analyze_divider_tolerance
Tolerance band of a resistor divider — nominal is not a specification. Reports BOTH the exact worst case (corner enumeration, valid because the transfer function is monotonic in each resistor) and the realistic statistical band…
Instructions
Tolerance band of a resistor divider — nominal is not a specification. Reports BOTH the exact worst case (corner enumeration, valid because the transfer function is monotonic in each resistor) and the realistic statistical band (first-order sensitivity propagation, NOT naive RSS of percentage tolerances — the output is a quotient of random variables, so RSS-ing the percentages directly is invalid; TI SNVA112 states this explicitly). Includes TCR, sqrt-of-time life drift, supply tolerance, and matched-pair ratio tolerance, and names which resistor dominates the error budget so you fix the right part.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| v_in | Yes | Input voltage to the divider, in volts. | |
| r1_ohm | Yes | High-side resistor (input to midpoint), in ohms. | |
| r2_ohm | Yes | Low-side resistor (midpoint to ground), in ohms. | |
| delta_temp_c | No | Temperature excursion from 25 °C that the design must hold accuracy over. | |
| tcr_ppm_per_c | No | Temperature coefficient in ppm/°C. Thick film is ~200, thin film ~25, metal foil ~2. | |
| tolerance_pct | No | Resistor value tolerance in percent at 25 °C. | |
| life_drift_pct | No | Life drift percent over the datasheet's stated hours. Scales with sqrt of the time ratio. | |
| v_in_tolerance_pct | No | Supply tolerance in percent, treated as an independent contribution. | |
| ratio_tolerance_pct | No | Ratio tolerance for a matched pair in one package. Replaces both absolute tolerances — the biggest free accuracy win. |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| v_in | Yes | Input voltage to the divider. | |
| notes | Yes | Human-readable findings: which term dominates, what to change, and any caveat. | |
| method | Yes | Which methods were used, so the numbers are auditable. | |
| r1_ohm | Yes | High-side resistor. | |
| r2_ohm | Yes | Low-side resistor. | |
| v_out_max | Yes | Statistical upper bound (sensitivity RSS). | |
| v_out_min | Yes | Statistical lower bound (sensitivity RSS). | |
| error_rss_pct | Yes | Statistical error band as a percentage of nominal. | |
| v_out_nominal | Yes | Output at nominal resistor values. | |
| sensitivity_r1 | Yes | ∂V_out/∂R1, in volts per ohm. | |
| sensitivity_r2 | Yes | ∂V_out/∂R2, in volts per ohm. | |
| error_worst_pct | Yes | Worst-case error as a percentage of nominal. | |
| v_out_worst_max | Yes | Exact worst-case upper bound (corner enumeration). | |
| v_out_worst_min | Yes | Exact worst-case lower bound (corner enumeration). | |
| dominant_resistor | Yes | Which resistor contributes more error — fix this one first. |