In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of $(1+\alpha )$ order lowpass magnitude responses are given as examples with fractional steps from $\alpha =0.1$ to $\alpha =0.9$ and compared to the second-order elliptic response. Further, MATLAB simulations of the $(1+\alpha )=1.25$ and $1.75$ using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for $(1+\alpha )=1.2$ and $1.8$ order filters.

This paper shows the topology design of a simple second-order oscillator based on two three-port current conveyors, two resistors, and two grounded capacitors, as well as its modification to a voltage-controlled oscillator (VCO). In comparison with many previous works, the following useful conceptual novelties and improvements were made in this study. Both resistors presented in the topology can be employed to tune of the oscillation frequency by the simultaneous driving of two optocouplers with resistive output stage. The current gain of the current conveyor ensures the control of the oscillation condition. The proposed solution offers advantages (in comparison with many standard so-called single-resistance-controllable types) of improved dependence of the frequency of oscillation (FO) on a driving force (extended tuning of the FO), constant ratio of amplitudes of generated waveforms when the FO is tuned, low complexity (taking into account auxiliary circuitry for optocouplers), and comfortable tuning of the FO by a single control voltage. The oscillator produces waveforms with tunable frequency having a constant 45-degree phase shift between them. The relative sensitivities of the proposed solution achieve typical values for these second-order systems (−0.5). Experimental verification confirmed the expected behavior in the operational band between 1 and 10 MHz tuned by a DC voltage from 1.7 to 5 V. This indicates a significant reduction of the driving force ratio (3:1 in our case) in comparison with standard tuning approaches required for a ratio of 10:1 for FO adjustment. Output amplitudes reached 100 and 150 mV in the observed tunability range with distortion ranging between 0.7 and 3.3%.

The paper presents proposal of a fully-differential (1 + α)-order low-pass filter. The order of the filter and its cut-off frequency can be controlled electronically. The filter is proposed using operational transconductance amplifiers (OTAs), adjustable current amplifiers (ACAs) and fully-differential current follower (FD-CF). The circuit structure is based on well-known Inverse Follow-the-Leader Feedback (IFLF) topology. Design correctness of the proposed filter is supported by PSpice simulations with transistor-level simulation models. The ability of the electronic control of the order has been tested for five individual values of parameter α. Furthermore, the ability of the electronic control of the cut-off frequency of the filter has been also tested for five different values. Additionally, the simulation results of the proposed fully-differential (F-D) filter are compared with the results of the single-ended (S-E) equivalent of the presented filter.DOI: http://dx.doi.org/10.5755/j01.eie.23.3.18332

This paper presents possible solution of fractional-order high-pass filter (FHPF) with electronically adjustable order between 1 and 2 and also with electronically adjustable pole frequency. It is based on well-known Follow-the-Leader Feedback (FLF) topology adjusted for utilization with operational transconductance amplifiers (OTAs) and adjustable current amplifiers (ACAs). This 3rd-order topology is used in order to approximate FHPF response in particular frequency band of interest. Design is supported by Pspice simulations for three particular values of the filter's order (1.25, 1.5, 1.75) and for several values of pole frequency. Moreover, simulation results with two different approximations are compared.