The maximum value of the current sense resistor is calculated based on the maximum power loss requirement. By applying Equation 1, the maximum value of the current-sense resistor is calculated to be 0.563 mΩ. This is the maximum value for sense resistor RSENSE; therefore, select RSENSE to be 0.5 mΩ because it is the closest standard resistor value that meets the power-loss requirement.
The next step is to select the appropriate gain and reduce RSENSE, if needed, to keep the output signal swing within the VS range. Using Equation 2, and given that IMAX = 40 A and RSENSE = 0.5 mΩ, the maximum current-sense gain calculated to avoid the positive swing-to-rail limitations on the output is 248.5. To maximize the output signal range, the INA180A4 (gain = 200) device is selected for this application.
To calculate the accuracy at peak current, the two factors that must be determined are the gain error and the offset error. The gain error of the INAx180 is specified to be a maximum of 1%. The error due to the offset is constant, and is specified to be 125 µV (maximum) for the conditions where VCM = 0 V and VS = 5 V. Using Equation 6, the percentage error contribution of the offset voltage is calculated to be 0.75%, with total offset error = 150 µV, RSENSE = 0.5 mΩ, and ISENSE = 40 A.
One method of calculating the total error is to add the gain error to the percentage contribution of the offset error. However, in this case, the gain error and the offset error do not have an influence or correlation to each other. A more statistically accurate method of calculating the total error is to use the RSS sum of the errors, as shown in Equation 7:
After applying Equation 7, the total current sense error at maximum current is calculated to be 1.25%, and that is less than the design example requirement of 1.5%.
The INA180A4 (gain = 200) also has a bandwidth of 105 kHz that meets the small-signal bandwidth requirement of 80 kHz. If higher bandwidth is required, lower-gain devices can be used at the expense of either reduced output voltage range or an increased value of RSENSE.