Dynamic Translinear Circuits—An Overview

Dynamic translinear circuits and log-domain filters form a promising and challenging approach to meet the dynamic range limitations that conventional analog implementation techniques are facing due to ever lower supply voltages, low power consumption and high-frequency demands. This paper aims to give an overview of this young, yet rapidly developing, circuit paradigm. Emphasis is placed on methods for analysis and synthesis and on state-of-the-art results obtained for both linear and non-linear applications.     

Nonlinear dynamics of first- and second-order log-domain circuits

Log-domain filters use the large-signal exponential current-voltage relationship of the bipolar junction transistor to convert signals to logarithmic form, where they are processed, and to map them back to the linear domain after processing. Due to their internally nonlinear nature, application of standard linear circuit design techniques to such networks can give rise to unexpected externally nonlinear behavior. Methods of nonlinear dynamics are used here to explain the undesired nonlinearities recently observed in a differential first-order log-domain integrator and to investigate the input/output behavior of the corresponding low-pass filter. The nonlinear behavior of a floating-capacitor differential second-order log-domain bandpass filter is also investigated and explained.     

Bernoulli operator: a low-level approach to log-domain processing

A low-level large-signal continuous-time operator, governed by the Bernoulli nonlinear differential equation is proposed. This cell consists of a suitably biased bipolar junction transistor and an emitter-connected grounded capacitor, and is shown to formalise in a convenient manner, with signal-processing in the log-domain     

An ON-OFF log domain circuit that recreates adaptive filtering in the retina

We introduce a new approach to synthesizing Class AB log-domain filters that satisfy dynamic differential-mode and common-mode constraints simultaneously. Whereas the dynamic differential-mode constraint imposes the desired filtering behavior, the dynamic common-mode constraint solves the zero-dc-gain problem, a shortcoming of previous approaches. Also, we introduce a novel push-pull circuit that serves as a current-splitter; it rectifies a differential signal into the ON and OFF paths in our log-domain filter. As an example, we synthesize a first-order low-pass filter, and, to demonstrate the rejection of dc signals, we implement an adaptive filter by placing this low-pass circuit in a variable-gain negative-feedback path. Feedback gain is controlled by signal energy, which is extracted simply by summing complementary ON and OFF signals-dc signals do not contribute to the signal energy nor are they amplified by the feedback. We implement this adaptive filter design in a silicon chip that draws biological inspiration from visual processing in the mammalian retina. It may also be useful in other applications that require dynamic time-constant adaptation.     

On the generalization of composite memristive network structures for computational analog/digital circuits and systems

The unique adaptive properties of memory resistors (memristors) are ideal for use in computational architectures. Multiple interconnected memristors demonstrate complicated overall behavior which significantly improves the efficiency of logic operations via massive parallelism. Nowadays, within an ever-growing variety of memristive systems, most of the research has so far focused on the properties of the individual devices; little is known about the extraordinary features of complex memristive networks and their application prospects. The composite characteristics of regular and irregular memristive networks are explored in this work. A generalized concept for the construction of composite memristive systems, efficiently built out of individual memristive devices, is presented. A new type of threshold-dependent programmable memristive switches, presenting different electrical characteristics from their structural elements, is proposed. As an example of the introduced approach, a SPICE simulation-based evaluation of several programmable analog circuits is presented. The proposed circuit design approach constitutes a step forward towards novel memristor-based nanoelectronic computational systems and architectures.     

A log-domain multiphase sinusoidal oscillator

A novel multiphase sinusoidal oscillator topology, realized by employing the concept of log-domain filtering, is introduced in this paper. The realization of the oscillator's topology is achieved by establishing a loop constructed from an inverting and non-inverting log-domain lossy integrators. Attractive benefits offered by the novel topology are the ability for independent electronic tuning of the condition of oscillation and the frequency of oscillation, and the ability for realizing both even- and odd-order oscillators without any manipulation of the basic configuration. The operation of the proposed oscillator has been verified through simulation results.     

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.     

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.     

A Log-Domain CMOS Transcapacitor: Design, Analysis and Applications

We present in this paper the CMOS implementation of a transcapacitor working in the log-domain. This circuit integrates a differential input current into an output pseudo-voltage, which is similar to the compressed voltage used as the internal variable in companding filters. This log-domain transcapacitor is compatible with pseudo-conductances implemented with a single transistor. The pseudo-transcapacitor circuit is analyzed and a collection of log-domain reactive components and small circuits using it is proposed.     

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.     

用对数域电流模式积分器实现的高频集成滤波器

文本提出了全差动对数域电流模式积分器．该积分器的时间常数受参考偏流控制,其直流增益可达60dB,在高频它具有比较平坦的相频特性。用该积分器设计的二阶滤波器和1dB波纹五阶Chebyshev低通滤波器,计算机仿真显示,“实际”频响特性几乎是理想的．且频率可在很宽的范围内调控．这种滤波器具有很低的THD。     

Sinh-Domain linear transformation filters

A new systematic method for designing Sinh-Domain linear transformation (LT) filters is introduced in this article. For this purpose, a substitution scheme containing the Sinh-Domain LT equivalent of each passive prototype has been introduced. The proposed equivalents have been realised by employing appropriate Sinh-Domain building blocks with low-voltage operation capability. As an example, a third-order Sinh-Domain elliptic LT filter has been designed and its performance has been evaluated through simulation results. In addition, a detailed comparison with the corresponding Sinh-Domain and log-domain counterparts has been performed and the obtained results have been further discussed.     

A Novel Log-Domain Differentiator

A log-domain differentiator circuit, constructed using an appropriate input stage and a multiplier block, is proposed in this Letter. The input stage compresses the voltage at the capacitor's nodes and simultaneously produces a replica of the current that flows through the capacitor. The multiplier block realizes the desired output current. The analysis of the proposed circuit has been verified through simulation results.     

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.     

Continuous-time and continuous–discrete-time unscented Rauch–Tung–Striebel smoothers

This article considers the application of the unscented transformation to approximate fixed-interval optimal smoothing of continuous-time non-linear stochastic dynamic systems. The proposed methodology can be applied to systems, where the dynamics can be modeled with non-linear stochastic differential equations and the noise corrupted measurements are obtained continuously or at discrete times. The smoothing algorithm is based on computing the continuous-time limit of the recently proposed unscented Rauch–Tung–Striebel smoother, which is an approximate optimal smoothing algorithm for discrete-time stochastic dynamic systems.     

Low-Voltage Log-Domain Complex Filters

Two systematic methods for designing low-voltage log-domain complex filters are introduced in this paper. The first one is based on the transposition of the signal flow graph representation of the linear-domain complex leapfrog prototype filter to the corresponding one in the log-domain. The last one is based on the transposition of the wave equivalents of the elements of the complex passive prototype filter to the corresponding log-domain complex equivalents. Both transpositions are performed by employing an appropriate set of complementary operators that facilitates the derivation of low-voltage log-domain filter configurations. Two design examples are given, where a 12th-order log-domain complex transfer function is realized in order to fulfill the Bluetooth specifications. The derived log-domain filter structures operate at a single 1.2-V-power supply-voltage, and their behavior was evaluated through simulation results. In addition, a comparison concerning important quality factors of both of the proposed structures is performed, and the obtained results are further discussed.      

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.     

A Study of Different Class AB Log Domain First Order Filters

Several different class AB log-domain/translinear filters are compared in terms of their noise and distortion behavior using both analytical and simulation results. A few of the circuit topologies shown have not been considered before and are derived using a new theory for class AB dynamical circuits recently proposed. The study, although approximate, suggests ways in which both noise and distortion performance may be optimized by appropriate choice of circuit topology. Other practical aspects of the designs are also discussed.     

Ionically Mediated Mechanical Deformation Associated with Memristive Switching

Ionically mediated phenomena underpin the functioning of various devices, including batteries, solid oxide fuel cells, memristors, and neuromorphic devices. The ionic behavior corresponding to ionically mediated phenomena causes not only variations in the electrical properties but also mechanical deformation, which is crucial for device reliability. However, the interrelation between ionically mediated electrical properties and mechanical deformation has not been elucidated yet. This study investigates ionically mediated mechanical deformation accompanied by memristive switching in a TiO₂ single crystal through simultaneous conductive atomic force microscopy and electrochemical strain microscopy. A comprehensive analysis indicates the existence of a relationship between mechanical deformation and memristive switching based on the ionic behavior. Furthermore, an ionic state variable is used to simplify the interrelation between the electrochemical strain hysteresis and memristive switching associated with applied voltage. This study provides insights on the ionic behavior and can be extended to other systems for the general analysis of the relationship between mechanical deformation and electrical properties.