Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Multi-zone TAP-reactors theory and application - IV. Ideal and non-ideal boundary conditions

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

Design of silicon IP cores for biorthogonal wavelet transforms

A methodology for rapid silicon design of biorthogonal wavelet transform systems has been developed. This is based on generic, scalable architectures for the forward and inverse wavelet filters. These architectures offer efficient hardware utilisation by combining the linear phase property of biorthogonal filters with decimation and interpolation. The resulting designs have been parameterised in terms of types of wavelet and wordlengths for data and coefficients. Control circuitry is embedded within these cores that allows them to be cascaded for any desired level of decomposition without any interface logic. The time to produce silicon designs for a biorthogonal wavelet system is only the time required to run synthesis and layout tools with no further design effort required. The resulting silicon cores produced are comparable in area and performance to hand-crafted designs. These designs are also portable across a range of foundries and are suitable for FPGA and PLD implementations.

Inverse Class E amplifier and oscillator phase noise characteristics

This paper gives the first experimental characterisation of the phase noise response of the recently introduced Inverse Class E topology when operated as an amplifier and then as an oscillator. The results indicate that in amplifier and oscillator modes of operation conversion efficiencies of 64%, and 42% respectively are available, and that the excess PM noise added as a consequence of saturated Class E operation results in about a 10 dB increase in PM over that expected from a small-signal Class A amplifier operating at much lower efficiency. Inverse Class E phase transfer dependence on device drain bias and flicker noise are presented in order to show, respectively, that the Inverse Class E amplifier and oscillator follow the trends predicted by conventional phase noise theory. © 2007 EuMA.

Inverse Class-E Amplifier With Transmission-Line Harmonic Suppression

This paper reports on the design methodology and experimental characterization of the inverse Class-E power amplifier. A demonstration amplifier with excellent second and third harmonic-suppression levels has been designed, constructed, and measured. The circuit fabricated using a 1.2-min gate-width GaAs MESFET is shown to be able to deliver 22-dBm output power at 2.3 GHz. The amplifier achieves a peak power-added efficiency of 64 % and drain efficiency of 69 %, and exhibits 11.6 dB power gain when operated from a 3-V supply voltage. Comparisons of simulated and measured results are given with good agreement between them being obtained. Experimental results are presented for the amplifier's response to Gaussian minimum shift keying modulation, where a peak error vector modulation value of 0.6% is measured.

Sensitivity characteristics of inverse Class-E power amplifier

In this paper, an analysis is performed in order to determine the effects that variations in circuit component values, frequency, and duty cycle have on the performance of the newly introduced inverse Class-E amplifier. Analysis of the inverse Class-E amplifier under the generalized condition of arbitrary duty cycle is performed and it is shown that the inverse Class-E amplifier is reasonably tolerant to circuit parameter variations. When compared to the conventional Class-E amplifier the inverse Class-E amplifier offers the potential for high efficiency at increased output power as well as higher peak output power levels than are available with a conventional Class-E amplifier. Further the inverse Class-E amplifier provides more flexibility for deployment with a pulsewidth modulator as the means of producing full-carrier amplitude modulation (AM) due to its ability to operate to high AM modulation indices.

Analysis of the effect of finite d.c. blocking capacitance and finite d.c. feed inductance on the performance of inverse class-E amplifiers

The first analysis and synthesis equations for the newly introduced inverse Class-E amplifier when operated with a finite d.c. blocking capacitance and a finite d.c.-feed inductance are presented in the paper. Closed-form design equations are derived in order to establish the circuit component values required for optimum synthesis. Excellent agreement between numerical simulation results and theoretical prediction is obtained. It is shown that drain efficiency approaching 100 at a pre-specified output power level can be achieved as zero-current switching and zero-current derivative conditions are simultaneously satisfied. The proposed analysis offers the prospect for realistic MMIC implementation.