The minimax approach for a class of variable order fractional differential equation
This paper introduces an approximate solution for Liouville-Caputo variable order fractional differential equations with order 0
Circuit Theory and Applications
On the modeling of dispersive transient photocurrent response of organic solar cells
The current methods used for estimating the electrical parameters of organic solar cells (OSC) from time-domain measurements are based on integer-order impedance models. Meanwhile, in the frequency-domain, the adopted circuit models usually contain a constant phase element which is known to capture effectively the fractional-order dispersive behavior of these devices. Therefore, inconsistency arises between the two analyses. In this work, we derive the time-domain relaxation response of an OSC, found to follow a Mittag-Leffler function, using the same fractional-order impedance model. The
Circuit Theory and Applications
Log-domain implementation of fractional-order element emulators
An Ultra-Low Power Wide-Band Single-Transistor Second-Order Allpass Filter in 65nm CMOS
In this paper, we propose a MOS design of a second-order voltage-mode allpass filter to be used as a time delay cell. The proposed filter is based on a single transistor, three resistors and two energy storage elements and was designed in a 65nm CMOS technology. Post-layout simulations demonstrate a group delay of approximately 13ps across a 30GHz bandwidth, while only consuming 809.7μW from a 1-V supply. As a proof of concept, the proposed filter was constructed and verified experimentally using discrete MOS transistors. The experimental results show a group delay of approximately 370ns
Circuit Theory and Applications
Single-Transistor Second-Order Allpass Filters
This paper presents two CMOS designs of a second-order voltage-mode allpass filters (APFs) for high-frequency applications. Each of the proposed filters is based only on a single transistor and four surrounding impedances. The first proposed allpass filter is an RL filter while the second proposed one is an RLC filter. A detailed analysis along with the parasitic effects is provided for each of the proposed filters. As a proof of concept, one design was constructed and verified experimentally using discrete MOS transistors at a 2.3MHz pole frequency. The experimental results showed a group
Here, the authors show that an asymmetric cross-coupled oscillator can be used to achieve independent-phase tunable outputs. In particular, a third-order cross-coupled oscillator, with non-balanced loads, is studied and expressions for its start-up condition, oscillation frequency, phase-shift between its two outputs as well as their amplitude ratio are derived. From these expressions, it is found that independent tuning of these design specifications is possible and a voltage-controlled phasetunable oscillator can be achieved. As a consequence of the non-balanced loads, the tail biasing
Circuit Theory and Applications
On the mechanism of creating pinched hysteresis loops using a commercial memristor device
In this short communication we analyze the impact of signal harmonics on the formation of the pinched hysteresis loop using a commercial memristor device. We show that by using only the fundamental frequency and the second harmonic components, extracted from the measured electrical current signal, a distortion-less pinched hysteresis loop is re-created. This loop is then used to simulate memristor-based AND/OR gates without any loss in digital functionality. This verifies that the generation of a pinched hysteresis loop requires a nonlinear frequency doubling mechanism to create a second
Circuit Theory and Applications
8-GHz low-power voltage-mode second-order allpass filter in 65-nm CMOS
Quantification of memory in fractional-order capacitors
In this study we quantify and interpret the inherent memory in fractional-order capacitors when subjected to constant current charging/discharging waveforms. This is done via a finite difference approximation of the fractional order rate equation I(t) = Cαdαv(t)/dtα (0 le; α ≤ 1) relating current to voltage in these devices. It is found that as the fractional exponent α decreases, the weight of the voltage memory trace that results from the contribution of past voltage activity increases, and thus the measured response of the device at any time is increasingly correlated to its past. Ideal