5 Calibration of V_OS, IB, and Gain Error

Calibration is the process where a system is measured to understand error sources and the errors are mathematically corrected. In many cases a micro-controller (where calibration coefficients are stored in a local EEPROM) performs the mathematical correction. The discovered errors are generally unique for each product, so each product needs to be individually calibrated. In the case of amplifiers, calibration can minimize the offset and gain error. For amplifiers, gain error is primarily due to resistor tolerance. Any deviation of the resistor value from the nominal value introduces a gain error.

Figure 5-1 shows a simple non-inverting op amp circuit and its associated DC transfer characteristic. To calibrate gain and offset of this circuit, two precision test signals need to be applied to the input. Generally, full system calibration includes error sources, multiple amplifier stages, as well as an analog to digital converter, but the same approach can be used as given in this simple example. The two calibration test signals need to be on the linear portion of the transfer function or the calculated gain and offset errors cannot be correct. In this example, an input signal of 0 V is not an acceptable calibration signal because the amplifier is nonlinear due to output swing limitations for a 0 V input signal. This example uses input signals of 0.25 V and 2.25 V to achieve an ideal output range of 0.5 V to 4.5 V. It is also important that the calibration signals are very accurate and low noise. Calibrating in non-linear regions or using noisy calibration signals can actually introduce additional error rather than correct the systems inherent error. See Op Amp Input and Output Swing Limitations for details on determining the linear range of amplifiers.

Equation 36 shows the general straight-line equation used in calibration of linear systems. Equation 37 and Equation 38 show the calculation of the gain and offset calibration coefficients. The ideal value for gain is 2.0 V/V, but 2.00088 V/V was measured due to resistor tolerance. Also, the ideal offset would be 0 V, but an offset of 31.25 µV was calculated. Equation 39 shows how the calibration coefficients can be used to correct the gain and offset error to determine a more accurate value for V_IN. This approach can be used to correct any signal in the amplifiers linear range. The simulation results for this example show that when the output is at 2.5 V, the input is at 1.2494 V. A circuit input of 1.25 V for a 2.5 V output (G = 2 V/V, V_OS = 0 V) is best. The calibration calculation determines a more accurate value for the input signal by eliminating gain and offset errors.

Overall, calibration is an effective way of minimizing gain and offset error sources. However, calibrating temperature drift, and effects such as PSRR and CMRR can be challenging. The temperature drift and other secondary effects are generally minimized by selection of low error precision amplifiers and low drift precision resistor networks rather than through calibration. Chopper amplifiers, such as OPA182, have maximum V_OS in the low microvolt level (V_OSMax = ±4 µV, V_OSDrift = ±0.012 µV/°C for OPA182). Resistor networks such as the RES11 can be used to minimize gain error and drift (gain error = ±0.05%, and gain drift = ±2 ppm/°C for RES11). Calibration can be costly as it increases the end-product manufacturing test time as well as requiring accurate calibration sources.

Figure 5-1 Op Amp DC Transfer Characteristic for Calibration