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I would like to add a low-pass RC filter (500Hz) to the power rail of a TLV2782 op-amp. Datasheet of TLV2782 recommends two decoupling capacitors: 0.1uF and 4.7uF and they are currently placed on the VDD pin of the TLV2782.

Where should I place the RC filter? Should I place it before those decoupling capacitors or after? Should I consider that the decoupling 0.1uF capacitor is the capacitor of my RC filter (then forcing a resistor value) or should I consider the decoupling and the filter independently?

Any advice would be appreciated.

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Typically, the decoupling capacitor is the C part of the RC filter, and the non-ideal inductance and resistance of the PCB traces is the R part. Sometimes (and this is not terribly common), a very small resistance or inductance will be placed like this:

schematic

but if you have so much noise on your power rails that a 500 Hz filter is necessary, you probably have bigger problems. The datasheet lists the supply voltage rejection ratio as 75dB minimum, power supply noise should not affect your measurement very much.

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    \$\begingroup\$ +1, It's also worth noting that on high speed digital and RF parts, its common practice to put an RL combination, along with the decoupling cap. It keeps the entire power bus from being contaminated with switching noise. \$\endgroup\$ – Matt Young Jan 21 '13 at 20:40
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It is a very good practice to put an RC filter on the power input of an op amp to prevent high frequency noise or stray RF from getting on to the opamp output, or preventing the op-amp from malfunctioning.

One of the previous comments said the power supply rejection ratio was 75db. Well this is only at very low frequencies. At higher frequencies the rejection gets less and less and may even approach 0db. So high frequencies go directly from the power pin to the op amp output. If the signals are strong enough, they can make the op amp offset voltage change, or even saturate the output of an op amp.

I am sure you are curious about how RF (radio frequency or high frequency) signals can get on a power line. This is very common during EMI/EMC compliance testing. In many parts of the world, you cannot sell a product with an op-amp in it unless you have proved by testing that the circuit will still work properly when injected with RF energy, or when cables to the circuit are immersed in an RF field.

In some testing RF signals are forced into the power lines through coupling coils, or are picked up by cables that are immersed in an RF field.

Have you heard the annoying buzz-buzz (217Hz) of a cell phone through a speaker. That annoyance can be minimized with this technique and other techniques.

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