SLPS755 Data sheet

SLPS755B October 2023 – October 2025 RES11A-Q1

PRODUCTION DATA

7.3.1.1 Absolute and Ratiometric Tolerances

The resistors of the RES11A-Q1 are described by the following equations:

Equation 10.

R_{IN1} = R_{INnom} \times (1+ t_{absRIN1}) = R_{INnom} \times (1+ t_{RIN1}) \times (1+ t_{SiCr})

Equation 11.

R_{IN2} = R_{INnom} \times (1+ t_{absRIN2}) = R_{INnom} \times (1+ t_{RIN2}) \times (1+ t_{SiCr})

Equation 12.

R_{G1} = R_{Gnom} \times (1+ t_{absRG1}) = R_{Gnom} \times (1+ t_{RG1}) \times (1+ t_{SiCr})

Equation 13.

R_{G2} = R_{Gnom} \times (1+ t_{absRG2}) = R_{Gnom} \times (1+ t_{RG2}) \times (1+ t_{SiCr})

R_INnom and R_Gnom are the nominal values of each resistor. The parameter t_abs is an error term that describes the absolute tolerance of the RES11A-Q1 resistor in question, such that |t_abs| ≤ 12%. For example, a nominally 1kΩ resistor with t_abs = 10% actually measures 1.1kΩ. This error is analogous to the specified absolute tolerance of most single-element resistors, or the end-to-end tolerance of more specialized resistor dividers.

Note: The RES11A-Q1 is not a laser-trimmed device. Each ratio of the RES11A-Q1 features a unique die specifically optimized for that ratio, providing the precise matching and consistent thermal characteristics necessary to achieve extremely low drift.

The absolute tolerance is dominated by the variation in the SiCr resistivity, t_SiCr. The four resistors of a given RES11A-Q1 are interdigitated and come from the same area of the wafer; therefore, t_SiCr is effectively the same for each of the four resistors, although t_SiCr varies on a part-to-part basis.

The following examples show that when each divider is considered in ratiometric terms, the t_SiCr error terms drop out. Parameter t_Rx is an residual error term that describes the remaining effective tolerance of each resistor of the given RES11A-Q1 device after accounting for the universal t_SiCr.

Equation 14.

\frac{R_{Gx}}{R_{INx}} = \frac{R_{Gnom} \times (1+ t_{RGx}) \times (1+ t_{SiCr})}{R_{INnom} \times (1+ t_{RINx}) \times (1+ t_{SiCr})} = \frac{R_{Gnom} \times (1+ t_{RGx})}{R_{INnom} \times (1+ t_{RINx})} = G_{nom} \times \frac{(1+ t_{RGx})}{(1+ t_{RINx})} = G_{x}

Equation 15.

\frac{R_{INx}}{R_{INx} + R_{Gx}} = \frac{R_{INnom} \times (1+ t_{RINx}) \times (1+ t_{SiCr})}{R_{INnom} \times (1+ t_{RINx}) \times (1+ t_{SiCr}) + R_{Gnom} \times (1+ t_{RGx}) \times (1+ t_{SiCr})} = \frac{R_{INnom} \times (1+ t_{RINx})}{R_{INnom} \times (1+ t_{RINx}) + R_{Gnom} \times (1+ t_{RGx})}

The individual values of t_RG1, t_RG2, t_RIN1, and t_RIN2 describe the tolerance of each individual resistor, but are not independent variables in a Gaussian sense. Rather, the matching of these values to each other (by design) is used to achieve highly stable ratiometric relationships between the resistors, giving an effective ratio with an extremely low error.

The limits of t_Dx for the RES11A-Q1 are enforced by precise parametric testing in production, with Kelvin connections used to better reject potential sources of error. Because the resulting t_D1 and t_D2 values are more randomized error terms, t_D1 and t_D2 can be treated as independent Gaussian distributions, making these variables much more useful for error analyses. Single-element resistors do not have an equivalent to t_Dx, because no part-to-part matching is considered other than the gradeout limit. In other divider data sheets, the equivalent of t_Dx is often called ratio tolerance.

Because any devices that do not meet these criteria are screened out at final test, these equations can technically be used with Equation 14 to prove additional relationships (such as effective maximum limits) between the values of t_Rx for a given device. This exercise ultimately gives overly conservative results, however. For more realistic statistical analysis with root-sum-of-squares methods, the Arbitrary Matching section of the Electrical Characteristics table provides measured standard deviations for some additional resistor-to-resistor relationships. See Section 8.1.3.2 for a practical example.