The load current, I_LOAD, flows through the shunt resistor, R_SHUNT, to develop the shunt voltage, V_SHUNT. The shunt voltage is then amplified by the difference amplifier consisting of U1A and R₁ through R₄. The gain of the difference amplifier is set by the ratio of R₄ to R₃. To minimize errors, set R₂ = R₄ and R₁ = R₃. The reference voltage, V_REF, is supplied by buffering a resistor divider using U1B. The transfer function is given by Equation 1.

Equation 1.

where

There are two types of errors in this design: gain and offset. Gain errors are introduced by the tolerance of the shunt resistor and the ratios of R₄ to R₃ and, similarly, R₂ to R₁. Offset errors are introduced by the voltage divider (R₅ and R₆) and how closely the ratio of R₄ / R₃ matches R₂ / R₁. The latter value affects the CMRR of the difference amplifier, ultimately translating to an offset error.

The value of V_SHUNT is the ground potential for the system load because V_SHUNT is a low-side measurement. Therefore, a maximum value must be placed on V_SHUNT. In this design, the maximum value for V_SHUNT is set to 100 mV. Equation 2 calculates the maximum value of the shunt resistor given a maximum shunt voltage of 100 mV and maximum load current of 1 A.

Equation 2.

The tolerance of R_SHUNT is directly proportional to cost. For this design, a shunt resistor with a tolerance of 0.5% is selected. If greater accuracy is required, select a 0.1% resistor or better.

The load current is bidirectional; therefore, the shunt voltage range is –100 mV to +100 mV. This voltage is divided down by R₁ and R₂ before reaching the operational amplifier, U1A. Make sure that the voltage present at the noninverting node of U1A is within the common-mode range of the device. Use an operational amplifier, such as the OPAx387, that has a common-mode range that extends below the negative supply voltage. The offset error is minimal because the OPAx387 has a typical offset voltage of merely ±0.25 µV (±5 µV, maximum).

Given a symmetric load current of –1 A to +1 A, the voltage divider resistors, R₅ and R₆, must be equal. To be consistent with the shunt resistor, a tolerance of 0.5% is selected. To minimize power consumption, 10‑kΩ resistors are used.

To set the gain of the difference amplifier, the common-mode range and output swing of the OPAx387 must be considered. Equation 3 and Equation 4 depict the typical common-mode range and maximum output swing, respectively, of the OPAx387 given a 3.3‑V supply.

The gain of the difference amplifier can now be calculated as shown in Equation 5.

Equation 5.

The resistor value selected for R₁ and R₃ is 1 kΩ. 15.4 kΩ is selected for R₂ and R₄ because this number is the nearest standard value. Therefore, the ideal gain of the difference amplifier is 15.4 V/V.

The gain error of the circuit primarily depends on R₁ through R₄. As a result of this dependence, 0.1% resistors were selected. This configuration reduces the likelihood that the design requires a two-point calibration. A simple one-point calibration, if desired, removes the offset errors introduced by the 0.5% resistors.