Digital algorithm research on radio frequency feedback in field programmable gate array

This paper describes the basic theory of radio frequency feedback, and then presents a digital algorithm which adopts the rotation matrix to adjust the gain and phase of the radio frequency feedback loop in the field programmable gate array. Experimental results show the loop delay is 1.2 μs, and the band width of the superconductivity cavity changes from 3.3 kHz to 4.8 kHz after adding the radio frequency feedback. And the quality factor of the superconductivity cavity changes from 150 550 to 104 130．