Lock-In, Tracking, and acquisition of AGC-aided phase- locked loops

The analysis of phase-locked loops (PLL´s) aided by a coherent automatic gain control circuit (AGC) is presented. From the basic differential equations describing separately the PLL and the AGC, the combined differential equations governing the PLL-AGC feedback structure is presented. The lock-in range of AGC-aided PLL´s is shown to be significantly larger than for standard PLL´s. It is shown that the linear tracking properties of AGC-aided PLL´s are much improved by being less sensitive to the input waveform parameters in comparison to standard PLL´s. First-order PLL´s are examined in detail in regard to acquisition; it is demonstrated that the AGC-aided first-order PLL acquires for all values of input frequency. Acquisition of the second-order AGC-aided PLL´s is discussed.