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Oscillation on buffer output

Other Parts Discussed in Thread: LMP2234

Hello guys,

I'm designing an analog circuit where I have only a single ended power supply but need to have symmetrical power for some Op. Amps. (LMP2234). To do so, I'm using a voltage reference of +1.25V as an offset votlage for those amps., while they are being powered by a voltage that ranges from 2.5V to 5V and GND. In the worst case, I have a range of +-1.25V (ideally, Rail-to-Rail), with respect to the offset voltage +VOS = 1.25V (to GND). The schematic below illustrates the circuit:

The problem is that the output of this buffer amp. is oscillating (1.25V +- 100mV peak-peak, f = 100kHz).

I have already tried to replace the short between pins 1 and 2 by adding resistance (47R, 1K, 10K) but it didn't improve the output (in fact, using a 10K resistor, the noise increased).

Any thoughts? 

Thanks in advance,

André.