Memristor‐based voltage‐controlled relaxation oscillators

Fouda, Mohammed E.; Radwan, Ahmed G.

doi:10.1002/cta.1907

Cited by 52 publications

(30 citation statements)

References 25 publications

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“…Another circuit could be obtained if the memristor M is exchanged with the resistor R a , but the control circuit F(V i ) in this case will be changed as shown in Fig. 4.2 [5]. …”

Section: Voltage Controlled Oscillatorsmentioning

confidence: 98%

“…In general, the oscillator circuit consists of a single memristor M, resistor R a , and control circuit F(V i ) to control the resistance swing of the memristor to keep it within the required resistance range [5]. Another circuit could be obtained if the memristor M is exchanged with the resistor R a , but the control circuit F(V i ) in this case will be changed as shown in Fig.…”

Section: Voltage Controlled Oscillatorsmentioning

confidence: 99%

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Memristor-Based Relaxation Oscillator Circuits

Radwan

Fouda

2015

Studies in Systems, Decision and Control

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Oscillators are the key component in electronic systems since there is always a need for a repetitive signal with a given frequency and waveform for timing, modulation, and test and measurement applications [1]. Oscillators circuits are designed to produce a repetitive, oscillating signal, often a sine wave or a square wave. The two main types of oscillators are sinusoidal and relaxation oscillators. Sinusoidal oscillators are based on positive feedback, where a frequency selective network is used to determine the frequency of oscillation of the sinusoidal output. Relaxation oscillators are used to produce square waves, pulses, and triangular waves. Square waves are one of the most important signals in digital applications. Relaxation oscillator is basically an astable multivibrator which is an electronic circuit that operates between two quasi-stable states (on and off states) at a certain frequency and whose period depends on the charging and discharging of a storing element which is conventionally a capacitor. This chapter discusses some relaxation oscillators which generate square waveform without using any reactive element.

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“…Another circuit could be obtained if the memristor M is exchanged with the resistor R a , but the control circuit F(V i ) in this case will be changed as shown in Fig. 4.2 [5]. …”

Section: Voltage Controlled Oscillatorsmentioning

confidence: 98%

Section: Voltage Controlled Oscillatorsmentioning

confidence: 99%

Memristor-Based Relaxation Oscillator Circuits

Radwan

Fouda

2015

Studies in Systems, Decision and Control

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“…One of the recent applications of the memristor is to design relaxation oscillators by replacing the capacitor with memristors as discussed in [44,45] which can also be used as a voltage-controlled oscillator [46,47]. The memristor is used to emulate the effect of charging and discharging of capacitor voltage where memristance increases or decreases depending on the polarity of the applied voltage.…”

Section: Testing Applicationsmentioning

confidence: 99%

“…Moreover, a simple model of double-loop hysteresis of a memristive element is discussed in [1] which is applied for memristance and transconductance which is given by 46) where G o is the initial transconductance and k m ( −1 C −1 ) is the transconductance mobility constant.…”

Section: Mathematical Modelmentioning

confidence: 99%

Memristor Mathematical Models and Emulators

Radwan

Fouda

2015

Studies in Systems, Decision and Control

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Recently, different mathematical models describing the generic memristors have been introduced [1][2][3]. But, the first model of the memristor was introduced by HP in [4], where the memristor current voltage relationship was described bywhere i(t) represents the current through the memristor, v(t) is the voltage across the memristor, R on and R off are the minimum and maximum achievable resistances of the memristor, respectively. The memristor resistance depends on state variable x d (t) which is the ratio between the doped region length and the full length D of the memristor and is given byIntegrating (3.2) and substituting in (3.1); assuming zero initial condition for the current, the memristance R m can then be given by (3.3)where η ∈ −1, 1 represents the memristor polarity, k =/C; μ v is the ion mobility, and R in is the initial resistance of the memristor.

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“…É possível notar o impacto do cálculo fracionário também na descrição de diversos problemas na área da Engenharia Elétrica, indo desde os fundamentos da teoria de circuitos [40][41][42], passando pela modelagem biomé-dica [43,44], estabilidade e controle de sistemas [45][46][47][48], modelagem de memristores [49] e indutores de radiofrequência [50] e teoria eletromagnética [51,52].…”

Section: Introductionunclassified

Uma introdução ao cálculo fracionário e suas aplicações em circuitos elétricos

Andrade

Lima

Dartora

2018

Rev. Bras. Ensino Fís.

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A extensão natural do cálculo diferencial, proposta inicialmente em uma troca de correspondências entre l'Hôpital e Leibniz, levou ao conceito de derivada de ordem fracionária. A aplicação da derivada fracionária permite uma melhor descrição da dinâmica de muitos sistemas reais, indo desde biossistemas até mercados financeiros, que apresentam efeitos de memória, dissipação e dimensionalidade fractal. No presente trabalho, os objetivos principais são a apresentação conceitual da derivada fracionária, algumas de suas definições tanto na forma de diferenças finitas de Grünwald-Letnikov quanto nas formas integrais de Riemann-Liouville, para posteriormente aplicá-las a problemas usuais da teoria de circuitos elétricos em circuitos do tipo RC e RL de ordem fracionária. Palavras-chave: derivada fracionária; derivada de Grünwald-Letnikov; integrais de Riemann-Liouville; circuitos elétricos A natural extension of differential calculus, initially proposed by l'Hôpital in a letter to Leibniz, leaded to the concept of fractional order derivatives. The application of fractional derivatives allows one to correctly describe the dynamics of many real systems, from biosystems to financial markets, where memory effects, dissipation and fractal dimensionality are present. This paper aims to present an overview of fractional derivatives and its representations, both in the form of Grünwald-Letnikov finite differences as well as in the form of Riemann-Liouville integrals, and to apply it in describing RC and RL electrical circuits of fractional order. Keywords: fractional derivatives; Grünwald-Letnikov derivatives; Riemann-Liouville integrals; electric circuits. IntroduçãoA maioria dos sistemas dinâmicos reais apresentam complexidade suficiente para produzir efeitos de memória, dissipação e dimensionalidade efetiva de ordem fracioná-ria. Alguns desses problemas levam a funções de natureza fractal, apresentando a propriedade de auto-similaridade, ou seja, os padrões que aparecem em uma determinada escala se repetem em escalas maiores e menores. Essas funções não são diferenciáveis no sentido convencional e muitas das leis que regem os processos difusivos e/ou transições de fase são melhor descritas por leis de potên-cias fracionárias. Todos esses aspectos podem ser melhor compreendidos através do uso do chamado cálculo fracionário e da geometria fractal [1][2][3][4][5].As origens do cálculo fracionário remontam ao ano de 1695, quando o matemático Guillaume François de l'Hôpital enviou uma carta para o matemático Gottfried Leibniz, conhecido por ser o pai da notação moderna do cálculo diferencial, onde discutia o possível significado de uma derivada de ordem n = 1/2. A resposta de Leibniz a l'Hôpital, levou às primeiras definições de derivadas e * Endereço de correspondência: cadartora@eletrica.ufpr.br.integrais de ordens não-inteira [2,4]. Desde então, grandes matemáticos, como Leonhard Euler e Joseph Louis Lagrange [6], dedicaram esforços ao problema do cálculo fracionário. Embora Pierre Simon Laplace tenha definido a derivada fraci...

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Memristor‐based voltage‐controlled relaxation oscillators

Cited by 52 publications

References 25 publications

Memristor-Based Relaxation Oscillator Circuits

Memristor-Based Relaxation Oscillator Circuits

Memristor Mathematical Models and Emulators

Uma introdução ao cálculo fracionário e suas aplicações em circuitos elétricos

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