Digital biquad filter

Abstract: A novel approach to filter design, based on Adams' [1] ‘log-domain’ filters, is proposed that yields a truly current-mode circuit realisation. Adams' idea, which was introduced in a limited context, is generalised to permit a complete distortionless synthesis procedure, which results in circuit implementations readily realisable using complementary bipolar processes. It is shown that, by introducing an exponential map on the state-space description of the desired linear system, a log-domain filter can be fully realised with transistors configured in current mirror-type groupings, current sources and capacitors. Owing to the mapping, the state variables are intrinsically related to current, and not voltage, in the resulting circuits, a fact that emphasises the current-mode nature of the design. A general biquadratic filter section is designed, and, following discussion of cascading sections, a seventh-order Chebychev lowpass filter is designed. All designed circuits are shown to be tunable over a two-decade range in frequency while their characteristics are accurately preserved, even for biquad sections whose f0Q product is greater than fT/10. The Chebychev filter is shown in simulation to possess nearly 60 dB dynamic range relative to 0.9% THD, with a cutoff frequency of nearly 5 MHz, using transistor models from AT&T's CBIC-R 300 MHz complementary bipolar process.

Abstract: Two closely related, low-sensitivity, active switched capacitor fitter topologies are presented. Each of these circuits comprises two operational amplifiers and at most nine capacitors. The topologies have been carefully constructed so that they are immune to the various parasitic capacitances normally present in switched capacitor networks. One filter topology is capable of realizing any stable biquadratic z-domain transfer function, while the second one is only slightly less than fully general. Most commonly used transfer functions can be realized with either topology and will require only seven capacitors. The choice between the two topologies will generally be made on the basis of total capacitance required, dynamic range behavior, and sensitivity. A complete set of synthesis equations is given for both circuits which cover both the general and all the important special cases of the biquadratic transfer function. Finally, several examples are given which illustrate the synthesis procedures and the versatility of the filter topologies.

Abstract: In this paper, a current-mode (CM) Kerwin–Huelsman–Newcomb (KHN) biquad is proposed. The circuit employs three differential-voltage current conveyors (DVCCs) as active elements together with two capacitors and four resistors as passive elements, which all are grounded. The circuit simultaneously provides the three basic filter functions, namely bandpass (BP), highpass (HP) and lowpass (LP) functions. The notch and allpass (AP) functions can be obtained by connecting appropriate output currents directly without using additional active elements. The output signals are obtained at high output impedance ports, which is important for easy cascading in CM operation. SPICE simulation results are given to verify the theoretical analyses.

Abstract: The use of active elements in linear networks offers new degrees of freedom to both network and system designers. A comprehensive report on the Biquad, an active topology based on analog computer concepts, is given. We describe the electrical characteristics of the Biquad that make it a manufacturable realization for precision networks. Analysis and experimental data describe the dependence of Biquad performance on nonideal operational amplifiers. Compensation techniques are derived which allow high- Q operation at several hundred kilohertz with existing devices. The 8-V rms signal capacity and 80-dB dynamic range of the voice-frequency Biquad are illustrated.

Abstract: An equivalent circuit for the translinear implementation of the second generation current conveyors with positive or negative current transfer is given. This circuit takes into account the various parasitic elements of the conveyor which induce frequency limitations (gain values, poles of the transfers, and parasitic impedances). The methods allowing the determination of the values for these parasitic elements are indicated and discussed. The effect of each element on the frequency responses of the circuits using the conveyors are studied in every detail. The frequency behavior of two circuits are analyzed as examples: a voltage amplifier without feedback and two configurations for a second order biquad filter operating in current-mode. All the theoretical results of the analysis are well confirmed from SPICE simulations.