Design of arbitrary-order minimal operational-amplifier BIBO stable Bode-type variable-amplitude active-RC equalizers

This paper presents a new technique for the exact design and minimal operational-amplifier realization of arbitrary-order bounded-input-bounded-output (BIBO) stable Bode-type variable-amplitude (VA) active-RC equalizers. This technique is based on the realization of the VA equalizer transfer function directly as the voltage transfer function from port 1 to port 2 of an active-R three-port network when its port 3 is terminated in the active-RC realization of the corresponding (positive-real) shaping impedance function. The salient feature of the resulting VA active-RC equalizers is that they permit the continuous variation of the equalizer transfer function from the corresponding shaping transfer function to its inverse through the use of one single (positive) variable resistor only. In addition, they permit arithmetically symmetric changes in the logarithmic magnitude-frequency response of the equalizer through geometrically symmetric changes in the value of the constituent variable resistor. An application example is given to illustrate the main results.