TABLE OF CONTENTS We consider first the biquadratic active- RC sections that use a single op amp, configured in either an inverting (negative-feedback) or noninverting (positive-feedback) mode, in a single-loop feedback configuration. The sections are subdivided into low-pass, band-pass, high-pass, and notch filters.
A low-pass biquadratic filter is characterized by a transfer function of the form
| (4-4) |  |
In searching the literature one can find a number of configurations capable of realizing Eq. (4-4). Two such representative configurations, one using positive feedback around an op amp configured in a noninverting mode and a second using negative feedback around an op amp configured in an inverting mode, are discussed here. Other interesting configurations are reserved for the exercises at the end of the chapter.
The first circuit, using positive feedback, is shown in Fig. 4-5. This circuit is one of many developed by Sallen and Key. The voltage transfer function assuming an ideal op amp is given by
| (4-5) |  |
where K is the closed-loop gain of a noninverting amplifier [Eq. (2-11)],
Note that the coefficient a 1/ 
in Eq. (4-5) involves a cancellation of terms. This cancellation mechanism, which is characteristic of positive-feedback biquadratic sections, will be shown to render large sensitivities to the elements that enter into the calculation, particularly when a 1 ? 1, (i.e., for large Q).
In a cascade design, the section described...
