Asymptotic derivation of traditional 1-bit arctangent phase discriminator (APD) is derived, even though neighboring quantized samples are dependent. The results reveal that high accuracy can be achieved by an APD in low signal-to-noise ratio (SNR) applications using sufficient samples. For high- SNR applications a novel phase discriminator called noise-balanced digital phase discriminator (NB-DPD), which has a complementary asymptotic performance of APD, is proposed to achieve high accuracy. The threshold SNR 2.6 dB that is suggested to identify either APD or NB-DPD is adopted in a specific application. Finally the sampling, quantization, and environmental noise effects on convergence of the asymptotic performance are discussed, and the simulations are provided to verify the analytical results.