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Non-linearity of LM7301 op-amp with high current load (~4mA)

Other Parts Discussed in Thread: LM7301, LM7321

I recently tried to load the output of a circuit which was being driven by an LM7301 op-amp. The load was around 1K and the output was DC and adjustable from 0v to 4v. The input to the op-amp was a DAC output, 0 to 3v, known to be linear. the LM7301 was set up with positive gain of ~1.3 to give a 4v full scale output. When we measured the output voltage on the LM7301 we discovered it was not linear, there were errors in linearity of up to 3% at some points. With a 10K load or higher it was OK.

Using a gain of 1 by shorting out the feedback resistor improved the linearity a little but did not solve the problem completely. We were using 5V supply voltage, when we increased that to ~7V the problem seemed to get worse.

Can anyone suggest why this is happening and how to prevent it?

The LM7321 is suggested by TI as a higher current replacement, does it not have this problem?

Are there other op-amps with the same pin out (SOT23) as the LM7301 which behave better, the LM7321 is not good for me as it has >1uA input offset current.