Tracking-Loop Bias Due to Costas Loop Arm Filter Imbalance

An expression is derived which shows that when the bandpass filter preceding a Costas loop is not symmetric and the arm filters are not balanced, a static phase error, which becomes larger as the SNR decreases, can occur due to noise. Conversely, if either condition does not apply, then no noise-induced phase error bias will exist. It is shown, for a modified Costas loop in which one arm filter is removed, that the static phase error may be significant.