Microwave and radio frequency fractional differentiation with a 49GHz Kerr soliton crystal microcomb source

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost.

A Practical Fractional-Order Sinusoidal Oscillator Design and Implementation

In this study, a new sinusoidal fractional oscillator circuit in which the fractional low-pass filter and fractional differentiator form a closed loop has been introduced. The single series [Formula: see text] pair and Valsa method have been used to imitate the fractional-order capacitor. Two different sinusoidal signals with different phases are available at output ports. An integer version of the proposed oscillator is not possible, only the fractional version is valid, that is a noticeable feature. The introduced circuit has been simulated by employing SPICE software. The proposed fractional oscillator is also verified by implementing circuit with AD817ANs and passive components, experimentally.

RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost.

RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost.

Robust Motion Control Using Combined Centralized Non-Integer Pre-Filter of Type FBLFD and Fractional Order Pdμ Controller

Designing and automation of a robust controller and pre-filter for multi-variable processes are a very challenging task. In this study, an automated and simple conception of multivariable QFT (QFT: Quantitative Feedback Theory) is proposed using fractional order controllers design. Contrary to the traditional manual QFT design, our methodology consists of obtaining all required performances in QFT without going to the QFT loop shaping process.A non-integer order proportional derivative controller PDµ is conceived for a robust control of MIMO (Multi Input Multi Out- put) systems through multi-objective optimization based genetic algorithm . In the designed approach an implicit fractional order pre-filter FBLFD (FBLFD : Frequency Band Limited Fractional Differentiator) is adopted and its parameters are optimized. A diagonal version of this fractional order pre-filter and a non diagonal one are proposed. The problem of loop interactions is eliminated by the non diagonal designed pre-filter. Consequently, the procedure of fractional controller and pre-filter parameters optimization is illustrated. A comparative study and the efficiency of the developed methodologies are considered through SCARA robot.

Order-Frequency Characteristics of a Promising Circuit Element: Fractor

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.