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The dual-slope integral analog-to-digital converter is widely used in low-speed, high-precision measurement owing to its high precision and strong resistance on crosstalk interference. To meet the requirements of higher accuracy and faster measurement, the integral sensitivity and conversion speed of the dual-slope integral analog-to-digital converter must be improved. Therefore, based on fractional-order calculus, we propose a fractional-order dual-slope integral analog-to-digital converter. First, constant-current charging curves were provided to explain the source of the idea of the fractional-order dual-slope integral analog-to-digital converter. Then, the working principle of the fractional-order dual-slope integral analog-to-digital converter is described in detail. The calculation formula of analog-to-digital conversion is derived and analyzed. Moreover, the relationship of the voltage-measurement error with the operation-order error of the fractor and the reference voltage error is theoretically derived. Furthermore, we theoretically analyze the resistance of the proposed analog-to-digital converter to crosstalk interference, as well as the requirements for the first fractional integral time when crosstalk interference is suppressed. Specifically, we prove that the proposed analog-to-digital converter has a higher sensitivity and conversion speed than the classical converter, and we provide a quantitative calculation formula. [ABSTRACT FROM AUTHOR]

Since we cannot solve the equation, we know nothing about the properties of the fracmemristor circuit. In this paper, HP memristor is used in fracmemristor circuit for the first time. After a series of mathematical processing, the HP fracmemristor can be equivalent to two parts which are represented as F and VM, respectively. The F part is the fractance. The VM part is related to the current, and it can best reflect the fracmemristor property of the circuit. Therefore, we hope that we can understand the fracmemristor circuit by the simulation research of the HP fracmemristor circuit. Firstly, the amplitude frequency characteristic and phase frequency characteristic of HP fracmemristor are obtained by using Matlab. And compared with the fractance, they have different characteristics. After that, the 1/2 order fracmemristor property is studied. By approximating processing the 1/2 Laplasse operator and then using Laplasse transform and inverse Laplasse transform, we can get the total resistance change with time, the changes of total resistance with the current figure, the voltage of part F changes with the current, the voltage of part VM with the current changes, as well as the total voltage with current changes. From these diagrams, the U-I diagram of the VM section intersects at two points. The currents at these two points are symmetrical about the origin, and the voltages at the two points are slightly different. Moreover, the magnitude of the current and voltage is stable at the point of intersection, and does not change with the magnitude of the input current. For HP fracmemristor circuits, its properties depend on the size of the current. When the current is very small, the HP fracmemristor exhibits the characteristics of fractance, and the influence of the VM part can be ignored. With the increase of current, the effect of fractance F is reduced, and the effect of VM is increased. When the current increases to a certain size, the output of the circuit is the same as that of the VM part, and the effect of the fractance F part can be ignored. [ABSTRACT FROM AUTHOR]

This paper presents a state-of-the-art application of fractional hopfield neural networks (FHNNs) to defend against chip cloning attacks, and provides insight into the reason that the proposed method is superior to physically unclonable functions (PUFs). In the past decade, PUFs have been evolving as one of the best types of hardware security. However, the development of the PUFs has been somewhat limited by its implementation cost, its temperature variation effect, its electromagnetic interference effect, the amount of entropy in it, etc. Therefore, it is imperative to discover, through promising mathematical methods and physical modules, some novel mechanisms to overcome the aforementioned weaknesses of the PUFs. Motivated by this need, in this paper, we propose applying the FHNNs to defend against chip cloning attacks. At first, we implement the arbitrary-order fractor of a FHNN. Secondly, we describe the implementation cost of the FHNNs. Thirdly, we propose the achievement of the constant-order performance of a FHNN when ambient temperature varies. Fourthly, we analyze the electrical performance stability of the FHNNs under electromagnetic disturbance conditions. Fifthly, we study the amount of entropy of the FHNNs. Lastly, we perform experiments to analyze the pass-band width of the fractor of an arbitrary-order FHNN and the defense against chip cloning attacks capability of the FHNNs. In particular, the capabilities of defense against chip cloning attacks, anti-electromagnetic interference, and anti-temperature variation of a FHNN are illustrated experimentally in detail. Some significant advantages of the FHNNs are that their implementation cost is considerably lower than that of the PUFs, their electrical performance is much more stable than that of the PUFs under different temperature conditions, their electrical performance stability of the FHNNs under electromagnetic disturbance conditions is much more robust than that of the PUFs, and their amount of entropy is significantly higher than that of the PUFs with the same rank circuit scale. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the order-frequency characteristics of a promising circuit element: fractor. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator or integrator in an analog circuit. In this paper, we studied some electrical properties of a fractor. In particular, the order-frequency characteristics of a fractor are introduced. First, the order-sensitivity characteristics of a fractor are proposed. Second, the order-frequency characteristics of a fractor are studied. Third, the time constant of a fractor is analyzed. Last, through mathematical analysis and simulation results, we discussed in detail some issues of the electrical properties of a fractor, especially its time constant. [ABSTRACT FROM AUTHOR]

In order to solve the most important problem of the fractional calculus (FC) application, the realization of analog circuit of fractance, continued fraction theory is applied to design the -1/2n order analog fractance approximation circuit. The author presents a network function of ideal fractance and decomposes it in continued fractions (CFs) form to obtain the corresponding analog fractance approximation circuit. The new circuit consists of ordinary passive RC component through network synthesis method. Simulations are performed for the verification of the new circuit. Experimental evidence has proved that the performance of novel -1/2n order analog fractance approximation circuit is good in both amplitude-frequency response and phase-frequency response. [ABSTRACT FROM AUTHOR]