Jitter: Random variations in the timing of signal transitions. Clock jitter
  converts directly to amplitude noise in PWAM systems.

=== Thermal terminology <thermal-terminology>

/ Isothermal: Having uniform temperature throughout. Isothermal layout places
  matched components along lines of constant temperature to ensure identical
  thermal environments.
/ Thermal Gradient: The spatial rate of change of temperature across a surface
  or volume, typically expressed in $unit("celsius per centimeter")$. Thermal
  gradients cause matched components to experience different temperatures,
  degrading their matching.
/ Ovenization: The practice of enclosing a critical component (typically a
  voltage reference) in a temperature-controlled enclosure maintained above
  maximum ambient temperature.
/ Thermal Time Constant: The time required for a thermal system to reach
  approximately $qty(63, "percent")$ of its final temperature after a step
  change in power or ambient temperature.
/ Thermal Tail: The slow settling of circuit parameters after a thermal
  transient, caused by the multiple thermal time constants in a system (die,
  package, PCB, enclosure).
/ Self-Heating: The temperature rise in a component caused by power dissipation
  within the component itself. Sel