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A resistor pair can have a shared shift in temperature coefficient while retaining good tracking, or a small average shift while the two coefficients separate. These outcomes have different consequences for a ratio-based circuit. Process comparison should therefore preserve pair identity and report both common and differential behavior after the relevant firing, trimming and subsequent steps. Pooling every resistor into one distribution loses the relationship the circuit needs.
Key design decisions
- Measure both members of each actual pair at the same defined temperature points and processing state.
- Separate average pair TCR from differential TCR, and retain their signs.
- Compare within-substrate, between-substrate and between-lot variation without rearranging pairs after seeing the results.
Preserve the pair used by the circuit
Assign a permanent identity to each resistor and its intended partner before measurement. The circuit may rely on adjacent elements, a shared printed structure or a defined assembly pairing. Combining all values and selecting favorable pairs afterward evaluates a different manufacturing strategy from producing those original pairs.
If selection or pairing is part of the intended route, define its rules, available population and resulting absolute-value constraints in advance. Keep rejected or unmatched elements in the study record. A selected subset can demonstrate what that selection method produced, but it cannot describe the tracking of an unselected production population without the same process being applied.
Use the same temperature interval and resistance reference
An interval TCR is calculated from resistance change divided by reference resistance and temperature difference. The chosen reference temperature and endpoints matter when resistance is not perfectly linear with temperature. Two laboratories can report different TCRs from the same resistor if they use different intervals.
Measure the pair together where practical and record actual sample temperatures. Use a low-excitation condition that keeps self-heating within the measurement budget. If the application includes a broad temperature range, retain the resistance-versus-temperature points instead of compressing the whole curve into one number. Compare hot and cold intervals separately when their behavior differs.
αi = [Ri(T2) − Ri(T1)] / [Ri(T1)(T2 − T1)]
- αi is the interval temperature coefficient of resistor i, in inverse degrees Celsius.
- Ri(T1) is the reference resistance at the lower named temperature point.
- Multiplying αi by one million gives parts per million per degree Celsius.
Both measurements represent the defined sample temperatures and the same electrical boundary; the result describes this interval, not necessarily the entire temperature curve.
Report the pair average and difference
For each pair, calculate common TCR as the average of its two coefficients and differential TCR as the second coefficient minus the first. The common term describes how both resistances tend to move together. The differential term describes first-order ratio change when both elements experience the same temperature change.
Suppose a hypothetical pair changes from coefficients of 80 and 90 to 100 and 110 parts per million per degree Celsius after a process step. Common TCR increases by 20, while differential TCR remains ten. Another pair changing from 80 and 90 to 70 and 100 has unchanged common TCR but differential TCR increases to 30. Reporting only the average would miss the second pair's tracking deterioration.
Measure the stages that can change the final relationship
A useful sequence can include the initial fired state, the trimmed state and the final state after protective or assembly processing. Use the same pair identities and temperature method at each stage. Record resistance values as well as coefficients, because the process can change absolute resistance and tracking differently.
Material suppliers describe resistor properties with specific processing and test conditions. A resistor material family does not guarantee identical TCR after a different substrate or thermal history; compare the actual processed construction. Keep paste identity, substrate, print sequence and thermal record attached to the measured pair comparison.
Separate variation within and between process groups
Pairs on one substrate share some conditions, while substrates and lots may differ in others. Keep these levels in the dataset. A small within-substrate differential spread can coexist with a lot-level shift in common TCR, and a pooled average can hide both patterns.
Use matched comparisons across stages whenever possible: subtract each pair's earlier differential TCR from its later differential TCR. This removes some baseline variation from the process-change question. Plot the result by location and lot, and retain sample counts. Do not assign a cause solely from a lot label; the label may also contain a change in material age, firing load, printing setup or measurement session.
Choose the next check from the pair-level result
The appropriate process action depends on whether the common behavior, tracking or measurement condition changed. Use the paired result to narrow the investigation before adjusting material selection or trim strategy.
| Measured pattern | Implication to investigate | Next comparison |
|---|---|---|
| Both coefficients shift together with stable difference | Common material or process response | Compare absolute circuit requirements and process references |
| Pair average is stable but coefficient difference grows | Tracking has changed despite a stable pooled mean | Compare individual trim histories and local geometry |
| Differential changes follow substrate position | A spatial process or thermal measurement gradient may matter | Repeat matched locations with verified sample temperatures |
| Only heavily trimmed members shift | Adjustment geometry may interact with temperature behavior | Compare trim amount at matched initial material condition |
| Different lots disagree only in one temperature interval | Curvature or interval-specific response may differ | Retain the full temperature curves and repeat the interval |
| Reordered measurements reverse the apparent trend | Measurement drift or equilibration may dominate | Use check specimens and alternate sequence order |
Check that the measurement does not create the mismatch
Differential TCR is derived from several resistance and temperature measurements. Common errors can cancel, while unequal temperature errors can create an apparent difference. Place the pair so it reaches comparable conditions and verify the sensing method's relation to actual element temperature.
Repeat selected temperature cycles and reverse the measurement order. Include a return to the reference temperature to distinguish reversible temperature behavior from retained resistance change. If the return value shifts, calculating one coefficient from the whole sequence can mix drift with TCR. Report that behavior separately and investigate the processing or exposure history before treating the result as a stable temperature characteristic.
Translate the study into a matching requirement
Specify absolute TCR and differential TCR separately where both matter. Name the temperature interval, final processing state, pair identity and measurement excitation. Include the circuit ratio and its permitted drift so the matching target can be checked against the actual function.
A uniform-temperature pair study does not establish behavior under unequal powered temperatures. Supply the application's power states for that separate assessment. For quotation, provide the paired data by stage and lot rather than only a best-case coefficient. This gives engineering a basis for reviewing material selection, layout and process consistency while keeping the conclusion within the measured conditions.
Send pair-level TCR data by process stage
Preserve the pairing and temperature definition so common and differential changes can be evaluated.
- Actual resistor pair identities, layout positions and lot or substrate grouping.
- Resistance measurements at named temperatures before and after relevant processing.
- Individual, common and differential TCR with the same sign convention.
- Trim amount, cut geometry, material identification and thermal sequence.
- Circuit ratio requirement, absolute impedance limits and powered operating states.
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