Design of a Digital Automatic Gain Control with Backward Difference Transformation

The design of a digital Automatic Gain Control (AGC) prior to a digital Phase Locked Loop (PLL) that uses the backward difference Transformation is described. This design is applicable to an Automatic Gain Control with an exponential gain controlled amplifier and a logarithmic amplifier, which obtains a gain settling time independent of the absolute gain. Use of this design permits the designer to specify the performance of the digital AGC system with respect to the similar analog AGC. A mathematical model for the digital AGC for the backward difference equation is established to investigate the characteristics of the scheme. Based on the backward difference equation, we analyze the transfer function and the transient response of the AGC. It has been verified that the results by the digital AGC agree with the analog AGC obtained on the condition that the sample interval is small.