In this paper, the generalized analysis of the first Butterworth filter based on two passive elements is introduced in the fractional-order sense. The fractional-order condition of the Butterworth circuit is presented for the first time where it will lead us back to the known condition of the integer-order circuit when the two fractional-orders equal one. Therefore, the conventional behavior of the integer-order circuit is a narrow subset of the fractional-order ones. The circuit is studied under same and different order cases, and verified through their numerical simulations. Stability analysis is also introduced showing the poles location in the fractional-order versus integer order cases. © 2011 IEEE.
Analog fault diagnosis by inverse problem technique
A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.
Reconstruction of target properties for different distributions using transient adjoint technique
This paper discusses the sensitivity analysis and the inverse problem solution using the Adjoint Variable Method (AVM) integrated with Transmission Line Modeling (TLM) for many examples having different distributions. The sensitivity analyses of the Gaussian function relative to its parameters is introduced where, great discrimination is observed of the sensitivity magnitude which reflects on the electromagnetic sensitivity and the solution of the inverse problem. Different obstacles with properties (? r, ?) having Gaussian, Poisson and exponential distributions are investigated.
The generalized exponential function and fractional trigonometric identities
In this work, we recall the generalized exponential function in the fractional-order domain which enables defining generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. Generalized hyperbolic function relations are also given. © 2011 IEEE.
Two-port oscillators based on three impedance structure
This paper investigates the general analysis of the three impedance common B oscillators based on two port network. The concept is applied for 12 different impedance structures to obtain a second order oscillator where the condition and the frequency of oscillation are studied for each case. Then three special cases of two-port networks whose transmission matrices contain two non-zero elements are studied which represent MOS, BJT and gyrator circuits where six cases only can be adapted to have oscillation using gyrators. The effect on non-idealities of the current conveyor used to build gyrator on the condition and the frequency of oscillation is also studied. Finally three different cases are validated using the circuit simulations which match the theoretical study. © 2014 IEEE.
State space modeling of Memristor-based Wien oscillator
State space modeling of Memristor based Wien ‘A’ oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.
Design, implementation and analysis of fully digital 1-D controllable multiscroll chaos
This paper introduces the fully digital implementation of a 1-D multiscroll chaos generator based on a staircase nonlinearity in the 3rd-order jerk system using the Euler approximation. For the first time, digital design is exploited to provide real-time controllability of (i) number of scrolls, (ii) position in 1-D space, (iii) Euler step size and (iv) system parameter. The effect of variations in these fields on the maximum Lyapunov exponent (MLE) is analyzed. The system is implemented using Verilog HDL and synthesized on an Xilinx Virtex 4 FPGA, exhibiting area utilization less than 3.5% and high performance with experimentally verified throughput up to 3.33 Gbits/s. This fully digital system enables applications in modulation schemes and chaos-based cryptosystems without analog to digital conversion. © 2011 IEEE.
The effect of numerical techniques on differential equation based chaotic generators
In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput. © 2011 IEEE.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity
High performance 2D and 3D approaches for adjoint variable method suitable for inverse problems
This paper discusses the sensitivity analysis and the inverse problem solution using the Adjoint Variable Method (AVM) integrated with Transmission Line Modeling (TLM) for many examples having different distributions