Loop performance analysis In this section, the loop performance is analyzed. In order to proceed, the proportional-integral (PI) filter is chosen to be the loop filter so that a pole is introduced into the feedback loop. The PI filter is (38) where and are the RC time constants that determine the shape of the filter response. Phase step applied to When there is a drive phase step, , in the drive (39) By using Eq. (37), (40) and applying the final value theorem to the above (41) Thus, the phase step error approaches zero as . Frequency step applied to When there is a frequency step, , in the drive (42) By using Eq. (37), (43) and applying the final value theorem to the above (44) Thus the frequency step error approaches zero as . Frequency ramp applied to When there is a frequency ramp, , in the drive (45)
Loop performance analysis In this section, the loop performance is analyzed. In order to proceed, the proportional-integral (PI) filter is chosen to be the loop filter so that a pole is introduced into the feedback loop. The PI filter is (38) where and are the RC time constants that determine the shape of the filter response. Phase step applied to When there is a drive phase step, , in the drive (39) By using Eq. (37), (40) and applying the final value theorem to the above (41) Thus, the phase step error approaches zero as . Frequency step applied to When there is a frequency step, , in the drive (42) By using Eq. (37), (43) and applying the final value theorem to the above (44) Thus the frequency step error approaches zero as . Frequency ramp applied to When there is a frequency ramp, , in the drive (45)
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