Gain and sensitivity limitations of active RC filters

Abstract

Pole-polynomial decomposition forms the basis for classifying active RC filters into ten groups. This classification serves two purposes. First, the gain and sensitivity properties are directly related to the type of decomposition. Thus the optimum gain and sensitivity values for any filter structure con be easily determined by simply finding the classification to which the filter belongs. Second, active filters have been developed for two new types of polynomial decomposition for which no active filters previously existed. These new circuits have very good gain-sensitivity properties.Even though this approach of realization has been shown to lead to lower pole sensitivities in certain cases [7], [S], the main advantage of this approach is the ease of postdesign corrective adjustments.The two system parameters commonly used to characterize a .second-order filter section are the Q of the pole pair and the pole frequency w. defined as s INCE inductorless filters were first proposed by Scott[1] in 1938, many different and novel approaches to realizing transfer functions by means of active RC filters have been proposed [2]-[6]. In the design of these active RC filters, the two items of most practical interest are the gain values of the amplifiers and the filter sensitivities with respect to the active and passive parameters. The gain values roughly determine the useful frequency range of the filter, and the sensitivities determine the maximum realizable selectivity by the filter configuration. In this paper a method for obtaining gain and sensitivity limitations of all types of second-order active RC filters is described. In order to derive these limitations without any specific reference to the actual configurations, the active filters are classified into basic groups. The basis for this classification is the manner in which the active elements are used to decompose the denominator polynomial to generate complex poles. The classification scheme encompasses every possible denominator decomposition. In the case of two such decompositions there were no existing active filters in those classes. Thus the classification scheme has also led to a new set of active filters. These filters have very good gain-sensitivity properties as suggested by their decomposition class.(2) wo = dbolP2.Throughout this paper we shall assume that the denominator polynomial D(S) has been normalized to wo= 1, i.e.,This is particularly helpful since it instantly displays the Q. By frequency and impedance scaling, one can easily convert a normalized circuit realization into a practical one. For the purpose of a general comparison of the performance of active filters, we shall use here the most commonly used Q sensitivity and pole-frequency sensitivity: S,Q A d(ln Q)/d(ln X) = (~/Q)(dQ/ds)XzWO = d(ln wo)/d(ln 2) = (z/wo)(dwo/dz) (6) where x is the active or passive parameter of interest. BASIC DE~NITIONS PRELIMINARY CONSIDERATIONS For convenience, active filters are realized as a cascade of filter sections characterized by second-order transfer fu...

A new second‐order multifunctional RC‐active filter circuit using two operational amplifiers

“…Third, we analyze then we can realize PS characteristics. Equations (2) and (3) have a common denomlnator and their Q-value, resonance frequency Wn, and gain factor H are given by (-kiKi (BEF, PS) (7)…”

“…Let V0m denote the maximum output voltage of operational amplifiers A 1 and A2, and let V & , and V a be the maximum allowable input signal amplitudes of A 1 and A2, respectively. Then we obtain Equations (1) and (2) Hence, the maximum allowable input signal amplitude of the proposed circuit is given by…”