Effect of Numerically Controlled Oscillator Bit Width in Phase Meters

Abstract: Projects aiming to detect gravitational waves (GWs) in space in the millihertz range will utilize interferometers to measure the separations between free-falling test masses. The phasemeter measures the phase changes of the interference signals caused by the test masses' relative movements. The measurement sensitivity of the phasemeter is one of the key factors in the detection. In this work, we reviewed the core metrology of the phasemeter and evaluated the ultra-low noise performance of the phasemeter with analog signals. Frequency readout noise related to the bit width of the numerically controlled oscillator (NCO) inside the phasemeter is identified as one of the main noise sources of phase measurement theoretically and experimentally. After increasing the NCO bit widths, the single-channel phase noise of the phasemeter reached 2.0 {\mu}rad/Hz^{1/2} at 6 mHz, and the differential phase noise reached 0.4 {\mu}rad/Hz^{1/2} at 6 mHz. The phase noise performances remained consistent within the carrier frequency range of 4.9 MHz to 25.1 MHz.