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Analog power is the power(AVDD) for the analog circuit(s) inside your chip, such as PLL(phase lock loop), ADC(analog-to-digital converter), DAC(digital-to-analog converter), ... .etc.
On the other hand, digital power(VDD) is the power for the digital circuit(s) in the chip, usually the CORE.
Because the digital signal(s), especially the clock(s) are usually switching very frequently. In order to reduce the influence (or you may call it "crosstalk" , "electro-magnetic interference(EMI)"), we usually use different power pad for analog & digital blocks.
Use several power pads in a chip should take the ESD(electro-static discharge) protection between different power pads into consideration.
For best results you must use to separate grounds like gnd(for digital ground)
and agnd(analog ground) and make the connect of them only in one
point , you can use for connect them also a ferrid filter and some caps .
Make sure when you make the pcb to reduce under the analog parts
digital layer of anything like power gnd and signals, and if you can't
also put a layer of analog ground to cross from them and the comp.
do not use the same ground pad. Use separate grounds for digital part and for analog part and connect them only in one point, as near to power supply as possible.
If you look at some datasheets from Analog Devices (especially A/D and D/A converters), you can find there the chapter "PCB desing and grounding". Look at this. Also, Analog Devices have some engineering notes about the subject of mixing digital and analog signals.