SLPS764 Data sheet

SLPS764 September 2024 RES60A-Q1

ADVANCE INFORMATION

6.3.1 Ratiometric Matching

The resistors of the RES60A-Q1 are described by the following two equations:

Equation 1.

R_{HV} = R_{HVnom} \times (1± t_{abs}) = R_{HVnom} \times (1± t_{RHV}) \times (1± t_{SiCr})

Equation 2.

R_{LV} = R_{LVnom} \times (1± t_{RLV}) \times (1± t_{SiCr})

where

R_HVnom and R_LVnom are the nominal values of each resistor.
t_abs is an error term that describes the absolute tolerance of the resistors of the RES60A-Q1, such that |t_abs| ≤ 15%.
t_SiCr is the variation in the SiCr resistivity for a wafer, and dominates the absolute tolerance for a given resistor. The two resistors of a given RES60A-Q1 are interdigitated and come from the same area of the wafer; therefore, t_SiCr is effectively the same for both of the two resistors, although t_SiCr varies on a part-to-part basis. When the divider is considered in ratiometric terms, these error terms drop out; see the following equations.
t_RHV and t_RLV are localized per-resistor variation or offset error terms. These terms describe the remaining effective tolerances of the respective resistors for a given RES60A-Q1 device, after accounting for the universal t_SiCr.

Equation 3.

\frac{R_{HV}}{R_{LV}} = \frac{R_{HVnom} \times (1± t_{RHV}) \times (1± t_{SiCr})}{R_{LVnom} \times (1± t_{RLV}) \times (1± t_{SiCr})} = \frac{R_{HVnom} \times (1± t_{RHV})}{R_{LVnom} \times (1± t_{RLV})} = G_{nom} \times \frac{(1± t_{RHV})}{(1± t_{RLV})} = G

Equation 4.

\frac{R_{HV}}{R_{LV} + R_{HV}} = \frac{R_{HVnom} \times (1± t_{RHV}) \times (1± t_{SiCr})}{R_{LVnom} \times (1± t_{RLV}) \times (1± t_{SiCr}) + R_{HVnom} \times (1± t_{RHV}) \times (1± t_{SiCr})} = \frac{R_{HVnom} \times (1± t_{RHV})}{R_{LVnom} \times (1± t_{RLV}) + R_{HVnom} \times (1± t_{RHV})}

The RES60A-Q1 is specified with a maximum initial divider ratio tolerance of 0.1%, meaning that the relationship between the actual divider ratio, G, and the nominal ratio, G_nom, of a given divider is described by the following:

Equation 5.

G = G_{nom} \times (1± t_{D})

such that t_D ≤ 0.1%. Because any devices that do not meet these criteria are screened out at final test, these equations can be used with the previous equations to prove the effective bounds of t_RHV and t_RLV. Therefore, despite the device absolute end-to-end tolerance bounds of ±15%, the effective error tolerances of each resistor (for ratiometric applications) are within approximately ±0.05%, for the worst-case t_RHV and t_RlV.