Costas loop

A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g. double-sideband suppressed carrier signals) and phase modulation signals (e.g. BPSK, QPSK). It was invented by John P. Costas at General Electric in the 1950s. Its invention was described as having had 'a profound effect on modern digital communications'.The primary application of Costas loops is in wireless receivers. Its advantage over the PLL-based detectors is that at small deviations the Costas loop error voltage is sin ⁡ ( 2 ( θ i − θ f ) ) {displaystyle sin(2( heta _{i}- heta _{f}))} as compared to sin ⁡ ( θ i − θ f ) {displaystyle sin( heta _{i}- heta _{f})} . This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking Doppler-shifted carriers especially in OFDM and GPS receivers. A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g. double-sideband suppressed carrier signals) and phase modulation signals (e.g. BPSK, QPSK). It was invented by John P. Costas at General Electric in the 1950s. Its invention was described as having had 'a profound effect on modern digital communications'.The primary application of Costas loops is in wireless receivers. Its advantage over the PLL-based detectors is that at small deviations the Costas loop error voltage is sin ⁡ ( 2 ( θ i − θ f ) ) {displaystyle sin(2( heta _{i}- heta _{f}))} as compared to sin ⁡ ( θ i − θ f ) {displaystyle sin( heta _{i}- heta _{f})} . This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking Doppler-shifted carriers especially in OFDM and GPS receivers. In the classical implementation of a Costas loop, a local voltage-controlled oscillator (VCO) provides quadrature outputs, one to each of two phase detectors, e.g., product detectors. The same phase of the input signal is also applied to both phase detectors and the output of each phase detector is passed through a low-pass filter. The outputs of these low-pass filters are inputs to another phase detector, the output of which passes through noise-reduction filter before being used to control the voltage-controlled oscillator. The overall loop response is controlled by the two individual low-pass filters that precede the third phase detector while the third low-pass filter serves a trivial role in terms of gain and phase margin.