Synthesis of Active RC Networks

Sipress, J.

doi:10.1109/tct.1961.1086786

Cited by 23 publications

(3 citation statements)

References 6 publications

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“…3d can now be redrawn as shown in Fig. 3e For the practical realisation of the filter C S ,C L , C' 6 and C\ are, of course, required to be positive. In the examples investigated so far, the author has found that this condition could always be satisfied by choosing a sufficiently large value for C M (Fig.…”

Section: Utilisation Of the Nonideal Inductor In Filter Designmentioning

confidence: 99%

Highpass and bandpass filters using a new single-amplifier simulated inductor

Ramsey

1978

IEE J. Electron. Circuits Syst. UK

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A new single-amplifier single-capacitor circuit simulating a grounded inductor, for use in active RC highpass and bandpass filters, is discussed, and a method of compensating for the nonideal behaviour of simulated inductors of this type is presented. In contrast to known compensation methods, the compensation procedure proposed here does not seek to improve the nonideal simulated inductors, but deliberately designs the simulating circuit to have a specific biquadratic impedance function and then modifies the filter circuit so as to produce the required loss/frequency response using these biquadratic impedances instead of the original inductors. For bandpass filters the compensation is only approximate. However, for highpass filters, complete compensation can be achieved over the entire frequency range in which the gain of the amplifier can be adequately described by a single-pole model; the cost of achieving this is some increase in sensitivity. The new design procedure has been applied successfully to a 5th-order Cauer-type highpass filter; computed incremental sensitivities and some measured results are presented.

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Section: Utilisation Of the Nonideal Inductor In Filter Designmentioning

confidence: 99%

Highpass and bandpass filters using a new single-amplifier simulated inductor

Ramsey

1978

IEE J. Electron. Circuits Syst. UK

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“…Specifically, consider an (N + 2)-port passive RC network characterized by the (N + 2) X (N + 2) short-circuit admittance matrix Y, and suppose t The realization of an arbitrary NX N matrix of constants as the short-circuit admittance matrix of an N -port network containing positive resistors, ideal transformers and controlled sources also requires, in general, at least N controlled sources. This follows from the fact that, in this case, Yo is the matrix of a nonnegative quadratic form, and hence it is possible to prescribe constant matrices Y such that, for the entire class of matrices Yo, [Y -Yo] is of rank N. The matrix Y is given, as a special case of (9), by (18) …”

Section: N-port Active Rc Realizationmentioning

confidence: 99%

Synthesis ofN-Port ActiveRCNetworks

Sandberg¹

1961

Bell System Technical Journal

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The following basic theorem concerning active RC networks is proved: Theorem: A n arbitrary N X N matrix of real rational functions in the complex-frequency variable (a) can be realized as the short-circuit admittance matrix of a transformerless active RC N-port network containing N real-coefficient controlled sources, and (b) cannot, in general, be realized as the short-circuit admittance matrix of an active RC network containing less than N controlled sources.

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“…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.…”

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Gain and sensitivity limitations of active RC filters

Soderstrand

Mitra

1971

IEEE Trans. Circuit Theory

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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...

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Synthesis of Active RC Networks

Cited by 23 publications

References 6 publications

Highpass and bandpass filters using a new single-amplifier simulated inductor

Highpass and bandpass filters using a new single-amplifier simulated inductor

Synthesis ofN-Port ActiveRCNetworks

Gain and sensitivity limitations of active RC filters

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