Single Amplifier Biquad Research Articles

Frequency‐dependent OP‐AMP gain influence on parameters of the single amplifier biquad filters

AbstractThe influence of the finite gain and gain‐bandwidth product of the operational amplifier on the parameters of the active RC filter has been investigated in the present paper. Single amplifier biquad filters were analysed for the case when the central frequency in the pole pair does not depend on the amplifier gain, i.e. when S = 0. The general results were obtained for such filters, describing well the filter behaviour at low as well as at high frequencies. On the basis of the results obtained, the deviation of the realized parameters from the desired values can be determined, and thereby the necessary correction of the filter calculation can be made. The experimental results agree well with the theoretical ones.

Noise and sensitivity optimization of a single-amplifier biquad

Many papers have dealt either with noise or sensitivity optimization of second-order active networks. In this article a joint optimization criteria is developed for a well-known single-amplifier biquad (SAB). The noise performance and the sensitivity properties of the SAB are described by two free network parameters, namely the resistor ratio r^2 and the capacitor ratio c^2 . A two-dimensional object function is left to minimize for either low-noise or low-sensitivity design. Curves which determine the best r,c values are given for both design objectives. A comparison indicates that only a slight sacrifice of the overall sensitivity properties is required by the optimum noise design, while a significant increase in output noise can result if the circuit is designed for minimum sensitivities.

A refined classification of single amplifier filters

AbstractIt 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.

Optimising two commonly used active-filter building blocks using the complementary transformation

In the paper, the minimisation of the gain-sensitivity product (g.s.p.) for two important active-filter types that are finding widespread use in voiceband communication systems, in the form of hybrid-integrated filter building blocks, is considered. The first comprises a twin I for zero realisation: this is incorporated in the positive-feedback loop of a single operational amplifier and is referred to as the twin-T s.a.b.b. The known conditions for minimum g.s.p. for the twin-T s.a.b.b. are briefly recapitulated and expanded. The second comprises a differential scheme for zero realisation, and combines positive and negative feedback. It is referred to as the single-amplifier biquad (s.a.b.). The paper shows that the two circuits are closely related by the complementary transformation, and that conditions for minimum g.s.p. in both cases are identical

Sensitivity minimization in a single amplifier biquad circuit

The single amplifier biquad (SAB) circuit of J. J. Friend is critically examined with a view to minimize its sensitivity properties. This is shown to involve the proper choice of the free design parameters to achieve a trade off between the contributions due to passive and active element variations. First the bandpass configuration is analyzed. A statistical measure of the overall pole variation due to both passive and active components is formulated. The analysis includes a novel but very simple approach for estimating the effects due to op amp variations which is applicable to many of the active filter topologies known. Using the figure of merit obtained in this fashion, it is shown that a near optimal design exists which permits ready physical realization, and which has the property that the transmission error terms are dominated by the irreducible fixed contribution due to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> product which defines the resonant frequency. From the aspect of sensitivity, therefore, it is concluded that no other circuit topology can have superior performance. The frequency range over which these conclusions remain valid are determined by using reasonable estimates of circuit component tolerances. For a simple operational amplifier of the 741-type this range is shown to extend to approximately 2 kHz, while if a more sophisticated two-pole single zero compensation is used for the operational amplifier the range of validity is extended to about 20 kHz. The above results are then shown to hold for all the other important

STAR: An active biquadratic filter section

This paper describes a thin-film hybrid integrated circuit (HIC) which is specifically manufactured to realize cascadable biquadratic active RC filter sections. The HIC consists of an RC network with one operational amplifier. This network is interconnected by a printed wiring board to realize Friend's Single Amplifier Biquad (SAB) and other filter sections. Design equations, components, predistortion method, and laser trimming are all discussed.

Generation and classification of single amplifier filters

AbstractA 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.

Stability Considerations in Nonlinear Feedback Structures as Applied to Active Networks

Active filters have recently acquired widespread use in the realization of frequency-selective networks. Unlike their passive counterparts, active filters have the potential of oscillating. Furthermore, it has been observed that the onset of oscillations in biquad active filters is dependent upon signal level. This led to the recognition that nonlinear stability theory would be necessary to comprehend this behavior. This paper develops a technique to analyze the stability of networks containing linear and nonlinear elements interconnected in multifeedback structures. This is accomplished by extending the concept of the “Describing Function” to include networks containing nonlinearities with frequency-dependent linear feedback. The technique is then applied to explain qualitatively and quantitatively nonlinear effects in op-amps and their relation to the stability of frequency-selective networks containing them (e.g., the Multiple Amplifier Biquad, MAB, and the Single Amplifier Biquad, SAB). The technique is also applied to explain frequency shifts in amplitude-limited oscillators. The most valuable result of this analysis is the discovery of nonlinear feedback circuits which circumvent the conditional stability of high-frequency biquads. This has allowed us to obtain Q's of 50 at 100 kHz in a MAB employing 709 op amps. Similarly, a MAB employing 702 op amps was made to operate at 2 MHz with a Q of 10.

A single-amplifier biquad active filter

A single-amplifier circuit is introduced and shown to be capable of realizing any second-order minimum-phase voltage transfer function while maintaining an isotopic structure. Sensitivity analysis demonstrates that the single-amplifier biquad (SAB) is comparable to other state-of-the-art active filters employing more amplifiers. A bandpass SAB together with an extra amplifiers enables the realization of right-half-plane zeros.