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I have seen circuit diagram in analog devices application note which shows that both supply rails have a 1uF and 0.1uF capacitor for dual supply opamp but only the Vcc has them in a single supply opamp.
Why are decoupling capacitors used on both supply rails in dual supply opamp?
The supply current for both supplies are different most of the time. Only if the output of the opamp with dual supply is at ground potential and the output current is zero both supply currents are (almost) equal. If the ouput jumps positive, there will be a short increase of the positive supply current and a decoupling capacitor is needed for positive supply. If the output jumps negative, the other decoupling capacitor is needed. If the output voltage of the opamp changes dynamically, both decoupling condensators are necessary. If there are no decoupling condensators, the opamp may oscillate in some cases. Decoupling capacitors are especially important for fast opamps. Both capacitors should have short connections to the supply terminals of the opamp and to ground.
The reason is that all supply rails have decoupling to ground, whether there is only one rail, or several.
If it's a supply rail, decouple it to ground.
A decoupling capacitor in the positive supply rail will source shortterm current peaks from the ground rail, in the negative supply rail it will sink shortterm peaks from the ground rail. The positive supply rail is a bad place to sink currents to, the negative supply rail is a bad place to source currents from.
The ground plane tends to be a better place to both source and sink current spikes to.
The seminal phrase here is "ground plane" as part of the power supply paths. Decoupling capacitors that are connected to the signal reference ground traces will add unwanted crossover distortion via the input.
