Single-input Multiple-output Tunable Log-domain Current-mode Universal Filter

This paper describes the design of a current-mode single-input multiple-output (SIMO) universal filter based on the log-domain filtering concept. The circuit is a direct realization of a first-order differential equation for obtaining the lossy integrator circuit. Lossless integrators are realized by log-domain lossy integrators. The proposed filter comprises only two grounded capacitors and twenty-four transistors. This filter suits to operate in very high frequency (VHF) applications. The pole-frequency of the proposed filter can be controlled over five decade frequency range through bias currents. The pole-Q can be independently controlled with the pole-frequency. Non-ideal effects on the filter are studied in detail. A validated BJT model is used in the simulations operated by a single power supply, as low as 2.5 V. The simulation results using PSpice are included to confirm the good performances and are in agreement with the theory

Quantitative Anderson localization of Schr\"odinger eigenstates under disorder potentials

This paper concerns spectral properties of linear Schr\"odinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we prove the existence of spectral gaps amongst the lowermost eigenvalues and the emergence of exponentially localized states. We quantify the rate of decay in terms of geometric parameters that characterize the potential. The proofs are based on the convergence theory of iterative solvers for eigenvalue problems and their optimal local preconditioning by domain decomposition.Comment: accepted for publication in M3A

Realization of Integrable Low- Voltage Companding Filters for Portable System Applications

Undoubtedly, today’s integrated electronic systems owe their remarkable performance primarily to the rapid advancements of digital technology since 1970s. The various important advantages of digital circuits are: its abstraction from the physical details of the actual circuit implementation, its comparative insensitiveness to variations in the manufacturing process, and the operating conditions besides allowing functional complexity that would not be possible using analog technology. As a result, digital circuits usually offer a more robust behaviour than their analog counterparts, though often with area, power and speed drawbacks. Due to these and other benefits, analog functionality has increasingly been replaced by digital implementations. In spite of the advantages discussed above, analog components are far from obsolete and continue to be key components of modern electronic systems. There is a definite trend toward persistent and ubiquitous use of analog electronic circuits in day-to-day life. Portable electronic gadgets, wireless communications and the widespread application of RF tags are just a few examples of contemporary developments. While all of these electronic systems are based on digital circuitry, they heavily rely on analog components as interfaces to the real world. In fact, many modern designs combine powerful digital systems and complementary analog components on a single chip for cost and reliability reasons. Unfortunately, the design of such systems-on-chip (SOC) suffers from the vastly different design styles of analog and digital components. While mature synthesis tools are readily available for digital designs, there is hardly any such support for analog designers apart from wellestablished PSPICE-like circuit simulators. Consequently, though the analog part usually occupies only a small fraction of the entire die area of an SOC, but its design often constitutes a major bottleneck within the entire development process. Integrated continuous-time active filters are the class of continuous-time or analog circuits which are used in various applications like channel selection in radios, anti-aliasing before sampling, and hearing aids etc. One of the figures of merit of a filter is the dynamic range; this is the ratio of the largest to the smallest signal that can be applied at the input of the filter while maintaining certain specified performance. The dynamic range required in the filter varies with the application and is decided by the variation in strength of the desired signal as well as that of unwanted signals that are to be rejected by the filter. It is well known that the power dissipation and the capacitor area of an integrated active filter increases in proportion to its dynamic range. This situation is incompatible with the needs of integrated systems, especially battery operated ones. In addition to this fundamental dependence of power dissipation on dynamic range, the design of integrated active filters is further complicated by the reduction of supply voltage of integrated circuits imposed by the scaling down of technologies to attain twin objective of higher speed and lower power consumption in digital circuits. The reduction in power consumption with decreasing supply voltage does not apply to analog circuits. In fact, considerable innovation is required with a reduced supply voltage even to avoid increasing power consumption for a given signal to noise ratio (S/N). These aspects pose a great hurdle to the active filter designer. A technique which has attracted the attention of circuit designers as a possible route to filters with higher dynamic range per unit power consumption is “companding”. Companding (compression-expansion) filters are a very promising subclass of continuous-time analog filters, where the input (linear) signal is initially compressed before it will be handled by the core (non-linear) system. In order to preserve the linear operation of the whole system, the non-linear signal produced by the core system is converted back to a linear output signal by employing an appropriate output stage. The required compression and expansion operations are performed by employing bipolar transistors in active region or MOS transistors in weak inversion; the systems thus derived are known as logarithmic-domain (logdomain) systems. In case MOS transistors operated in saturation region are employed, the derived structures are known as Square-root domain systems. Finally, the third class of companding filters can also be obtained by employing bipolar transistors in active region or MOS transistors in weak inversion; the derived systems are known as Sinh-domain systems. During the last several years, a significant research effort has been already carried out in the area of companding circuits. This is due to the fact that their main advantages are the capability for operation in low-voltage environment and large dynamic range originated from their companding nature, electronic tunability of the frequency characteristics, absence of resistors and the potential for operations in varied frequency regions.Thus, it is obvious that companding filters can be employed for implementing high-performance analog signal processing in diverse frequency ranges. For example, companding filters could be used for realizing subsystems in: xDSL modems, disk drive read channels, biomedical electronics, Bluetooth/ZigBee applications, phaselocked loops, FM stereo demodulator, touch-tone telephone tone decoder and crossover network used in a three-way high-fidelity loudspeaker etc. A number of design methods for companding filters and their building blocks have been introduced in the literature. Most of the proposed filter structures operate either above 1.5V or under symmetrical (1.5V) power supplies. According to data that provides information about the near future of semiconductor technology, International Technology Roadmap for Semiconductors (ITRS), in 2013, the supply voltage of digital circuits in 32 nm technology will be 0.5 V. Therefore, the trend for the implementation of analog integrated circuits is the usage of low-voltage building blocks that use a single 0.5-1.5V power supply. Therefore, the present investigation was primarily concerned with the study and design of low voltage and low power Companding filters. The work includes the study about: the building blocks required in implementing low voltage and low power Companding filters; the techniques used to realize low voltage and low power Companding filters and their various areas of application. Various novel low voltage and low power Companding filter designs have been developed and studied for their characteristics to be applied in a particular portable area of application. The developed designs include the N-th order universal Companding filter designs, which have been reported first time in the open literature. Further, an endeavor has been made to design Companding filters with orthogonal tuning of performance parameters so that the designs can be simultaneously used for various features. The salient features of each of the developed circuit are described. Electronic tunability is one of the major features of all of the designs. Use of grounded capacitors and resistorless designs in all the cases makes the designs suitable for IC technology. All the designs operate in a low-voltage and low-power environment essential for portable system applications. Unless specified otherwise, all the investigations on these designs are based on the PSPICE simulations using model parameters of the NR100N bipolar transistors and BSIM 0.35μm/TSMC 0.25μm /TSMC 0.18μm CMOS process MOS transistors. The performance of each circuit has been validated by comparing the characteristics obtained using simulation with the results present in the open literature. The proposed designs could not be realized in silicon due to non-availability of foundry facility at the place of study. An effort has already been started to realize some of the designs in silicon and check their applicability in practical circuits. At the basic level, one of the proposed Companding filter designs was implemented using the commercially available transistor array ICs (LM3046N) and was found to verify the theoretical predictions obtained from the simulation results

0.5 V log-domain realization of tinnitus detection system

A low-voltage tinnitus detection system using log-domain technique has been introduced in this paper. The design offers the advantages of resistorless design, electronic tunability of performance characteristics, and less complexity than the reported ones. The performance of the tinnitus detector has been verified by HSPICE simulation software using the parameters of TSMC CMOS 130 nm process

Passive cascaded-lattice structures for low-sensitivity FIR filter design, with applications to filter banks

A class of nonrecursive cascaded-lattice structures is derived, for the implementation of finite-impulse response (FIR) digital filters. The building blocks are lossless and the transfer function can be implemented as a sequence of planar rotations. The structures can be used for the synthesis of any scalar FIR transfer function H(z) with no restriction on the location of zeros; at the same time, all the lattice coefficients have magnitude bounded above by unity. The structures have excellent passband sensitivity because of inherent passivity, and are automatically internally scaled, in an L_2 sense. The ideas are also extended for the realization of a bank of MFIR transfer functions as a cascaded lattice. Applications of these structures in subband coding and in multirate signal processing are outlined. Numerical design examples are included

CMOS Hyperbolic Sine ELIN filters for low/audio frequency biomedical applications

Hyperbolic-Sine (Sinh) filters form a subclass of Externally-Linear-Internally-Non- Linear (ELIN) systems. They can handle large-signals in a low power environment under half the capacitor area required by the more popular ELIN Log-domain filters. Their inherent class-AB nature stems from the odd property of the sinh function at the heart of their companding operation. Despite this early realisation, the Sinh filtering paradigm has not attracted the interest it deserves to date probably due to its mathematical and circuit-level complexity. This Thesis presents an overview of the CMOS weak inversion Sinh filtering paradigm and explains how biomedical systems of low- to audio-frequency range could benefit from it. Its dual scope is to: consolidate the theory behind the synthesis and design of high order Sinh continuous–time filters and more importantly to confirm their micro-power consumption and 100+ dB of DR through measured results presented for the first time. Novel high order Sinh topologies are designed by means of a systematic mathematical framework introduced. They employ a recently proposed CMOS Sinh integrator comprising only p-type devices in its translinear loops. The performance of the high order topologies is evaluated both solely and in comparison with their Log domain counterparts. A 5th order Sinh Chebyshev low pass filter is compared head-to-head with a corresponding and also novel Log domain class-AB topology, confirming that Sinh filters constitute a solution of equally high DR (100+ dB) with half the capacitor area at the expense of higher complexity and power consumption. The theoretical findings are validated by means of measured results from an 8th order notch filter for 50/60Hz noise fabricated in a 0.35μm CMOS technology. Measured results confirm a DR of 102dB, a moderate SNR of ~60dB and 74μW power consumption from 2V power supply

Adjoint BFKL at finite coupling: a short-cut from the collinear limit

In the high energy Regge limit, the six gluons scattering amplitude is controlled by the adjoint BFKL eigenvalue and impact factor. In this paper we determine these two building blocks at any value of the 't Hooft coupling in planar $\cal{N}$=4 SYM theory. This is achieved by means of analytic continuations from the collinear limit, where similar all loops expressions were recently established. We check our predictions against all available data at weak and strong coupling.Comment: 30 pages plus appendices, 12 figures. References added; published versio