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An analytical technique for designing automatic gain control (AGC) circuits is presented. This technique is directly applicable to high-gain high-performance radio receiving equipment. Use of this technique permits the designer to specify the performance of the AGC system completely with respect to step changes in signal level, ramp changes in signal level, frequency response, receiver gain error as a function of receiver noise, etc., before the receiver is constructed and tested. When used in conjunction with the statistical filter theory the technique has been used to synthesize optimal AGC systems when the characteristics of the signal and noise are appropriately defined. The mathematical derivation of the closed-loop equations is presented. The resulting expressions are simple and easy to understand by anyone acquainted with linear servo theory. Furthermore, the underlying assumptions used in theory have been tested experimentally, and the close agreement between theory and experiment attests the usefulness of the design technique.