Active RC synthesis of transfer function with adjustable coefficients

RC active filters have been constructed using various kinds of active elements, such as negative-impedance convertors, gyrators and amplifiers. The paper shows a new synthesis method which can independently control the coefficients of both numerator and denominator of a transfer function of nth degree. The conventional method which has the above ability needs many integrators, but the proposed circuit contains only amplifiers of finite gain and an RC multiport network. First, the synthesis method of an RC multiport network, which is necessary to fulfil the above condition, and the circuit configuration using feedback and feedforward techniques, are given. We then apply the method to biquadratic transfer functions. The results show that, in view of the sensitivities and the number and values of the elements, it is desirable to construct the function in a cascade of biquadratic functions rather than to construct the whole function in one circuit. As an example, the 4th-degree lowpass filter with one attenuation pole is synthetised, and experimental results show quite good agreement with the theory. The filters designed by this method are intended for use as controlled equalisers in communication systems, speech synthetisers etc.