SLPS755 Data sheet

SLPS755A October 2023 – December 2023 RES11A-Q1

ADVMIX

Package Options

Refer to the PDF data sheet for device specific package drawings

Mechanical Data (Package|Pins)

DDF|8

Thermal pad, mechanical data (Package|Pins)

Orderable Information

slps755a_oa

7.3.1 Ratiometric Matching

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

Equation 1.

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

Equation 2.

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

Equation 3.

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

Equation 4.

R_{G2} = 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 device in question, such that |t_abs| ≤ 12%. 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, these error terms drop out. Parameter t_Rx is an 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 5.

\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 6.

\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 RES11A-Q1 is specified with a maximum divider ratio tolerance of 0.05%, meaning that the relationship between the actual divider ratio G_x and nominal ratio G_nom of a given divider x is described by the following:

Equation 7.

G_{x} = G_{nom} \times (1+ t_{Dx})

such that t_Dx ≤ 0.05%. Because any devices that do not meet these criteria are screened out at final test, these equations can be used with Equation 5 to prove the effective bounds of t_Rx. Therefore, despite the device absolute end-to-end tolerance bounds of ±12%, the effective error tolerances of each resistor (for ratiometric applications) are within approximately ±0.025%, for the worst-case t_Rx.

The RES11A-Q1 is specified with a maximum divider matching tolerance of 0.1%, meaning that the relationship between the ratio of divider 1 (G₁) and ratio of divider 2 (G₂) is described by the following:

Equation 8.

t_{M} = t_{D2} - t_{D1} = \frac{G_{2} - G_{1}}{G_{nom}}

By definition, |t_M| ≤ 0.1%. Again, the previous equations relate t_M to the parameters t_DX and t_RX. As a result of the interdigitation of the two dividers, the actual typical magnitude of t_M is significantly lower than this maximum value, depending on the specific RES11A-Q1 device. This value is used to calculate the common-mode rejection ratio (CMRR) when implementing a difference amplifier circuit. For example, typical t_M for the RES11A40-Q1 is approximately 85 ppm, and the typical CMRR is 95.4 dB.