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I was looking at Arduino Mega's reference schematic here and trying to understand how the circuit functions. However, I am unable to understand what these schematic symbols (marked in black rectangles) represent or what their function is. Can anyone please explain it to me?

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@Transistor accurately answered what they are. I'll approach their specific function.

The Arduino Mega documentation gives some information on "RESET-EN" and "UBOOT."

  1. "RESET-EN" allows you to enable/disable the auto-reset feature. By default there is a trace between the pads. That's why it look like there is a short in parallel below it. Cut the trace to disable auto-reset. Solder bridge back together to re-enable.

    With auto-reset enabled, the board will automatically reset every time the serial communication is initially established. This causes problems if you are using a non-usb power supply and want to plug in for some debugging or have a design that opens and closes serial comm.

  2. "UBOOT" is related to the DFU (Device Firmware Update) bootloader. This may be on the back of the board and will be different between revs.

The ATmega16U2/8U2 is loaded with a DFU bootloader, which can be activated by:

  • On Rev1 boards: connecting the solder jumper on the back of the board (near the map of Italy) and then resetting the 8U2.
  • On Rev2 or later boards: there is a resistor that pulling the 8U2/16U2 HWB line to ground, making it easier to put into DFU mode.

You can use this to update the USB firmware and even change the device name when you plug it in. More info here.

  1. "GROUND" can optionally link USB ground (UGND) to the main circuit ground. I don't know enough about USB comm circuit design to understand what the advantages or disadvantages are here. Perhaps someone else can clarify this idea. ATMEGA8U2-MU datasheet for reference.
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The symbol indicates a pair of solder pads that can be bridged by the user using a blob of solder.

Here's something similar.

enter image description here

Figure 1. Source: CyberGibbons.

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