A state-space approach to cascade transfer function synthesis with grounded amplifier and capacitor realizations†

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Abstract
The desired transfer function is expanded into factors having quadratic denominators. Each factor is identified with the set A, B, C, D of matrices of the state-space representation of a capacitively terminated two-port network that is specified by a transmission matrix T. An equivalence is obtained between the required state A matrix and the corresponding T matrix. Then, T matrix synthesis techniques that were developed specifically for use with differential operational amplifiers are applied to obtain realizations of the A matrix. By synthesizing different decompositions of the T matrix, different equivalent realizations are obtained and the problem of determining appropriate input and output access ports corresponding to the B, C and D state matrices is facilitated. A practical feature of the method is that all of the basic transfer functions can be realized with grounded amplifiers and capacitors.

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