Modular log-domain filters realized using wave port terminators

Log-domain wave filters that simulate the passive LC ladder prototype filters are introduced in this paper. The proposed circuits are constructed from the wave equivalents of the reactive elements corresponding to those in the prototype circuit. The wave equivalent circuits are obtained by using a novel log-domain wave port terminator. The wave equivalent of a capacitor in a shunt branch was chosen as an elementary building block for creating high-order filters. The wave equivalent circuits of all other reactive elements in a shunt or in a series-branch connection can be readily obtained using the elementary building block plus some inverters. This way the derived high-order filter configurations are modular. A design example of a third-order elliptic low-pass filter is given, and the performance of the filter was verified by simulation.     

Differential log-domain filters with high-gain common-mode feedback

A new class of differential log-domain filters based on common-mode feedback (CMFB) is demonstrated. Conditions for adding CMFB to differential log-domain integrators while preserving external linearity are derived. Because signals within differential log-domain circuits are nonlinear, the definition of "common-mode" in these circuits is not unique. Three possible definitions are explored, and each is illustrated with a simple but practical circuit. The circuits provide large CMFB loop gain, which forces common-mode signals to follow a desired nonlinear function. This allows closed-form expressions for the nonlinear internal signals to be derived, which is highly advantageous for design. Second-order filters using CMFB were compared to filters without CMFB through simulation and through measurements of fabricated filters. Adding CMFB is shown to allow greatly increased undistorted signal swings.     

Novel first-order differential class-AB log-domain allpass filters

The first-order differential class-AB log-domain filters are proposed. They are systematically derived using the state–space synthesis procedure. It is also demonstrated that the present second filter cannot be realized without using differential class-AB type. To the best knowledge of the authors, the filters are the first log-domain first-order allpass filters in the literature. PSPICE simulations are performed using both, bipolar junction transistors (BJT) and ideal devices to confirm the theoretical analysis. Tolerable differences are observed due to BJT non-idealities such as finite-beta, non-zero ohmic junction resistances and early voltages.     

Synthesis of class-AB log-domain filters based on nonlinear transconductance

In this paper a new generalized method for synthesis of class-AB current-mode log-domain filters, using nonlinear transconductance cell, is presented. The proposed nonlinear transconductance cell is designed by employing floating-gate MOS (FG-MOS) transistors that operate in weak inversion. It allows deriving current-mode nonlinear transconductance-capacitor (G_m-C) structure from its corresponding conventional transconductance-capacitor (g_m-C) in a systematic way. In this method, synthesis complexity is independent of system size, and thus high-order systems can be readily realized. In addition, it keeps the transconductance-capacitor topology invariant, leading to a very regular, general and simple topology. The filters are designed based on the transistors that are working in weak inversion and feature, low supply voltage, low-power consumption, immune to body effect and with low circuit complexity. For illustration of this new synthesis method, two different filters were designed and verified by simulation. The simulation results by HSPICE show the validity of the proposed technique.     

Simplified technique for syllabic companding in log-domain filters

It is shown that when syllabic companding is applied to log-domain filters using dynamic biasing, their large signal linearity can be exploited to eliminate the state variable compensation circuit. Owing to its simplicity, the proposed technique has several advantages over previous approaches     

Analysis and compensation of transistor non-idealities in log-domain wave active filters

A very important issue concerning the implementation of log-domain filters in integrated form is the effect of BJT transistor non-idealities. This paper is dealing with the above practical problem in the design of log-domain wave filters. For this purpose, a detailed analysis of the effects of the non-idealities on the frequency behavior of log-domain wave active filters is performed. In addition, a systematic method for compensating the caused imperfections is introduced. The validity of the proposed compensation scheme has been verified through simulation results.     

Modular realization of multi-dimensional filters

A method is proposed for the exact decomposition of a general multi-dimensional (m-d) rational transfer function in terms of order one, each one of which is a function of only one of the m variables. This method is used for the realization of general, linear m-d filters, with great modularity, and high parallelism. By using known nonsingular matrices, the coefficients of the decomposed filter can be expressed in terms of the coefficients of the given transfer function and the elements of these matrices. An algorithm for the determination of these coefficients is given and a class of matrices is proposed which leads to simple realizations.     

基于信号流图的任意阶对数域滤波器设计

本文给出了一种基于信号流图的任意阶对数域电流模式滤波器的通用设计方法.用该方法产生的,n阶滤波器由2n个对数单元电路和n个接地电容组成,易于集成.在此基础上给出了三阶Butterworth滤波器的设计实例及其PSpice计算机模拟结果.     

Modular analysis and design of log-domain circuits based on LIN↔ELIN transformations

We systematized and developed some procedures for the modular design of externally-linear internally nonlinear (ELIN) circuits resulting in a general LIN↔ELIN transformation procedure. This one was also extended to analysis of these types of circuits. The procedure is exemplified on log-domain circuits. In the design one starts with the linear block diagram (LIN) described by transfer functions and one substitutes directly each linear building block by a corresponding nonlinear one. The parameters of each nonlinear component depend on the given parameters of its linear correspondent. Input F ⁻¹ and output F blocks are added. In the analysis one identifies the nonlinear basic circuit components and each of them is substituted by its corresponding linear building block. Input and output F ⁻¹-F cells are removed. The ideal transfer function can be calculated on the linear block diagram now. The LIN↔ELIN transformations make a direct connection between equivalent linear and ELIN circuits, simplify their design and analysis procedures and permit the development of CAD procedures.     

Chemical log-domain filter

Presented is a chemical log-domain filter in which an ion sensitive field effect transistor (ISFET) is used to expand a naturally log-compressed chemical signal to derive a chemically-dependent lossy-integrator, whose gain and bandwidth are functions of ion concentration. This is used to integrate small chemical signals or have a filter adaptable to changes in chemical concentration.     

Simple log-domain chaotic oscillator

A log-domain chaotic oscillator generated from a simple model with double-scroll-like dynamics is presented. The circuit operates in current-mode and is well suited to integrated circuit implementation. Experimental verification of the proposed circuit is provided     

Micropower log-domain active inductor

An alternative implementation for emulating an active inductor is proposed. Based on a classical gyrator active inductor architecture, the new active inductor is implemented by using a log-domain current integrator instead of a voltage integrator. Inductance and Q-factor can be tuned independently Simulation results confirming the idea are shown. The proposed circuit is a micropower active inductor operating in the weak inversion region of the MOSFETs     

Table-based log-domain linear transformation filter

A design table for realising log-domain linear transformation filters is presented. Based on this design table, doubly terminated LC ladder filters with or without finite transmission zeros can be efficiently synthesised. Moreover, two design procedures are also given. A canonical log-domain elliptic ladder filter can be realised using one of these procedures. Simulation results are given to verify the theoretical analysis     

Low-Voltage CMOS subthreshold log-domain filtering

This paper presents both a complete set of very low-voltage basic building blocks and a compact design methodology for log filtering in standard or even digital CMOS technologies. The new proposals are based on an alternative translinear loop principle for the MOSFET operating in its subthreshold region. Three different sets of complete basic building blocks are proposed along with all required auxiliary circuitry and a specific matrix design procedure to obtain stable and compact filter implementations. Also, all-MOS filter implementations following these circuit techniques are studied. Simulated and experimental examples are given at 1-V supply voltage for 1.2and 0.35-/spl mu/m CMOS technologies. The resulting circuit techniques are suitable to integrate very low-voltage low-power system-on-a-chip audio applications, such as hearing aids, in standard CMOS technologies.     

Modular and numerically stable fast transversal filters formultichannel and multiexperiment RLS

The authors present scalar implementations of multichannel and multiexperiment fast recursive least squares algorithms in transversal filter form, known as fast transversal filter (FTF) algorithms. By processing the different channels and/or experiments one at a time, the multichannel and/or multiexperiment algorithm decomposes into a set of intertwined single-channel single-experiment algorithms. For multichannel algorithms, the general case of possibly different filter orders in different channels is handled. Geometrically, this modular decomposition approach corresponds to a Gram-Schmidt orthogonalization of multiple error vectors. Algebraically, this technique corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operations. Modular algorithm structures that are amenable to VLSI implementation on arrays of parallel processors naturally follow from the present approach. Numerically, the resulting algorithm benefits from the advantages of triangularization techniques in block processing     

Unifying perspective on log-domain filter synthesis

A unifying framework is presented for the in-depth understanding of the seemingly unrelated state-space-based and translinear methods proposed for the synthesis of externally linear but internally nonlinear logdomain filters. The translinear methods exploit either the 'dynamic translinear principle' or the Bernoulli Cell dynamics. Light is shed in an insightful manner on key interconnections between Frey's nodal state-space-based synthesis relations, translinear loop-based synthesis conditions and the archetypal linear filter dynamics by considering the form of the state variables used in each case.     

A novel first-order log-domain allpass filter

This paper proposes a first-order allpass log-domain filter, which is systematically derived using the state-space synthesis procedure. To the best knowledge of the authors, the filter is the first log-domain first-order allpass filter in the literature. The proposed filter has a simple structure and can be electronically tuned. PSPICE simulations are given to confirm the theoretical analysis.     

A compact low-power BiCMOS log-domain filter

A third-order Chebyshev filter based on the log-domain principle and integrated in a 1-μm BiCMOS process is presented. It has a nominal cutoff frequency of 320 kHz corresponding to a bias current of 1 μA, and can be frequency tuned over almost three decades up to about 10 MHz. It operates with a nominal supply voltage of 1.2 V, maintaining a dynamic range (DR) at 1% THD of 57 dB. For cutoff frequencies in the range of 10 kHz, the supply voltage can be reduced down to 0.9 V. The filter occupies an active area of 0.25 mm² and dissipates 23 μW, corresponding to a power consumption per pole and edge frequency of only 24 pJ. These results demonstrate the potential of log-domain filters for very low-voltage and low-power applications     

规范正交梯形结构对数域滤波器

提出了一种基于规范正交梯形网络信号流图模拟的对数域滤波器设计方法.能直接对给定的任意高阶传输函数进行综合.用该方法设计了1dB波纹三阶椭圆埘数域低通滤波器.Pspice仿真表明,所设计的滤波器实际频响特性几乎是理想的,而且具有电路结构简单、需要的元件数少、灵敏度低和最优的动态范围等特性.