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Using AD5542 in bipolar mode

I need an output swing of -5V to +5V, so I'm using the congifuration included in the datasheet. I'm using a Vref of 5V and a AD8643 as the output buffer. I decided on the AD8643 because it's a part that's present in the rest of my circuit, but I can change it if it's necessary. I'm also sending the data to the DAC via a PIC18F4553, but it doesn't appear in the image.

Without connecting the opamp, the output of the DAC works correctly (a 0 to 5V swing), but when I add the opamp, problems arise. As I power on the circuit, the opamp behaves unexpectedly, and I meassure -3.4V at Vin-, -0.28V at Vin+ and -0.89V at its output. If I try to set a voltage with the DAC, the opamp it goes to the negative rail.

The AD8643 has 4 opamps and, as I'm only working with this area of the circuit, I left the other 3 with their pins in the air. Does it really matter or should I connect them?

Maybe the DAC changes the output faster than the opamp can follow (I don't think so, because it has a 3V/us slew rate and a 3MHz bandwidth), or maybe It has to do with the powering up sequence.

I'm not sure if I should post this here or in the opamp support zone...

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