A closed loop automatic gain control (AGC) circuit with high dynamic range capabilities having an amplifier circuit for receiving an input signal, which is susceptible to variations in signal power, and a control signal. The amplifier circuit is responsive to the control signal for amplifying the input signal at a gain level corresponding to the control signal so as to provide a corresponding output signal. A measurement circuit is coupled to the amplifier means for measuring logarithmic signal power of the amplified input signal and providing a corresponding linear measurement signal. An integration circuit is included for receiving the measurement signal, and a reference signal which corresponds to a desired signal power of the output signal. The integration circuit integrates with respect to time the difference between the measurement signal and the reference signal, and generates the control signal which corresponds to the result of the integration.