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In an ideal world where interconnections had zero resistance and zero inductance, there would be no practical difference. The reason for separate grounds is to prevent current spikes from digital circuits from flowing in the ground connection to sensitive analog circuits. The current spikes in the analog ground can create voltage drops that are indistinguishable from the desired analog signal voltages. The top figure shows a connection scheme that prevents the current from digital circuits from flowing in the analog ground connections. The other figures show undesirable grounding schemes that result in current from the digital circuits flowing in the analog ground connection.
It isn't just the power returns that you must be concerned with but also the signal returns. The grounds need to be arranged so that the signal returns for the digital signals not travel through the analog ground. On PCBs with digital and analog circuits a separate analog and digital ground plane is often used (or a split ground) with the two connected together only at one point.
So in Atmega8 microcontroller,there are two GND.ONE GND and the other AGND.Can we short these two points or should we leave AGND pin disconnected?which will be better?
The AGND must be connected to the GND at some point. If you are using an analog input, such as a built-in ADC, then you need a separate AGND on the circuit board for any analog components to minimize pickup of digital noise. The two grounds can be connected together at one point near the Atmega8.
Besides having a separate analog and digital ground plane, you don't want to run any digital signal traces over the analog plane as that will introduce a corresponding noise current in the analog ground.
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