Some small SINGLE CYLINDER compressors have a different kind of relief valve. In stead of a pressure switch operated valve, they have a special valve in the tank inlet from the pump. The valve has a light spring in it. When air is not being pushed down on the valve from the pump, the valve springs up, closing off the tank, and opens up ports to relieve the head pressure in the pipe from the pump. The next push of air from the pump drives this valve down, allowing air to enter the tank, and closing off the head pressure relief.
This is an in-efficient design in that every stroke of the pump it relieves the head pressure, and the pump has to expend much of the air from each stroke to re-fill the pipe down to the tank. Thus every cycle of the piston, you hear the valve relieving air. This is usually found only on single cylinder pumps.
These valves are very prone to sticking and will stick in the open to the tank position, leaving head pressure on the pump.
Charles