SBOSAF3 Data sheet

SBOSAF3 November 2023 TMCS1126

ADVANCE INFORMATION

Package Options

Refer to the PDF data sheet for device specific package drawings

Mechanical Data (Package|Pins)

DVG|10

Thermal pad, mechanical data (Package|Pins)

Orderable Information

sbosaf3_oa

9.1.1 Total Error Calculation Examples

Users can calculate the total error for any arbitrary device condition and current level. Consider error sources like input-referred offset current (I_OS), Common Mode Rejection Ratio (CMRR), Power Supply Rejection Ratio (PSRR), sensitivity error, nonlinearity, as well as errors caused by any external magnetic fields (B_EXT). Compare each of these error sources in percentage terms, as some are significant drivers of error and some have inconsequential impact to current measurement error. Offset (Equation 21), CMRR (Equation 22), PSRR (Equation 23), and external magnetic field error (Equation 24) are all referred to the input, and so are divided by the actual input current I_IN to calculate percentage errors. For sensitivity error and nonlinearity error calculations, the percentage limits explicitly specified in the Electrical CharacteristicsElectrical CharacteristicsElectrical CharacteristicsElectrical CharacteristicsElectrical Characteristics table can be used.

Equation 21.

e_{I o s} = \frac{I_{O S}}{I_{I N}} = \frac{V_{O E}}{S \times I_{I N}}

Equation 22.

e_{C M R R} = \frac{C M R R \times V_{C M}}{I_{I N}}

Equation 23.

e_{P S R R, A} = \frac{P S R R \times (V_{S} - 5 V)}{I_{I N}}; e_{P S R R, B} = e_{P S R R, C} = \frac{P S R R \times (V_{S} - 3.3 V)}{I_{I N}}

Equation 24.

e_{B e x t} = \frac{B_{E X T} \times C M F R}{I_{I N}}

where

V_OE is the output-referred offset voltage error.
V_CM is the input common-mode voltage.
e_PSRR,A is the power supply rejection error for TMCS1126Axx devices.
e_PSRR,B is the power supply rejection error for TMCS1126Bxx devices.
e_PSRR,C is the power supply rejection error for TMCS1126Cxx devices.
V_S is the supply voltage.
CMFR is the common-mode magnetic field rejection.

When calculating error contributions across temperature, only offset error and sensitivity error contributions vary significantly. To determine the offset error across temperature, use Equation 25 to calculate total input-referred offset error current, I_OS, at any ambient temperature, T_A.

Equation 25.

e_{I o s, ∆ T} = \frac{V_{O E, 25 ℃} + (V_{O E, d r i f t} \times ∆ T)}{S \times I_{I N}}

where

V_OE,25°C is the output-referred offset error at 25°C.
V_OE,drift is the output-referred offset drift with temperature in µV/°C.
ΔT is the change in temperature from 25°C.
S is the sensitivity of the device variant.

Sensitivity error at 25°C is specified as e_S,25°C in the Electrical CharacteristicsElectrical CharacteristicsElectrical CharacteristicsElectrical CharacteristicsElectrical Characteristics table along with sensitivity variation over temperature as sensitivity thermal drift S_drift,therm in ppm/°C. To determine the sensitivity error across temperature, use Equation 26 to calculate sensitivity error at any ambient temperature, T_A, over the given application operating ambient temperature range between –40°C and 125°C.

Equation 26.

e_{S, ∆ T} = e_{S, 25 ℃} + (S_{d r i f t, t h e r m} \times ∆ T)

To accurately calculate the total expected error of the device, the contributions from each of the individual components above must be understood in reference to operating conditions. To account for the individual error sources that are statistically uncorrelated, use a root sum square (RSS) error calculation to calculate total error. For the TMCS1126, only the input-referred offset current (I_OS), CMRR, and PSRR are statistically correlated. These error terms are lumped in an RSS calculation to reflect this nature, as shown in Equation 27 for room temperature and in Equation 28 across a given temperature range. The same methodology can be applied for calculating typical total error by using the appropriate error term specification.

Equation 27.

e_{R S S} = \sqrt{{(|e_{I o s}| + |e_{P S R R}| + |e_{C M R R}|)}^{2} + e_{B e x t}^{2} + e_{S}^{2} + e_{N L}^{2}}

Equation 28.

e_{R S S, ∆ T} = \sqrt{{(|e_{I o s, ∆ T}| + |e_{P S R R}| + |e_{C M R R}|)}^{2} + e_{B e x t}^{2} + e_{S, ∆ T}^{2} + e_{N L}^{2}}

The total error calculation has a strong dependence on the actual input current, therefore always calculate total error across the dynamic range that is required. These curves asymptotically approach the sensitivity and nonlinearity error at high current levels, and approach infinity at low current levels due to offset error terms with input current in the denominator. Key figures of merit for any current-measurement system include the total error percentage at full-scale current, as well as the dynamic range of input current over which the error remains below some key level. Figure 9-1 shows the RSS maximum total error as a function of input current for a TMCS1126A2A at room temperature and across the full temperature range with a 5.25V supply.

Figure 9-1 RSS Error vs Input Current