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Post-trim drift is a comparison between two resistance observations, not a property of one reading. Its reported value depends on the baseline, the denominator and any corrections applied before subtraction. This calculation starts after a recovery interval has been selected and the reference state has been specified. It preserves the original reference throughout later observations, separates changes between stages, and explains why collecting many later readings does not eliminate uncertainty in the shared baseline.
Key design decisions
- Keep nominal-value error, endpoint change and reference-based drift as separate quantities.
- Combine successive fractional changes multiplicatively when their denominators differ.
- Carry reference uncertainty into every later drift point instead of treating the points as independent.
Fix the reference observation before reducing the time series
Identify the specimen, reference timestamp, elapsed time from the final trim pulse, resistance, temperature and electrical sensing boundary. The resistance used as R0 should be the agreed recovered baseline, not whichever later reading makes the trend look smallest. Preserve the trim-station endpoint separately so the initial recovery change remains visible.
A second trimming operation creates a new physical geometry. Do not append its later measurements to the original drift curve as though only time had passed. Similarly, coating or assembly can define an explicit intermediate stage. The arithmetic can compare those stages, but the record must show the operation between them. A baseline is a named observation under a controlled condition, not a generic label such as final test.
Calculate signed change using the actual reference value
Subtract the reference resistance from the later resistance, divide by that same reference and multiply by one million for parts per million. A positive result denotes an increase. Keep the reference as measured, even when it differs slightly from the drawing nominal. Rounding it to nominal changes the question from drift to error against a design target.
If the reference already has nominal error e0 and later fractional drift is d, the final nominal error is (1 + e0)(1 + d) − 1. The cross-product is usually small for precision resistors, but retaining it prevents ambiguous accounting. A stable specimen can remain outside its nominal acceptance band; conversely, a signed drift can initially move a specimen toward nominal without demonstrating better long-term stability.
Dppm(t) = 10^6[Rt/R0 − 1]; D02 = D01 + D12 + D01 D12/10^6.
- R0: actual resistance at the fixed post-trim reference state in ohms.
- Rt: later comparable resistance in ohms.
- D01: drift from state 0 to state 1 in ppm; D12: drift from state 1 to state 2 in ppm.
- D02: overall drift from state 0 to state 2, retaining the denominator cross-term.
Same specimen and electrical boundary, positive reference resistance, and comparable temperature/excitation or explicitly qualified corrections.
Reconcile direct and incremental drift calculations
For a hypothetical specimen, let R0 = 10000 Ω, R1 = 10002 Ω and R2 = 10005 Ω. Direct drift at the first observation is +200 ppm and at the second is +500 ppm. The change from R1 to R2 is 3/10002 × one million, approximately +299.940 ppm. Adding 200 and 299.940 alone gives 499.940 ppm because the intervals use different denominators.
The missing cross-term is approximately 0.060 ppm, recovering +500 ppm when the exact interval relationship is used. This is deliberately a small example: the arithmetic discrepancy can be negligible relative to measurement uncertainty while still revealing whether a worksheet uses consistent definitions. Retain direct baseline comparisons as the primary time series; use incremental changes to identify which interval introduced the movement.
| Comparison | Resistance change | Denominator | Signed drift |
|---|---|---|---|
| Reference to first reading | +2 Ω | 10000 Ω | +200 ppm |
| First to second reading | +3 Ω | 10002 Ω | +299.940 ppm |
| Reference to second reading | +5 Ω | 10000 Ω | +500 ppm |
| Sum including cross-term | 200 + 299.940 + 0.060 | Reconciled to reference | +500 ppm |
Normalize temperature only with an applicable response model
When the later specimen temperature differs from the reference, the raw resistance change combines time evolution with temperature response. If a measured linear coefficient alpha applies over the small interval, one possible reduction is Rnormalized = Rmeasured/[1 + alpha(Tmeasured − T0)]. Write alpha in inverse kelvin; a coefficient supplied in ppm/K must be multiplied by one millionth.
For the 10005 Ω observation, assume a separately established alpha of +80 ppm/K and a temperature 0.5 K above the baseline. The denominator is 1.00004, giving about 10004.5998 Ω and +459.98 ppm after normalization. This does not prove the remaining change is permanent trim damage. Coefficient uncertainty, sample gradients, hysteresis and unrecorded operations still matter. Show both raw and normalized results, and do not fit alpha from the same two readings to force a zero drift.
Retain the correlation between paired resistance readings
The sensitivities of fractional drift to Rt and R0 are 1/R0 and −Rt/R0². Applying them to the paired reading uncertainties introduces a covariance term with a negative sign. A common multiplicative calibration effect can largely cancel in the ratio, whereas independent remounting or temperature error does not. Specify the components rather than assigning an arbitrary correlation coefficient to improve the result.
Near 10000 Ω, independent standard uncertainties of 0.2 Ω for the reference and 0.3 Ω for the later observation give approximately 36 ppm standard uncertainty in drift before temperature terms. If a justified covariance is present, the result changes. For illustration only, correlation 0.8 yields approximately 18.4 ppm. Neither number is a tolerance or demonstrated instrument performance; both show the importance of using a defensible measurement model.
Validate the reduction using identities and retained raw data
Check that substituting Rt = R0 returns zero, doubling resistance returns one million ppm, and changing ohms to kilohms leaves the result unchanged. Verify that the direct state-zero-to-state-two calculation agrees with the multiplicative interval reconstruction. A failure in these identities usually indicates a percentage conversion, column mismatch or wrong denominator.
For physical validation, interleave a stable check specimen with the trimmed parts and repeat selected readings after remounting. Compare calculations from independently transcribed raw observations and retain timestamp order. Where normalization is used, repeat at the reference temperature to test whether it predicts the directly observed value. Acceptance should compare both drift and final resistance against their respective agreed criteria, with uncertainty attached to the actual reported state.
Read the shape of arithmetic and measurement failures
A discontinuity appearing exactly when the reference column changes is likely a baseline-management problem. Opposite-signed curves from the same data indicate reversed subtraction or a changed definition. A trend tied to fixture exchange calls for a check of sensing boundaries. Common motion of trimmed and check specimens questions instrument or environmental stability before a trim-specific cause is assigned.
Repeated later readings that agree closely while their absolute offset remains unresolved are not proof of zero drift. Report the retained signed change, the observation interval and the uncertainty that still includes the baseline. Keep missing temperatures or interrupted histories explicit in the internal record. The calculation establishes what changed relative to a defined reference; it does not predict service life from an uneventful short observation period.
Provide the fixed-baseline drift record
Send the unrounded readings and state definitions used in the comparison.
- Specimen-linked trim endpoint, recovered reference and later resistance readings with actual timestamps and intervening operations.
- Reference temperature, sample-temperature observations, measurement excitation and identical sensing coordinates.
- Applicable temperature-response data, proposed normalization, calibration/remounting uncertainty and shared-error components.
- Nominal resistance band, allowed drift at each named interval, data-reduction conventions and acceptance decision rule.
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