A general synthesis procedure capable of realizing any stable transfer function is described; generalized-immittance converters are used in which the input immittance is proportional to s^{2} \times load immittance. The resulting realizations are shown to have low sensitivity to element variations. The sensitivity in realizations of second-order transfer functions is independent of the selectivity and it is shown to be much lower than the sensitivity in realizations using positive-gain amplifiers or negative-immittance converters. A unique feature is that in some cases the same circuit can be used as a low-pass as well as a high-pass filter. The synthesis procedure is illustrated by examples and experimental results.

Novel RC-active-network synthesis using generalized- immittance converters

A unified approach is presented for generating configurations for circuits containing one operational amplifier together with RC elements and capable of realizing a general second-order voltage transfer function. Systematic application of the generation procedure leads to various single amplifier biquads with the known circuits, as well as some new ones, obtained as special cases. The insight gained from the generalized approach as well as the results of a general sensitivity analysis (including the effects of the amplifier limited bandwidth) offer a method for categorizing and classifying single amplifier filters. The different filter classes are illustrated and compared with the aid of extensive design tables. General equations for the effect of the amplifier limited bandwidth are also given.

Generation and classification of single amplifier filters

Two new biquad circuits based on the Sallen-Key positive feedback structure are introduced and shown to be capable of realizing all possible second-order filter functions. The pole design equations and pole sensitivities are identical to those of the Deliyannis bandpass circuit which is the basis for the Friend biquad. The new circuits, however, display lower transmission zero sensitivities than the Friend notch realizations. Design details and experimental results are given.

Optimum configurations for single-amplifier biquadratic filters

The primary purpose of this article is to present a unified, comprehensive survey of accomplishments in the field of network synthesis for linear, lumped, and finite networks from 1965 through early 1968.* Because of the large number of contributions made during this period, only a sampling of the many significant works is presented here, with much of the material in the form of results. It is the author's hope that the extensive list of references included will be useful in providing the additional information necessary.

Synthesizing active filters

It is shown that Single Amplifier Biquads (SAB's) may be grouped into two major categories, the Enhanced Negative Feedback (ENF) and the Enhanced Positive Feedback (EPF). These two major classes of circuit are related by the complementary transformation and hence exhibit identical sensitivity performance. In the extreme, the ENF class degenerates to the familiar Negative Feedback (NF) class while the EPF class reduces to the Positive Feedback (PF) case where the op amp is connected in a unity-gain configuration. Depending on the order of the RC feedback network, each class includes two subclasses with different sensitivity performance. The paper examines in detail the ‘enhanced feedback’ mechanism, and investigates the optimum design of the Deliyannis—Friend circuit and its complement the Sallen and Key positive feedback configuration.

A refined classification of single amplifier filters

The sensitivity, to μ−1 (where μ is the open-loop amplifier gain), of the Q factor of a 2nd-order Sallen-Key circuit can be reduced from the conventional value 2Q2/μ to 3Q/μ by increasing the closed-loop gain from 1 to 4/3. However, this increases the sensitivity to passive-element variations. An optimum engineering solution is found by minimising, for given maximum component variations, the resulting variation of Q, rather than the sensitivities. This makes single-amplifier circuits usable for higher Q factors than previously, which is of particular interest for microelectronic realisations of such circuits.

W. Saraga

Papers

Sensitivity of 2nd-order Sallen-key-type active RC filters