• TX looks fine, RX fails: bytes sent but not received, or decode shows intermittent framing errors.
• Only certain baud rates fail: one setting is stable while the adjacent step fails (often divider quantization / rounding artifacts).
• Temperature or time makes it worse: room temperature passes but high/low temp, aging, or long run time causes drops.
• Short frames pass, long frames fail: errors accumulate toward the end of a frame and break at stop-bit sampling.

• Budget formula template: inputs (frame bits, stop bits, oversampling policy, implementation margin) → outputs allowable total error X% (placeholder).
• Budget Row table fields: a fixed structure for TX and RX that converts ppm/percent/step error into a single worst-case sum.
• Strategy tree: choose clocking (XTAL/RC/PLL), divider approach, and calibration/auto-baud based on required margin.
• Verification plan: baud × temperature × voltage × frame-length × stop-bits matrix with pass/fail gates (production-ready).

baud_error = (T_actual - T_ideal) / T_ideal
Where:
- T_ideal  : ideal bit period (1 / nominal baud)
- T_actual : actual bit period produced by the endpoint clock + divider
Interpretation:
- Positive error  → bit period longer (baud slower)
- Negative error  → bit period shorter (baud faster)

This definition maps directly to sampling-point drift: each bit contributes a fraction of timing slip that accumulates toward the stop-bit decision.

• TX side: oscillator accuracy + temperature drift + aging + supply sensitivity + divider/PLL artifacts + calibration residual.
• RX side: same categories (receiver timebase + sampler clocking), plus any fixed configuration bias that shifts sample timing.
• Systematic terms matter: divider quantization often dominates at specific baud targets even when ppm looks “good.”

Worst-case total timing error (template):
E_total_worst = |E_TX| + |E_RX| + |E_step| + |E_residual|

Why absolute-sum?
- UART failure is a window-crossing event (stop-bit decision),
  so same-direction drift is the most dangerous case.
- RMS is for random noise statistics and can under-estimate worst-case drift.

The pass/fail gate is not “average error.” The gate is whether the worst-case accumulated drift remains inside the receiver’s decision window across the full frame length.

BudgetRow (per endpoint: TX and RX)
- initial_accuracy_ppm        : ____ ppm   (datasheet / measured)
- temp_drift_ppm              : ____ ppm   (over operating temperature range)
- aging_ppm                   : ____ ppm   (over lifetime target)
- supply_sensitivity_ppm      : ____ ppm   (if RC/PLL sensitive to V)
- divider_quantization_percent: ____ %     (reference clock & divisor step error)
- calibration_residual_ppm_or_percent: ____ (remaining after calibration / auto-baud)

Endpoint worst-case:
E_endpoint = sum( absolute(each term) )

System worst-case (template):
E_total = |E_TX| + |E_RX| + extra_systematic_terms

This template forces consistent accounting: every later chapter (strategy, verification, IC selection) references the same fields rather than inventing new definitions.

• Only counting one side: budgeting TX ppm but ignoring RX ppm (or vice versa) underestimates worst-case mismatch.
• Ignoring divider quantization: the divisor step creates a fixed percent bias that can dominate ppm at specific baud targets.
• Mixing definitions: switching between time-based and frequency-based error mid-page causes inconsistent totals.
• Using RMS in place of worst-case: RMS can hide same-direction drift that triggers stop-bit window crossing.
• Skipping temperature/lifetime terms: passing at room temp does not prove budget across temp and aging.

• Start edge = reference: the RX establishes a timing origin at the start-bit transition.
• Local advance: the RX then steps forward by its own bit period; any TX/RX mismatch becomes a consistent slip each bit.
• Cumulative effect: a small mismatch that is harmless over 1–2 bits can cross the decision window after many bits.

• Drift accumulates with bit count: by the time the stop bit is checked, the RX has advanced through N bit intervals since the start alignment.
• Longer frames shrink margin: the same total error can pass short frames but fail long frames near the end.
• Practical takeaway: if failures cluster at the last byte or at stop-bit check, treat baud mismatch and drift accumulation as the first-order suspect.

• Finer timing grid: higher oversampling provides more sub-bit “ticks” to place the sampling point and to re-center decisions.
• More robust decision: common implementations use a stable sampling-point policy that effectively widens the safe region (timing-only view).
• Budget implication: oversampling influences the effective decision window size (W) used in worst-case budgeting.

• N (bit count): number of bit intervals from start alignment to stop-bit decision (frame length sensitivity driver).
• E_total (worst-case mismatch): total endpoint mismatch from H2-2 accounting (|TX| + |RX| + step + residual).
• W (decision window): effective safe timing window based on the RX sampling policy and oversampling mode (implementation-dependent).
• Policy knobs: stop bits, oversampling, and decision rules that change the effective W.

Conceptual relationship:
- drift_per_bit  ∝  E_total
- cumulative_drift  ∝  N × E_total
Failure condition:
- cumulative_drift  >  W  (decision window)

Therefore (template form):
E_total_allowable  =  X%  (a threshold derived from W and policy)
Trend (always true):
- Larger N  → smaller allowable E_total
- Larger W (via policy/oversampling) → larger allowable E_total

The correct output is not a single “magic %” but a defensible threshold X% that matches the receiver’s implementation and the intended frame/policy corner cases.

• Why short frames “hide” budget issues: fewer bits means less accumulated slip, so the stop-bit window is not challenged.
• Why long frames expose issues: accumulated drift scales with N; the stop-bit decision is the first hard boundary.
• Budget practice: select N based on the worst expected frame format (including parity/stop bits and maximum payload patterns).

Conversion anchors:
- 1% = 10,000 ppm
- % ≈ ppm / 10,000
Accounting rule:
- keep each term as ppm or % (relative error) and sum as worst-case magnitudes

The budget needs relative error. Whenever a datasheet provides accuracy/drift/aging, capture the conditions (temperature range, lifetime, mode) and record the number directly as ppm or %.

• Clock source specs: initial accuracy (ppm), temperature drift across operating range (ppm), aging over lifetime target (ppm).
• Generation chain bias: PLL/RC mode-dependent frequency offset and mode transitions (record as ppm/% under stated conditions).
• Divider quantization (step error): when refclk/divisor cannot hit the target baud exactly, the TX baud carries a fixed percent bias (often dominant at specific baud points).

• RX timebase: same three spec buckets as TX (initial / temp / aging), captured with conditions.
• Sampler clock domain: if oversampling clocks come from a different divider/PLL path, account its bias as an RX term.
• Implementation bias: sampling-point policy may introduce a fixed offset that affects the effective decision window (record as a separate “RX policy residual” if applicable).

• Adjustable divisor step: finer step (integer+fractional) reduces quantization error; record remaining step error as a budget term.
• Runtime calibration: reduces endpoint bias but leaves calibration residual and between-calibration drift (set by calibration period).
• Auto-baud: pulls initial mismatch toward a known pattern; record residual error after convergence under worst conditions.

• Allowable total error: X% (from the window/policy in H2-4).
• Worst-case frame length: N bits from start alignment to stop check.
• Environment envelope: temperature range, voltage, lifetime years.
• Baud set: the list of baud targets that must be robust (coverage table below).

1. List the baud targets: include the defaults and the highest-risk operating points.
2. Fix the sampling policy: choose a default oversampling mode for the scan.
3. Scan refclk/divisors: derive per-baud step error (%) and rank candidate clock plans.
4. Select “coverage optimal”: choose the plan that keeps key baud points under the budget threshold X% with guardband.

• Default baud: choose a target with small step error and broad ecosystem compatibility (from coverage scan results).
• Default oversampling: favor the mode that provides a larger effective decision window (implementation-dependent).
• Default stop bits: reserve margin for unknown endpoints and long-field conditions; tighten only after verification.
• Escalation policy: if higher baud is required, converge calibration/auto-baud before switching to the fastest mode.

• Bias reduction: moves the effective baud closer to the target by correcting divisor selection.
• Residual remains: estimator uncertainty + quantization + model mismatch become a bounded calibration residual.
• Drift returns over time: temperature and aging accumulate between calibrations, becoming a bounded between-calibration drift.

Budget accounting rule (worst-case):
E_total_worst = |TX terms| + |RX terms| + |step error| + |cal residual| + |between-cal drift|

• Training must be stable: define a known sequence length and edge density; unstable training inflates residual bounds.
• Convergence must be defined: require K consecutive estimates within a tolerance band before accepting the divisor update.
• Disable conditions must exist: if the training stream is not guaranteed (bursty, noisy, or protocol-dependent), treat auto-baud as an assist, not a continuous guarantee.

• Data bits: more bits increase N and reduce margin at the stop boundary.
• Parity bit: adds one more accumulation step; treat it as an N increase in the worst-case budget.
• Stop bits: can alter when/where the stop check is performed; use stop configuration as a margin knob under uncertainty.
• Inter-frame gap: near-zero gaps and continuous streams reduce opportunities for re-alignment depending on implementation policy.

Corner Case Checklist (matrix columns)
- frame_format         : data bits / parity / stop bits
- max_payload_or_burst : ____ (bytes) ; gap: 0 / min / normal
- baud_corners         : low / typical / high (include worst step-error points)
- oversampling_mode    : default / alternative
- power_state          : boot / wake / DVFS / ref switch
- temperature_points   : cold / room / hot + fast transitions
- calibration_state    : none / just applied / end-of-period
- endpoint_pair        : worst TX + worst RX combination
- pass_criteria        : framing/parity/stop error rate threshold (X-based)

The checklist is intentionally timing-only: it targets N growth, stop-boundary exposure, and temporary bias expansion during state transitions.

• Baud tiers: include common rates and the known “step-error islands”.
• Temperature points: cold / room / hot plus fast transitions.
• Voltage points: low / typical / high (especially across clock-path modes).
• Frame length tiers: short / long / max N (must include worst-case N).
• Stop bits + oversampling: cover default and any alternative policy options.

• max-N long frames or long bursts exist
• high baud or frequent baud switching is required
• wide temperature range or fast temperature transitions occur
• frequent low-power wake-to-send behavior exists
• cross-board / harness connections and multiple endpoints exist