“…Since its invention by Cady [1] in 1923, the crystal oscillator has undergone significant developments, including the resolution of aging issues in the 1940s and 1950s [2], the achievement of low-power operation in the 1970s and 1980s [3,4], and widespread use in wireless communications [5], navigation [6], satellites [7], and radar [8], among other fields. In wireless communication applications, such as radio frequency transceivers [9,10] and digital circuits [11,12], crystal oscillators are utilized to generate stable and accurate reference clocks.…”