Pseudo-exponential Function Research Articles

Simultaneous Bandwidth-Extended and Precisely-Gain-Controlled dB-Linear PGA Based on Active Feedback and Binary-Weighted Switches

A simple yet effective approach for programmable gain amplifier (PGA) with a high precision decibel (dB)-linear characteristic and wide bandwidth is presented in this brief. This novel approach is presented by innovatively combining two techniques. Based on the binary-weighted switching technique, the circuit can approach an accurate pseudo-exponential function without using an additional exponential generator for gain control. By adopting the active feedback circuit structure, the bandwidth of PGA can be extended and it also contributes to improve the robustness, both of which cleverly reached a good consistency. The proposed PGA is fabricated in a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.18~{\mu }\text{m}$ </tex-math></inline-formula> CMOS technology, the core circuit occupies an area of 0.11 mm2. Operated at a supply voltage of 1.8 V, the PGA consumes 8.21 mW. The measurement results show that the voltage gain of the proposed PGA can be controlled from −4.2 dB to 25.9 dB with a gain error less than ±0.09 dB, and the minimum −3dB bandwidth is almost 630 MHz. The input 1dB compression point is measured from −28.7 to 0.5 dBm, while the input referred noise is from 22.4 to 70.9 nV/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${{\sqrt {}}}$ </tex-math></inline-formula> Hz.

Fuzzy transform for high-resolution satellite images compression

Many compression methods have been developed until now, especially for very high-resolution satellites images, which, due to the massive information contained in them, need compression for a more efficient storage and transmission. This paper modifies Perfilieva's Fuzzy transform using pseudo-exponential function to compress very high-resolution satellite images. We found that very high-resolution satellite images can be compressed by F-transform with pseudo-exponential function as the membership function. The compressed images have good quality as shown by the PSNR values ranging around 59-66 dB. However, the process is quite time-consuming with average 187.1954 seconds needed to compress one image. These compressed images qualities are better than the standard compression methods such as CCSDS and Wavelet method, but still inferior regarding time consumption.

Analog Building Blocks Using QFGMOS Technique

In this paper, quasi-floating gate MOSFET (QFGMOS) based current divider and pseudo-exponential function generator circuits are proposed. The use of QFGMOS makes the proposed circuits suitable for low voltage/low power operation. The proposed circuits have lower power supply voltage requirement, lower power dissipation and lower THD than the existing circuits available in literature. Both the circuits have been designed and simulated in Cadence virtuoso analog design environment using 180 nm CMOS technology. The simulation results have also been presented to validate the performance of the proposed circuits.

A new current mode CMOS variable gain amplifier using a new pseudo-exponential function

In this paper, a new pseudo-exponential function is described and a new CMOS exponential-control variable gain amplifier (VGA) based on the new function is introduced. No multiplier is needed in the proposed approach. The VGA operates in current mode and includes two different stages. The first stage is a simple current amplifier while the second stage is an attenuator. The overall behavior of the stages gives the new pseudo-exponential function. The VGA circuit has been designed and simulated for a 0.18 μ CMOS process. Post layout results show that the circuit has a bandwidth of 164 MHz and a gain range of 32.5 dB between − 21 and + 11.5 dB.

Pseudo-exponential maps, variants, and quasiminimality

We give a construction of quasiminimal fields equipped with pseudo-analytic maps, generalising Zilber's pseudo-exponential function. In particular we construct pseudo-exponential maps of simple abelian varieties, including pseudo-$\wp$-functions for elliptic curves. We show that the complex field with the corresponding analytic function is isomorphic to the pseudo-analytic version if and only the appropriate version of Schanuel's conjecture is true and the corresponding version of the strong exponential-algebraic closedness property holds. Moreover, we relativize the construction to build a model over a fairly arbitrary countable subfield and deduce that the complex exponential field is quasiminimal if it is exponentially-algebraically closed. This property asks only that the graph of exponentiation have non-trivial intersection with certain algebraic varieties but does not require genericity of these points. Furthermore Schanuel's conjecture is not required as a condition for quasiminimality.

A D/A converter based on a pseudo-exponential function

In this article, a D/A converter employing a novel generalised technique that achieves wide-output linear-in-dB dynamic ranges is proposed. The feasibility of the approach is demonstrated by constructing a linear-in-90 dB exponential amplifier. In addition, a pseudo-exponential circuit employing two operational amplifiers and a few resistors that simulate the exponential function over a predefined range of 15 dB is proposed as a building block. The theoretical results were experimentally confirmed using readily available components in a circuit with a static power consumption of 22 mW when powered with a ±2.75 V supply.

Approximate pexiderized Cauchy's additive type mappings

We prove the stability of the Pexiderized Cauchy's additive functional equation with a general form; f(x+y )= g(x)+h(y)+λ(x,y) where λ(x,y) is a logarithm of a pseudo exponential function. From this result, we obtain the stability with the following form; 1 1+ φ(x,y) f(x+y) e(x,y)g(x)h(y) 1+ φ(x,y), where e(x,y) is a pseudo exponential function. It is a generalized result for the stability of the Pexiderized Cauchy's functional equation.

Low-voltage FGMOS based analog building blocks

Novel floating gate MOSFET (FGMOS) based low-voltage analog circuits such as current-to-voltage converter, current-mode divider and pseudo-exponential function generator are proposed in this paper. The inherent advantages of these circuits are their simplicity, accuracy and low power dissipation. The current-to-voltage converter is operated with a single power supply of 0.9V. The current-mode divider and pseudo-exponential function generator are operated at supply voltages of ±0.9V. It was observed that the power dissipation of the current-to-voltage converter is reduced to 12μW using a single power supply. The power dissipations of the current-mode divider and pseudo-exponential function generator are found to be 356 and 471μW, respectively. The proposed circuits are simulated using SPICE in 0.5μm CMOS process technology to demonstrate the feasibility and the effectiveness of the proposed circuits.

Comments on "Improved Accuracy Pseudo-Exponential Function Generator With Applications in Analog Signal Processing

Recently a new CMOS current-mode pseudo-exponential function generator circuit was reported by Popa. The entire analysis and exponential function generator circuit, given in Popa's paper, is based on a current-squaring circuit module. In this comment paper we show that the current-squarer circuit, presented in Popa's paper, does not work as a current squarer. Consequently the pseudo-exponential generator also does not work as described in Popa's paper. We present a detailed mathematical analysis in this paper to derive its actual operation. Simulation results of the circuit module using Mentor Graphics custom IC design tool set, in a TSMC 0.18-μm CMOS process, are also shown in this paper. Simulation results match the behavior predicted by mathematical analysis.

SUPERSTABILITY OF A GENERALIZED EXPONENTIAL FUNCTIONAL EQUATION OF PEXIDER TYPE

We obtain the superstability of a generalized exponential functional equation f(x+y)=E(x,y)g(x)f(y) and investigate the stability in the sense of R. Ger [4] of this equation in the following setting: <TEX>$$|\frac{f(x+y)}{(E(x,y)g(x)f(y)}-1|{\leq}{\varphi}(x,y)$$</TEX> where E(x, y) is a pseudo exponential function. From these results, we have superstabilities of exponential functional equation and Cauchy's gamma-beta functional equation.

Improved Accuracy Pseudo-Exponential Function Generator With Applications in Analog Signal Processing

A new CMOS current-mode pseudo-exponential circuit based on the n-order Taylor series expansion will be presented. The most important advantage of the circuit with respect to the previously reported similar ones is the smaller value of the total computing error (under 0.3 dB), for a maximal output range of the proposed function generator greater than 40 dB. The total error could be very easily reduced by increasing the number of terms considered in the Taylor expansion. The circuit also presents the advantage of the independence of the output current on technological parameters. The frequency response is improved due to the strong inversion operation of all MOS transistors and to the current-mode operation of the circuit. The circuit area is relatively small due to the exclusively utilization of MOS transistors. The SPICE simulations confirm the theoretical estimated results. The proposed exponential function generator is designed in 0.12-mum CMOS technology and it consumes a reasonable power (less than 0.3 mW) for obtaining the previous mentioned computing error and has a low-voltage operation (a minimal accepted supply voltage under 1.2 V). The total silicon occupied area of the exponential function generator with third-order approximation is about 5.9 mum times 7.9 mum.

Novel pseudo-exponential circuits

In this paper, two voltage-mode circuits that implement the pseudo-exponential function using controllable gain blocks are presented. The gain block of the proposed circuits each utilize a current conveyor and an operational amplifier in a novel manner. They offer the advantages that they are precise, easily implemented in integrated circuit (IC) form and can employ a bank of switched resistors, MOS transistors in triode or transconductors to change their gain according to a control parameter /spl chi/ that is determined by a ratio of resistances. Experimental results using discrete IC components confirm the theory and show the circuits having an output range of approximately 22 dB, with an error of less than 1 dB for x greater than -0.55 and less than 0.63.

CMOS current-mode divider and its applications

Compact, accurate and low-power analog CMOS circuits for current-mode division and pseudo-exponential function generation are presented, based on a new variable transresistance amplifier. Experimental results of the circuits fabricated in a 0.5-/spl mu/m 2P2M n-well CMOS process show better than 0.3% total harmonic distortion. Measured power is less than 0.22 mW at 100-MHz bandwidth and /spl plusmn/1.5-V supply voltages.

Low-voltage, high dB-linear, exponential V-V converter

A new idea is proposed to make use of the disadvantages at low-voltage operations to widen the output dynamic range and the input swing of the exponential voltage-to-voltage circuit with differential input, at low-voltage low-power applications. The pseudo-exponential function is used to realise the exponential characteristic. Based on 0.25 µm CMOS technology, simulations show a 16 dB linear improvement of the output voltage range while dissipating less than 0.2 mW from 1.25 V supply voltage.

CMOS current-mode pseudo-exponential function circuit

A current-mode analogue circuit that implements a pseudo-exponential function is proposed. The design of the circuit is based on Taylor&apos;s series approximation, using MOS transistors in the saturation region. The advantages of this circuit is that the output current presents a very low temperature coefficient (TC) and is also immune to the body-effect. Simulation and experimental results show that the circuit offers a maximum output range of ~30 dB, with an error of less than 1 dB and TC = –233 ppm/°C.

Pseudo-exponential function for MOSFETs in saturation

In this paper, according to the Taylor's series expansion, two pseudo-exponential circuits were realized. The proposed circuits provide a simple method to synthesize pseudo-exponential circuits. Both of the circuits were composed of MOS transistors operating in saturation. One of the pseudo-exponential function circuits is voltage-mode and was tested using discrete components. The other one is current-mode, which is verified with the 0.8 /spl mu/m CMOS process by Hspice simulations. The results confirm the feasibility of the proposed circuits.

CMOS exponential current-to-voltage converter

A CMOS current-to-voltage converter with exponential characteristics is presented. The exponential behaviour is achieved using a pseudo-exponential function and is implemented with two back-to-back connected current mirrors. The circuit used is in the design of a compact low-voltage low-power automatic gain control circuit (AGC) with a control range of /spl sim/30 dB.