Fractional‐order electronically controlled generalized filters

Novel topologies of fractional‐order generalized filters are introduced in this paper. These offer the following benefits: (1) realization of lowpass, highpass, bandpass, allpass, or bandstop filter functions by the same topology; (2) resistorless realizations; (3) electronic adjustment of their frequency characteristics as well as their order; and (4) employment of only grounded capacitors. All the above have been achieved using Operational Transconductance Amplifiers as active elements and appropriate multi‐feedback topologies. The behavior of the proposed designs is verified through simulation results using the Cadence IC design suite and the Design Kit provided by the Austrian Micro Systems 0.35‐µm complementary metal–oxide–semiconductor process. Copyright © 2016 John Wiley & Sons, Ltd.     

On the transposition of Gm–C filters to DC stabilized log‐domain filters

High‐order log‐domain filters could be designed by transposing the already known linear‐domain G_m–C filter topologies to the corresponding topologies in the log‐domain. This is achieved by using a non‐linear transconductor configuration, where the output current is exponentially related to its input and output voltages. A drawback of the non‐linear transconductor configuration already introduced in the literature is that a number of the transposed log‐domain filter topologies suffer from DC instability, while in some others a DC offset current appears at their output. In order to eliminate the aforementioned problems a modified non‐linear transconductor configuration for transposing G_m–C filter topologies to log‐domain filter topologies is introduced in this paper. The achieved improvements are demonstrated through a number of log‐domain filter configurations derived using the already introduced and the proposed transposition schemes. Copyright © 2006 John Wiley & Sons, Ltd.     

Ultra‐low voltage fractional‐order circuits using current mirrors

Fractional‐order blocks, including differentiators, lossy and lossless integrators as well as filters of order 1 + a (0 < a < 1), are presented in this paper. The proposed topologies offer the benefit of ultra low‐voltage operation; in addition, reduced circuit complexity is achieved compared to the corresponding companding schemes, which have been already introduced in the literature. The ultra‐low voltage operation is performed through the employment of metal oxide semiconductor transistors biased in the subthreshold region. The reduction of circuit complexity is achieved through the utilization of current mirrors as active elements for realizing the required building blocks. The performance of the proposed fractional‐order circuits has been evaluated through the Analog Design Environment of the Cadence software and the design kit provided by the Taiwan Semiconductor Manufacturing Company (TSMC) 180 nm complementary metal oxide semiconductor process. Copyright © 2015 John Wiley & Sons, Ltd.     

A DC stabilized log‐domain nth‐order multifunction filter based on the decomposition of nth‐order HP filter function to FLF topology

The design of high‐order log‐domain filters can be easily accomplished by transposing already known linear‐domain G_m‐C filter topologies to their counterparts in the log‐domain through the employment of a set of complementary operators. To achieve the G_m‐C filter topologies, the multiple feedback approach is widely used due to its accrued advantages. In this paper a synthesis approach for the development of an nth‐order multifunction log‐domain filter comprising lowpass (LP), highpass (HP) and bandpass (BP) filter functions is proposed. The approach is based on the decomposition of nth‐order HP filter function to follow‐the‐leader‐feedback (FLF) topology. The design is simple and simultaneously achieves nearly all of the chief advantages. The design offers superior performance factors vis‐à‐vis the ones recently reported. To verify the high‐order behavior of the topology, a 5th‐order multifunction filter was designed and the achieved simulated results verify the theory. Copyright © 2008 John Wiley & Sons, Ltd.     

Balanced Gm‐C filters with improved linearity and power efficiency

A novel G_m‐C filter design technique is presented. It is based on floating‐gate metal oxide semiconductor (FGMOS) transistors and consists in a topological rearrangement of conventional fully differential G_m‐C structures without modifying the employed transconductors at transistor level. The proposed method allows decreasing the number of active elements (transconductors) of the filter. Moreover, high linearity is obtained at low and medium frequencies of the pass band. Drawbacks inherent to the use of FGMOS transistors are analyzed, such as large occupied area, high sensitivity to mismatch, or parasitic zeros in transfer functions. The features of the proposed technique are fully exploited in all‐pole G_m‐C filter design, specially implementing unity gain Butterworth transfer functions. Thus, two low‐power second‐order Butterworth G_m‐C filters have been designed and fabricated to compare the proposed FGMOS technique with their equivalent topologies obtained by a conventional design method. Measurement results for a test chip prototype in a 0.5‐µm standard complementary MOS process are presented, confirming the advantages of the proposed FGMOS design technique. Copyright © 2014 John Wiley & Sons, Ltd.     

A simulation study of high‐order CMOS hyperbolic‐sine filters

This paper advances the field of externally linear–internally nonlinear (ELIN) filters by introducing a synthesis method that enables the design of high‐order class‐AB sinh filters by means of complementary metal–oxide semiconductor (CMOS) weak‐inversion sinh integrators comprising only one type of devices in their translinear loops. The proposed transistor‐level synthesis approach is demonstrated through the examples of (1) a biquadratic and (2) a fifth‐order filter, and their simulated performance is studied. The biquadratic filter achieves a dynamic range of 94 dB and has a tunable quality factor Q up to the value of 8, whereas its natural frequency can be tuned for four orders of magnitude. Its static power consumption amounts to 6.2 μW for Q = 1 and f_o = 2 kHz. The fifth‐order Chebyshev sinh CMOS filter with a cut‐off frequency of 100 Hz, a pass band ripple of 1 dB, and a power consumption of ~300 nW is compared head‐to‐head with its pseudo‐differential class‐AB CMOS log domain counterpart. The sinh filter achieves similar or better signal‐to‐noise ratio (SNR) and signal‐to‐noise‐plus‐distortion ratio (SNDR) performances with half the capacitor area but at the expense of higher power consumption from the same power supply level. All three presented filter topologies are novel. Cadence design framework simulations have been performed using the commercially available 0.35 µm AMS (austriamicrosystems) process parameters. Copyright © 2013 John Wiley & Sons, Ltd.     

Low‐power,low‐noise,active‐RC band‐pass filters using a ‘lossy’ LP–BP transformation

A new and straightforward design procedure for simple canonical topologies of allpole, active‐RC, low‐selectivity band‐pass (BP) filters, with low sensitivity to component tolerances is presented. The procedure is primarily intended for discrete‐component, low‐power filter applications using just one amplifier for relatively high‐order filters. The design procedure starts out with an ‘optimized’ low‐pass (LP) prototype filter, yielding an ‘optimized’ BP filter, whereby the wealth of ‘optimized’ single‐amplifier LP filter designs can be exploited. Using a so‐called ‘lossy’ LP–BP transformation, closed‐form design equations for the design of second‐ to eighth‐order, single‐amplifier BP filters are presented. The low sensitivity, low power consumption, and low noise features of the resulting circuits, as well as the influence of the finite gain‐bandwidth product and component spread, are demonstrated for the case of a fourth‐order filter example. The optimized single‐opamp fourth‐order filter is compared with other designs, such as the cascade of optimized Biquads. Using PSpice with a TL081 opamp model, the filter performance is simulated and the results compared and verified with measurements of a discrete‐component breadboard filter using 1% resistors, 1% capacitors, and a TL081 opamp. Copyright © 2011 John Wiley & Sons, Ltd.     

Log‐domain linear transformation filters revised: improved building blocks and comparison results

A method for designing high‐order log‐domain filters has already been proposed in the literature based on the concept of the classical linear transformation (LT) filters. For this purpose, a substitution table containing the log‐domain LT equivalent of each passive element has been introduced. Drawbacks of the log‐domain filter topologies derived according to this table are the following: (a) a dc offset current appears at the output of all pole filters and (b) dc instability is observed in the case of the substitution of LC resonators. In addition, an alternative technique already proposed for simulating filters with LC resonators is valid only under small‐signal conditions. In order to overcome the aforementioned problems, new log‐domain LT equivalents of a number of passive elements are introduced in this paper. The correct operation of the novel blocks has been verified through simulation results. Also, a comparison concerning the behaviour of the log‐domain LT filters and that of the filters derived according to the leapfrog and the wave methods has also been performed. Copyright © 2007 John Wiley & Sons, Ltd.     

Explicit design formulas for current‐mode leap‐frog OTA‐C filters and 300 MHz CMOS seventh‐order linear phase filter

The leap‐frog (LF) configuration is an important structure in analogue filter design. Voltage‐mode LF OTA‐C filters have recently been studied in the literature; however, general explicit formulas do not exist for current‐mode LF OTA‐C filters and there is also need for current‐mode LF‐based OTA‐C structures for realization of arbitrary transmission zeros. Three current‐mode OTA‐C structures are presented, including the basic LF structure and LF filters with an input distributor or an output summer. They can realize all‐pole characteristics and functions with arbitrary transmission zeros. Explicit design formulas are derived directly from these structures for the synthesis of, respectively, all‐pole and arbitrary zero filter characteristics of up to the sixth order. The filter structures are regular and the design formulas are straightforward to use. As an illustrative example, a 300 MHz seventh‐order linear phase low‐pass filter with zeros is presented. The filter is implemented using a fully differential linear operational transconductance amplifier (OTA) based on a source degeneration topology. Simulations in a standard TSMC 0.18µm CMOS process with 2.5 V power supply have shown that the cutoff frequency of the filter ranges from 260 to 320 MHz, group delay ripple is about 4.5% over the whole tuning range, noise of the filter is 420nA/√Hz, dynamic range is 66 dB and power consumption is 200 mW. Copyright © 2008 John Wiley & Sons, Ltd.     

0.5‐V bulk‐driven OTA and its applications

A new 0.5‐V bulk‐driven operational transconductance amplifier (OTA), designed in 50 nm CMOS technology, is presented in the paper. The circuit is characterized by improved linearity and dynamic range obtained for MOS devices operating in moderate inversion region. Some basic applications of the OTA such as a voltage integrator and a second‐order low‐pass filter have also been described. The filter is compared to other low‐voltage filters presented in the literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Realization of log‐domain high‐order transfer functions using first‐order building blocks and complementary operators

High‐order log‐domain filters could be easily designed by using the functional block diagram (FBD) representation of the corresponding linear prototype and a set of complementary operators. For this purpose, lossy and lossless integrator blocks have been already introduced in the literature. Novel first‐order log‐domain highpass and allpass filter configurations, which are fully compatible with the already published integrator blocks, are introduced in this paper. These are realized using integration and subtraction blocks or a novel differentiation configuration. As a result, a complete set of first‐order building blocks would be available for synthesizing any arbitrary high‐order transfer function. In order to verify the correct operation of the proposed structures, the performance of the introduced highpass filters was evaluated through simulation results. In addition, a fifth‐order log‐domain bandpass filter was designed and simulated using one of the introduced first‐order highpass filter configurations. Copyright © 2006 John Wiley & Sons, Ltd.     

Structure generation and performance comparison of elliptic Gm‐C filters

Starting from a set of matrices describing a general G_m‐C filter topology, a procedure is developed for generating structures of lowpass filters. As the matrices and the filter topologies have a one‐to‐one correspondence, an algebraic method is used to identify filter topologies with desired properties, here, transfer functions with finite jω‐axis transmission zeros, specifically elliptic filters. Sensitivity expressions for these structures are derived and a performance comparison based on a set of chosen criteria is made. For a specified elliptic transfer function, filters with only grounded capacitors and those containing also floating capacitors emerge as alternative realizations, as are filters with a single input and those with distributed inputs. For third‐order functions, a detailed comparison is performed of leapfrog (LF) and inverse follow‐the‐leader‐feedback (IFLF), the most popular special cases, and of topologies that have also floating capacitors (LF_f, IFLF_f), as well as of a novel configuration that uses also distributed inputs (DI_f) and leads to a reduced element count. Design guidelines and restrictions are given, which follow from the derived results with focus on the circuits' sensitivity performance and other properties important for IC implementation. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytical synthesis of odd/even‐nth‐order elliptic Cauer filter structures using OTRAs

The operational transresistance amplifier (OTRA), the dual of the well‐known operational transconductance amplifier, is an attractive element for use in circuit design. One odd‐nth‐order and two even‐nth‐order OTRA‐R‐C or OTRA‐MOS‐C elliptic Cauer filter structures are presented using new analytical synthesis methods (ASMs). Because it is assumed in the synthesis procedure that the transresistance R_m → ∞, but in view of the fact that R_m is finite in practice, the more the number of OTRAs employed, the worse the precision of the output signals. By studying the sensitivity of the output to component variations, more precise output may be obtained by selecting one or two appropriate capacitance(s)/resistance(s) and adjusting their values suitably. H‐spice simulations are given to validate and demonstrate the theoretical predictions. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical synthesis of voltage‐mode even/odd‐nth‐order differential difference current conveyor and fully differential current conveyor II‐grounded resistor and capacitor universal filter structures

A complete definition of an odd/even‐nth‐order notch or band‐reject filter transfer function is presented. Based on the differences between the input voltage and (i) an nth‐order high‐pass; (ii) a traditional nth‐order notch; and (iii) an nth‐order all‐pass filtering transfer function, a systematic method has been proposed to derive a universal filter structure that can realize voltage‐mode odd/even‐nth‐order low‐pass, band‐pass, high‐pass, all‐pass and traditional notch filters. The intrinsic capability of voltage‐mode addition and subtraction of the two active elements, differential difference current conveyors and fully differential current conveyors, is used to advantage in the aforementioned synthesis procedure. Based upon the definition of an nth‐order notch or band‐reject filter transfer function proposed in this paper, the aforementioned universal one has been further extended to the newly defined nth‐order band rejection filter. The voltage and current tracking errors of the two active elements are compensated by varying the resistances of the proposed filter. Filtering feasibility, stability, component sensitivities, linear and dynamic ranges, power consumption, and noise are simulated using H‐Spice with 0.35 µm process. Compared to some of the recently reported universal biquads, the new one is shown to enjoy the lowest component sensitivities and the best output accuracy for all‐pass signals. Moreover, Monte Carlo and two‐tone tests for intermodulation linearity simulations are also investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

Square‐root domain wave filters

In this paper the wave method is used for designing high‐order square‐root domain filters, which emulate the topology of the corresponding LC ladder prototypes. This is achieved by transposing the signal flow graph that corresponds to the wave equivalent of the elementary two‐port subnetwork in the linear domain to the corresponding one in the square‐root domain, by employing an appropriate set of complementary operators. As the equivalents of the other reactive elements are derived from the wave equivalent of the elementary subnetwork, by interchanging the terminals of the appropriate wave signals and/or using inverters, an advantage offered by the proposed technique is the modularity of the derived filter configurations. As an example, a fifth‐order lowpass square‐root domain wave filter was designed and its behaviour was studied through simulation results in order to demonstrate the validity of the proposed design technique. Copyright © 2006 John Wiley & Sons, Ltd.     

Nearly monotonic passband low‐pass filter design by using sum‐of‐squared Legendre polynomials

A new type of filter approximation, which utilizes orthonormal Legendre polynomials, referred to as sum‐of‐squared Legendre polynomials, is presented in this paper. Power transmission coefficient and the group delay of the proposed filter are compared with those of the Butterworth, Legendre–Papoulis, and Halpern filters. In order to illustrate the design of the proposed filter function, sum‐of‐squared Legendre polynomials coefficients and normalized element values of the low‐pass LC (inductor‐capacitor) ladder network prototype are given, up to the 10th degree. For continuous‐time domain filtering, doubly terminated LC ladder network topologies have very low sensitivities to changes of component values. In order to determine the effect of variation of all reactive components on the filter attenuation characteristic, the new sensitivity function has been proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

Square‐root domain linear transformation filters

A new systematic method for designing square‐root domain (SRD) linear transformation (LT) filter is introduced in this paper. For this purpose, a substitution table containing the SRD LT equivalent of each passive element has been introduced. The proposed equivalents have been realized by employing appropriate SRD building blocks with low‐voltage operation capability. As a design example, a 3rd‐order SRD LT filter has been realized and its performance has been evaluated through simulation results. In addition, the most important performance factors of the SRD filter have been compared with those achieved by the SRD filters derived according to the leapfrog, wave, and topological emulation methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Design of Sinh‐Domain filters using complementary operators

A new systematic method for designing Sinh‐Domain filters is introduced in this paper. This is achieved by employing an appropriate set of complementary operators, in order to transpose the conventional functional block diagram representation of each linear operation to the corresponding one into the Sinh‐Domain. The proposed method offers the benefits of facilitating the design procedure of high‐order Sinh‐Domain filters and of the absence of any restriction concerning the type and/or the order of the realized filter function. As an example, a third‐order Sinh‐Domain leapfrog filter is designed by employing the proposed set of operators. Two possible realizations are given and their performance has been evaluated and compared through simulation results. Copyright © 2011 John Wiley & Sons, Ltd.     

MOS‐only reduced‐order ELIN cochlear channels: comparative performance evaluation

This paper introduces and applies practical area‐reduction techniques on the analogue, externally linear‐internally nonlinear, complementary metal‐oxide semiconductor (CMOS) implementation of a cochlear channel. This channel is constructed on the basis of the biomimetic auditory filter called One‐Zero Gammatone Filter, and it has been synthesised using ultra‐low power Class‐AB biquadratic filters, which employ MOS transistors that operate in their weak inversion regime. The realisation of linear capacitors with appropriately configured MOS transistors, the order reduction of the One‐Zero Gammatone Filter transfer function and the employment of hyperbolic sine companding filters can lead to area reductions that range from 61.8% up to 91.9% of the original size. Comparative simulation results highlight the trade‐offs between performance, linearity, noise and power consumption of the designs. Copyright © 2016 John Wiley & Sons, Ltd.     

1.5 V square‐root domain universal biquad filters

Square‐root domain universal biquad topologies are introduced in this paper. One of them is single input multiple output, while the other one is multiple input single output biquad. Important benefits offered by the proposed topologies are the electronic adjustment of the resonant frequency and the capability for operating in a low‐voltage environment; also, the resonant frequency could be adjusted without disturbing the Q factor and vice‐versa. Simulation results using the Spectre simulator of the Analog Design Environment of Cadence software validate the correct operation of the proposed topologies and provide important performance characteristics. Copyright © 2011 John Wiley & Sons, Ltd.