As-Fired Dimensions for Printed Resistor Geometry

1. Define electrical active length at fired termination boundaries

Define where the resistor electrically begins and ends. The visible pigment edge may extend over a conductor, while the active boundary depends on current entry and termination geometry. Mark both ends on calibrated fired images and use the same rule across parts. Do not substitute artwork overlap or nominal conductor edge after firing. If the boundary is uncertain, report a length interval and show how that uncertainty affects resistance rather than choosing the most favourable edge.

2. Measure fired width as a profile, not one centre value

Measure width at multiple axial positions and retain the minimum, distribution and location. A centre reading misses tapered ends, scalloped edges or a narrow region near a trim approach. Use an imaging threshold validated against the actual contrast and record pixel scale, focus and orientation. Width perpendicular to the local current path is relevant; a diagonal caliper distance can overstate it. Report edge uncertainty and avoid smoothing away functional necks.

3. Separate artwork, wet print, dried and fired geometry

Keep artwork, wet deposit, dried film and fired film as distinct states. Print spread can widen one edge while drying or firing changes another dimension. Comparisons across states require the same coordinate reference and feature definition. A fired-resistance model should use fired dimensions unless a validated transformation is explicitly part of the design method. Do not present screen opening or artwork width as a manufacturing result for the finished resistor.

4. Retain edge taper, voids and local necks

Map taper, voids, edge roughness, conductor intrusion, corners and trim kerfs. A local void may reduce conducting width without changing the outside visual envelope. Decide whether the simple rectangle can conservatively bracket the shape; otherwise segment the body or use field analysis. Preserve images before destructive sectioning. Cosmetic edge variation is not automatically a failure, but it must not be hidden when it controls the current path or hot spot.

5. Calculate a bounded number-of-squares estimate

The starting estimate R0=Rs(L/W). With 100 ohms per square, 2.4 mm active length and 0.8 mm width, the ideal value is 300 ohms. This assumes a uniform sheet, rectangular field and negligible end correction. Recalculate with measured length and width bounds to show sensitivity. The example is not a paste value or product tolerance. Keep units and do not add nominal end corrections from an unrelated termination construction.

Calibrate image scale in both axes and check lens distortion across the field before measuring distributed resistors. A local pixel scale derived at the centre may bias edge positions. Preserve the raw image and measurement overlay. Reprocessing with another threshold creates a new analysis revision and should not overwrite the original dimensions.

6. Pair geometry and resistance on the same specimen

Measure resistance and geometry on the same identified specimen or a justified paired coupon. Lot-average geometry cannot explain an outlier from another firing. Record temperature, contact topology, stabilization and sense boundaries. Plot residual between measured resistance and the simple prediction against width, length, position and termination type. A constant residual may suggest an end term; a position pattern may indicate sheet or firing variation. Neither pattern proves chemistry.

Sheet resistance used in the simple estimate must correspond to the same fired material state. A supplier nominal or another firing cannot explain an individual resistor. Where a coupon supplies the sheet basis, record its geometry, position and end correction limitations. Treat coupon-to-product transfer as an assumption to be validated.

7. Escalate nonuniform shapes to a suitable model

Escalate when end regions occupy a large fraction of length, width varies substantially, terminals are asymmetric, corners or trim cuts disturb current, or residuals show structure. A segmented one-dimensional model may bound gradual width change; complex entry fields require numerical or empirical treatment. Choose the simplest model that matches the decision and validate it against measured parts. More complex computation does not repair uncertain boundaries or mixed genealogy.

Use sensitivity derivatives or bounded recalculation to show whether width, length or sheet variation controls the estimate. Because width is in the denominator, a narrow lower bound can dominate. Do not combine worst cases from physically incompatible states, and do not assume contributors are independent merely to obtain a smaller statistical total.

8. Release measured geometry distributions by drawing

Release the measured geometry record with drawing revision, fired images, calibration, active-boundary rule, width profiles, exceptions, paired electrical data, model assumptions and uncertainty. Specify which resistor family and termination construction the distribution represents. Do not claim a universal print tolerance, sheet resistance, resistance capability or yield. Changes in paste, screen, firing, termination overlap or trim route require a bridge before reusing the model.

For trimmed resistors, distinguish pre-trim body geometry from the final kerf-created path. The original rectangle may predict starting value, while final current flow needs the cut geometry. Record trim location and remaining neck with the same specimen resistance. Do not call a laser cut an ordinary width tolerance.

Tolerance review should retain correlations. A print that becomes longer and wider together may partly cancel resistance change, whereas combining longest length with narrowest width creates a conservative but possibly impossible corner. Present both physically observed combinations and any deliberate worst-case envelope. Explain which is used for design margin. Validate with measured resistance across the same population. If residuals are larger than geometry and measurement uncertainty can explain, investigate sheet state, terminations or current-field assumptions instead of tightening a dimension that is not controlling.

The RFQ should include the resistance target, allowable trim strategy, power or voltage boundary, and the feature whose geometry constrains layout. Those inputs determine whether a simple starting-value estimate is useful. They do not authorize a paste grade or printable tolerance. Engineering should return explicit requests for missing fired dimensions, terminal definition and validation samples before making a manufacturing commitment.