Tunable Fractional Order Research Articles

An electronically tunable fractional order inductor employing VD-EXCCII

An electronically tunable Fractional Order Inductor (FOI) for both grounded as well as floating circuits is designed using a Voltage Differencing Extra-X Current Conveyor (VD-EXCCII), grounded MOS resistor, and grounded Fractional Order Capacitor (FOC) with four MOS switches. The grounded positive and negative fractional order functionality can be easily executed by using the gate voltage (VG) of an MOS transistor. Ideal as well as the non-ideal port characteristics of VD-EXCCII are also studied in the presence of the parasites available in the active block VD-EXCCII. The verification of the proposed FOI is first simulated through PSPICE in which the VD-EXCCII uses 0.18 μm TSMC CMOS parameter. In addition to traditional impedance verification of the proposed FOI, an application of the FOI is translated for the design of sixth order High-Pass Filter (HPF), sixth order Low-Pass Filter (LPF), and a voltage mode Multiple Input Single Output Universal Filter (MISO-UF) design. Moreover, the performance of the proposed negative FOI circuit is also demonstrated through a Fractional Inductance Cancellation Circuit (FICC).

Electronically Tunable Fractional Order All Pass Filter

In this paper, an electronically tunable fractional order all pass filter (FOAPF) based on operational transconductance amplifier (OTA) is presented. It uses two OTAs and single fractional order capacitor (FC) of non-integer order α to provide FOAPF of α order. Two different values of α, in particular 0.5 and 0.9, for FC are taken for investigation. The functionality of the proposal is verified through SPICE simulations using TSMC 0.18 μm Complementary Metal Oxide Semiconductor (CMOS) process parameters. Simulated and theoretical frequency and time domain responses are found to be in close agreement.

Electronically Tunable Fractional Order Filter

In this paper, an electronically tunable resistorless fractional order filter (FOF) based on operational transconductance amplifier (OTA) is presented. It uses two fractional capacitors (FC) of same order and provides fractional order low-pass filter and fractional order band-pass filter responses simultaneously. Mathematical formulations are outlined for various critical frequencies and transfer function sensitivities for presented FOF. The FCs of orders 0.5 and 0.9 are considered for illustrating the proposal. The FCs are realized using the fourth-order continued fraction expansion-based RC ladder and are characterized using SPICE simulations. Functional verification of presented FOF with FC of orders 0.5 and 0.9 is exhibited through SPICE simulations. The OTA is implemented using $$0.5\,\upmu \hbox {m}$$ CMOS technology model parameters. Electronic tunability of half power and right-phase frequencies of presented FOF is achieved through bias current variation of OTA. The transfer functions’ sensitivity with respect to various circuit parameters is also examined through simulations, and it is found that the values remain well within unity for most of the circuit parameters. Furthermore, the presented FOF is attractive from integration viewpoint as it achieves tunability via bias current variation in contrast to tuning through resistor variation in existing FOFs.

Silicon-Based Integrated Tunable Fractional Order Photonic Temporal Differentiators

Two integrated fractional-order photonic temporal differentiators based on two Mach–Zehnder interferometer (MZI) structures implemented on a silicon-on-insulator (SOI) platform are designed, fabricated, and experimentally evaluated. The first photonic temporal differentiator employs a multimode interference (MMI) coupler as one of the two 3-dB couplers of the MZI. By changing the polarization state of the input optical signal, the coupling coefficient of the MMI is changed, which leads to the change of the phase shift in the destructive interference wavelength, and a photonic temporal differentiator with a tunable fractional order is implemented. The second photonic temporal differentiator is designed to have two cascaded MZIs, a balanced MZI, and an unbalanced MZI. A phase modulator (PM) is incorporated in one of the two arms of each of the MZIs. The balanced MZI with a PM forms an active tunable coupler, which is used to actively tune the fractional order of the temporal differentiator. The PM in the unbalanced MZI is used to tune the operating wavelength. The two photonic temporal differentiators are designed and fabricated in a CMOS compatible SOI platform, and their performance is evaluated experimentally. The experimental results show that both temporal differentiators can have a tunable fractional order from 0 to 1. In addition, the use of the active temporal differentiator to perform high-speed coding with a data rate of 16 Gb/s is experimentally evaluated.

Practical Realization of Tunable Fractional Order Parallel Resonator and Fractional Order Filters

This paper introduces a tunable fractional order parallel resonator (FOPR) whose resonating frequency can be tuned by the coefficient of a fractional order (FO) element (fractor). At the same time, its $Q$ - factor can be set very high (theoretically infinite) by varying its resistor. Using this FOPR circuit, two simple FO filters (FO bandpass and FO notch) are also developed. The paper includes detail sensitivity analyses of these circuits for various circuit parameters and describes how different design parameters of proposed FOPR and FO filters are chosen accordingly. Proposed FOPR and FO filters are simulated in MATLAB and realized in hardware. The hardware circuits are tested practically, and detail experimental results are provided. It is found that the experimental data are in good agreement with the simulation data. In hardware, the realized FOPR has achieved a $Q$ -factor up to 360, and the realized FO notch filter has ${Q}>10$ when its attenuation is more than 30 dB. Different practical aspects of filter tuning are also described in detail.

Tunable fractional-order differentiator using an electrically tuned silicon-on-isolator Mach-Zehnder interferometer.

We propose and experimentally demonstrate a tunable fractional order photonic differentiator using an on-chip electrically tuned Mach-Zehnder interferometer (MZI) structure. The phase shift at the resonant frequency of the MZI varies when applying different voltages, which can implement the fractional differentiation. Due to the large 3-dB bandwidth of the MZI, the differentiator is expected to have an operation bandwidth of several hundred GHz. The proposed fractional order differentiator is demonstrated experimentally. A Gaussian-like pulse with a bandwidth of about 200 GHz is temporally differentiated with a tunable order range from 0.83 to 1.03.

Continuously Tunable Fractional Hilbert Transformer by Using a Single $\pi$-Phase Shifted FBG

A continuously tunable fractional Hilbert transformer (FHT) using a π-phase shifted fiber Bragg grating ( π-PSFBG) is proposed and experimentally demonstrated. An FHT has an output that is a weighted sum of the original input signal and its classical Hilbert-transformed signal. The classical Hilbert transform is implemented using a π-PSFBG. The output from the classical HT and the original input signal are controlled to be orthogonally polarized. The combination of the two signals at a polarizer would generate a weighted sum with the weighting coefficients determined by the angle between the principle axis of the polarizer and the polarization direction of the original input signal. A π-PSFBG is fabricated. The performance of the π-PSFBG as a classical HT is evaluated. The incorporation of the π-PSFBG into the proposed system to implement an FHT is studied. A continuously tunable FHT with a tunable fractional order of ρ = 0.7, 0.86, 0.92, 1, 1.06, 1.17, and 1.24 to perform Hilbert transformation of a Gaussian pulse with a temporal width of 80 ps is experimentally demonstrated.

Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler

An optically tunable fractional order temporal differentiator implemented using a silicon-on-isolator microring resonator with a multimode interference (MMI) coupler is proposed and experimentally demonstrated. Through changing the input polarization state, the self coupling coefficient and the loss factor of the designed ring resonator with the MM! coupler are changed. Correspondingly, the coupling regime is changed. Through changing the coupling regime from over-coupled to under-coupled regime, the phase shift in the resonance wavelength is changed from π. This tunable phase shift is used to implement a tunable fractional order photonic differentiator with an order tunable from <;1 to 1. The proposed fractional order differentiator is demonstrated experimentally. A Gaussian pulse with a bandwidth of 45 GHz is temporally differentiated with a tunable order of 0.37, 0.67, 1, 1.2, and 1.3.

Tunable Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating

We propose and demonstrate an optically tunable photonic fractional temporal differentiator using a tilted fiber Bragg grating written in an erbium/ytterbium (Er-Yb) co-doped fiber. Thanks to the high absorption of the Er-Yb co-doped fiber, when it is pumped the refractive index is changed, and thus the phase of a cladding mode resonant wavelength is changed continuously by continuous tuning of the pumping power. By locating the wavelength of the input light wave at the location of a cladding mode resonant wavelength, a temporal differentiator with a tunable fractional order is achieved. The proposed technique is experimentally evaluated. A temporal differentiator with a tunable fractional order is demonstrated. The use of the fractional differentiator to implement temporal differentiation of a Gaussian pulse with a bandwidth of 28 and 75 GHz is also demonstrated.

Photonic-Assisted Tunable Microwave Pulse Fractional Hilbert Transformer Based on a Temporal Pulse Shaping System

A photonic-assisted fractional Hilbert transformer with tunable fractional order implemented based on temporal pulse shaping (TPS) is proposed and experimentally demonstrated. The proposed fractional Hilbert transformer consists of a phase modulator and two dispersive elements with complementary dispersion. The fractional Hilbert transform (FHT) is realized if a step function is applied to the phase modulator to introduce a phase jump. The proposed technique is investigated numerically and experimentally. The results show that a real-time FHT is achieved with a tunable fractional order by tuning the step function applied to the phase modulator.