Pilot reported on downwind leg taking evasive action to avoid an overtaking aircraft resulted in a NMAC.

Narrative

As pilot-in-command of Aircraft X; was practicing touch and goes at (ZZZ) at the time of the incident. I kept my eyes on the outside during my climb out from the field and made a turn to left crosswind and downwind for Runway XX. I made an announcement on the CTAF when I turned downwind. Right after my announcement; another pilot transmitted 'Aircraft X; where are you on downwind? I'm here too but don't know where you are at.' In the interest of safety I announced that I was abeam the numbers XY. I continued to fly a predictable downwind leg and was nearly abeam the numbers XX when my lighting inside the flight deck changed. I glanced back to see the other aircraft; Aircraft Y; coming up on me and closing fast. I began a dive to pick up some speed and the other pilot passed above me. He then transmitted 'I didn't expect you to be there; I was looking in a totally different area. I got really close' I continued to fly the rest of my traffic pattern in a predictable manner and decided that one close call was too many; and that my next landing should be the last for the day. The pilot of the other aircraft extended his downwind leg and I was able to safely bring my aircraft to the ground. I estimate that the distance between our aircraft at the closest during the near mid air collision was 100 feet.