Biquadratic Sections Research Articles

A reconfigurable floating-gate-transistor-capacitor filter for analog signal processing

This paper introduces a fully reconfigurable floating-gate-transistor-capacitor (FGT-C) filter that exhibits compactness and power efficiency. The proposed filter incorporates a biquadratic section, enabling the generation of lowpass (LP) and bandpass (BP) outputs with adjustable filter parameters, including gains, natural frequency, quality factor, and DC levels for input and output signals. Moreover, the FGT-C filter topology demonstrates a modular structure, facilitating easy cascading and scalability of the biquadratic sections to implement high-order frequency responses. A prototype chip has been fabricated in the 0.35 μm CMOS process, where each biquadratic section occupies an area of 0.0313 mm2. The chip measurements were conducted with a supply voltage of 1.8 V and both output voltage levels programmed at 0.9 V. The biquadratic FGT-C filter exhibits a power consumption of 118.4 nW and achieves a spurious free dynamic range of 43 dB in a 10 kHz bandwidth setting. It is suitable for low-power analog signal processing in large-scale field programmable analog arrays.

Cost function to analyze the passband and the stopband of Digital Biquadratic Filters

This paper focuses on filter design in the frequency domain; specifically, the frequency behavior of one type of IIR filter called digital biquadratic filter is analyzed. First, similar mathematical approaches were used to define two normalized functions: one for the stopband and another for the passband. These two functions can be combined to create a cost function, and therefore, used by optimization algorithms to design digital filters. Computer simulations allowed building color maps to analyze this cost function. These maps describe areas that allow understanding visually the effect of the poles and zeros of the filter over its frequency behavior. The areas described by these maps introduce background information that can be used to design or optimize digital filters with custom frequency responses. Several tests were performed to establish the validity of the proposed cost function.Additionally, it was shown that the cost function can be easily computed using a polynomial approximation. Therefore, instead of using uniformly distributed frequency points, the frequency analysis is performed at the Chebyshev nodes improving accuracy while using very few terms in the approximation. This approximation can be used to speed up the computation of the cost function, and consequently reduce optimization time for complex filters composed of several biquadratic sections.

A Power-Efficient Reconfigurable OTA-C Filter for Low-Frequency Biomedical Applications

A power-efficient operational-transconductance-amplifier-capacitor (OTA-C) filter for biomedical applications is presented with detailed noise analysis. This filter consists of a cascade of biquadratic sections, each of which is configured via a serial-peripheral-interface circuit embedded with non-volatile memories to provide low pass or bandpass response. All filter parameters, including the gains, natural frequency, and quality factor, are orthogonally adjustable by programming charges on floating-gate bias transistors. The reconfigurable biquadratic section is composed of four power-efficient linearized OTAs. Each OTA consists of complementary hextuple-diffusor-quadruple-differential-pairs (HDQDPs) and a floating-gate common-mode feedback scheme. A developed computer algorithm for transistor dimension optimization is adopted to extend the input linear range of the HDQDP based on nonlinearity cancellation. A prototype chip is designed and fabricated in a $0.35~ \mu {\mathrm{ m}}$ CMOS process to demonstrate reconfigurability and performance of the proposed filter. Each biquadratic section occupies $0.12{\mathrm{ mm}}^{2}$ with a frequency tuning range more than five decades. Measured spurious-free dynamic ranges (SFDR) at the low pass and bandpass outputs from one of the biquadratic sections are 52.6 and 54.55 dB, respectively, when the natural frequency is programmed at 2 kHz with power consumption of 107.2 nW. A fourth-order Chebyshev low pass and an eighth-order Butterworth bandpass responses are implemented with characterized SFDRs of 50.43 and 48.3 dB, respectively.

Matrix Methods for the Dynamic Range Optimization of Continuous-Time $G_{m}$-$C$ Filters

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents a synthesis procedure for the optimization of the dynamic range of continuous-time fully differential <formula formulatype="inline"> <tex>$G_{m}$</tex></formula>-<formula formulatype="inline"><tex>$C$</tex> </formula> filters. Such procedure builds up on a general extended state-space system representation which provides simple matrix algebra mechanisms to evaluate the noise and distortion performances of filters, as well as, the effect of amplitude and impedance scaling operations. Using these methods, an analytical technique for the dynamic range optimization of weakly nonlinear <formula formulatype="inline"><tex>$G_{m}$</tex></formula>-<formula formulatype="inline"> <tex>$C$</tex></formula> filters under power dissipation constraints is presented. The procedure is first explained for general filter structures and then illustrated with a simple biquadratic section. </para>

Single Amplifier Bi-Quadratic Filter Topologies in Transimpedance Configuration

Active-RC configurations, implemented as cascaded bi-quadratic sections (biquads), are the filters of choice for low distortion applications in the base-band. For low power and area applications, single amplifier biquads are best, and are well studied in literature. However, in many applications the input signal is in current domain while the output is a voltage. Output of a current steering digital-analog converter, and output of a down-conversion mixer, are two such examples. In this paper, the authors propose two generic classes of single amplifier bi-quadratic low-pass filter topologies, achieving a second order roll-off in transimpedance (-to-) configuration. Both these topologies are derived with the constraint of fully differential signal processing. The transimpedance active-RC configurations presented here eliminate redundant current-voltage-current conversion and hence provide immense advantages in terms of noise and linearity.

Nonidealities of Tow-Thomas biquads Using VOA- and CFOA-based Miller integrators

An analysis and comparison of the performance of Tow-Thomas biquadratic filter sections, implemented with Miller integrators based on current feedback opamps (CFOAs) and voltage opamps (VOAs) was carried out. We found that the implementations with CFOAs show less parameter accuracy and an increased tendency to become unstable. Design criteria to partially overcome these drawbacks and to maximally exploit the inherent high-speed potential of CFOAs were also derived. The theoretical derivations and related results were experimentally validated through implementations from commercially available devices.

SIGMA-DELTA IIR FILTER REALIZATION USING THIRD-ORDER REMODULATORS

In general, Sigma-Delta (ΣΔ) IIR filters are realized using cascades of second-order sections. The existing biquadratic structures do not exploit the high signal-to-noise ratio (SNR) of the higher-order ΣΔ modulators. A second-order IIR structure which achieves this high SNR is proposed. For this purpose a third-order ΣΔ remodulator, necessary to provide the ΣΔ output samples and eliminate the multipliers, is incorporated into the filter structure. The performance of the proposed biquadratic section is investigated and compared to existing counterparts. A cascade of three such sections is used to implement a sixth-order IIR filter.

Current mode biquadratic filter realizations employing operational amplifiers

New circuit configurations for realizing current mode biquadratic filter sections using operational amplifiers are presented. Each circuit uses a single operational amplifier and seven passive elements at most. The merits and demerits of the proposed realizations are discussed.

Design, Fabrication, and Comparative Study of Electronically Tunable Active Filters

The Kerwin-Huelsman Newcomb (KHN) biquad is the natural choice for use as a ‘universal’ filter building block out of the several existing 3-amplifier biquadratic filter sections based on the two integrator loop or state variable realization of 2nd order systems. A modified version of the KHN biquad, which is electronically tunable almost linearly over a decade range of center frequency, is presented. For electronic tunability, instead of the direct use of a FET as a voltage variable resistance to control the time constants of the integrators, a novel approach of using voltage-controlled variable-gain amplifiers at the inputs of both the integrators and one immediately after the input signal has been suggested. The circuit is suitable for use as a tunable universal filtering module and can be easily digitally programmed.Comparative treatment of general tuning methods of active filters, and some methods of electronic tuning of active filters are discussed. A brief description of tuning algorithms of active filters is also given.

Novel CCI-OTA-Based Grounded Capacitor Current-Mode Biquadratic Bandpass and Lowpass Filters

A novel current-mode active filter topology using a first generation current conveyor (CCI) and an operational transconductance amplifier (OTA) is presented. Using this topology, grounded-capacitor biquadratic bandpass and lowpass filter sections, with at most five one-port passive elements, are realized. In these realizations, the parameterω0can be adjusted without disturbing the parameterω0/ Q0

Novel voltage-controlled grounded resistor

The letter presents a new tunable grounded resistor in which a single MOS transistor, operating in the triode region, is linearised via feedback of the drain/source potentials to the gate terminal. Preliminary simulation results show that a biquadratic section realised using the proposed resistor would exhibit less than 0.4% total harmonic distortion (THD) for input signals of 1 Vpp, increasing to 1% for 4 Vpp inputs.

A parasitic-insensitive area-efficient approach to realizing very large time constants in switched-capacitor circuits

A novel switched-capacitor technique for realizing very large time constants is presented. The technique is insensitive to parasitic capacitances and is very area-efficient. It does not require a complicated clocking scheme. The technique yields a complete family of integrators which in turn can be used to realize higher-order filtering functions based on cascaded biquadratic sections or ladder filters. These integrators have been used to implement an experimental 60-Hz notch filter working from a 128-kHz clock. >

Design of a general biquadratic filter section with only transconductances and grounded capacitors

A method is presented for the implementation of all stable second-order filters using only tunable transconductance elements and grounded capacitors (TGC filters). Although other voltage-to-current converters can be used, the simple four-transistor transconductance is particularly convenient because of its reduced circuitry. The synthesis technique is based on the signal-flow-graph corresponding to the state-space model of a second-order section. The approach is general and can be applied to obtain higher-order filters in the same manner, provided that the corresponding signal flow graph exists. >

Passivity properties of low-sensitivity digital filter structures

A general representation of a class of low passband sensitivity digital filter structures is proposed. The proposed representation for a transfer function of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> consists of an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(N + 1)</tex> -pair memoryless system terminated at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -pairs by delays. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(N + 1)</tex> -pair system contains only adders and multipliers, and is described by an orthogonal transfer matrix. The set of terminating delays can be looked upon as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -pair system with transfer matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z^{-1}{\bf 1}</tex> . Certain wave digital filter structures, Gray-Markel lattice structures and the coupled-form biquadratic section belong to the general form advanced here. Several properties satisfied in these special cases are derived in a unified manner using the generalized representation. Also, a quantization scheme that makes the structure free from zero-input limit cycles even under time-varying conditions is advanced, unifying similar such results independently reported for the above well-known structures.

Group delay transfer functions with least squares error

This paper presents tables of group-delay functions, ranging in order from 3 to 11, which approximate a nominal one second delay over bandwidths up to 17.5 rad/s. The functions, which can be arranged in all-pole or non-minimum phase forms, are based on a least-squares minimization of the delay error and therefore exhibit `unequal ripple? characteristics. These and other features of the leastmean-square approximations are discussed and comparisons drawn with maximally-flat and equi-ripple forms. A versatile RC-active biquadratic section, which has been found particularly useful in implementing non-minimum phase functions, is also described.

Micropower switched capacitor biquadratic cell

The implementation of the double correlated sampling noise reduction technique in conventional strays-insensitive switched capacitor biquad building blocks is described. The function is performed by an offset cancellation circuit which is incorporated into the structure without the use of any additional capacitor, only minor modifications in the switching topology, and one supplementary clock phase. Consequently, a significant reduction of the low-frequency (1/f) noise is made possible and the usual differential amplifiers may be replaced by simple inverting amplifiers operated in class AB, featuring high-speed, low-quiescent power dissipation and low noise. An experimental micropower SC biquadratic filter section designed for `leapfrog' or `follow-the-leader feedback' structures has been developed using high gain (>80 dB) CMOS push/pull inverting amplifiers together with a three-phase clocking sequence. The integrated circuit, implemented in a low-voltage Si-gate CMOS process, achieves excellent accuracy and less than 5 /spl mu/W power dissipation with a 32 kHz sampling rate and /spl plusmn/1.5 V supplies; dynamic range is 66 dB.

A class of active RC filters having the same decomposition of denominator

A class of active RC biquadratic sections is presented which has identical properties with respect to passive elements as the Mikhael-Bhattacharyya network. The circuits are obtained by an exhaustive computer generation of graphs. As a result, 17 structures have been derived. The circuits have been examined subject to their inherent compensation for the finite gain-bandwidth products of operational amplifiers and interesting solution are pointed out.

State-variable biquads with optimum integrator sensitivities

We show how to derive state-variable biquadratic sections with lowest possible sensitivity to their integrators. The resulting structures turn out to satisfy the condition for optimum dynamic range given by Mullis and Roberts [1]. The sensitivity optimum obtained is very ‘strong’ in the sense that these biquads simultaneously attain lower bounds for several practical measures of sensitivity. Furthermore, it is shown that this class of filters exhibits sensitivities that are either equal to or lower than those of doubly-terminated LC ladders.

A new approach to the design of an RC active biquadratic section containing real amplifiers

In the paper, a general method of calculating relative errors of Q-factor and ma pole frequency for second order active RC networks is given. The analysis of pole quality and frequency was carried out assuming a two-port model of amplifier with input and output impedances and one-pole gain characteristics, The presented analysis is a generalization of tho Wilson-Bedri-Brown method for active KC networks with operational amplifiers. The general stability condition was determined from relative-errors of Q-factor and ω0 frequency. It was shown that the stability condition of networks with op-ams was a specific case of the general one. The condition for zero relative error of the Q-factor for design procedure of active networks was given. It was shown that for the network designed in such a way the sensitivity coefficient of the Q factor with respect to gain is equal to zero. The analysis and design procedure of the network are illustrated by synthesis of the ‘biquad’ section.

Generation of active RC filters: signal flow graph approach

In this paper a method is presented which allows one to generate all basic signal flow graphs (SFG) for a given decomposition of the denominator of a biquadratic section. This approach is based on a binodal representation of a RC network with operational amplifiers (op amp) and classification of biquadratic sections. The classification is made with respect to a type of the SFG representation and a type of the passive RC circuits associated with the op amp. A program has been written for an exhaustive generation of graphs representing the assumed decomposition of the denominator. The circuits have identical properties with respect to passive elements.