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Abstract There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin–Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin–Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

A novel kind of non-integer order bilinear filters, named double-order bilinear filters, is introduced in this work. They are based on the employment of two non-integer orders, offering the maximum design flexibility in comparison with their fractional-order and power-law counterparts. An attractive offered benefit is that this is achieved without increasing the circuit complexity, since the proposed structure is capable of realizing all non-integer kinds of filters. Two design examples are provided, where it is shown that lead/lag compensators utilized in control applications and low/high shelving filters employed in acoustic applications are actually bilinear filters with suitably selected pole/zero frequencies. Simulation and experimental results, using the OrCAD PSpice simulator and a Field Programmable Analog Array device, respectively, support the findings of this work.

A systematic method for realizing filters with a Gaussian impulse response is introduced in this work. For this purpose, the Laplace transform is used to obtain the transfer function which corresponds to the Gaussian impulse response. Since this transfer function has an exponential term, a rational integer-order approximating transfer function is derived by employing a curve-fitting based method applied on both gain and phase responses of the original transfer function. This concept is also applied on the derivatives of the Gaussian impulse response, leading to wavelet filter transfer functions. The findings in this work are supported by both simulation and experimental results using the Cadence IC design suite as well as a Field Programmable Analog Array (FPAA) platform.

Higher-order fractional filters with fully controllable frequency characteristics are realized in this work, after fitting the filter’s magnitude response data using a minimum-phase state-space model. Subsequently, rational integer-order transfer functions are derived and implemented using as active elements: a) Operational Transconductance Amplifiers (OTAs) and b) a Field Programmable Analog Array (FPAA) device. The realized filters enjoy electronic adjustability of their type, order, and characteristic frequencies while being easily validated on the digitally programmable FPAA platform.

In this paper, a new versatile first-order voltage-mode analog filter using a single multiple-input voltage differencing differential difference amplifier for extremely low-voltage supply and low-frequency applications is presented. Using multiple-input MOS transistor technique, the filter can realize the first-order transfer functions of non-inverting and inverting low-pass, high-pass, and all-pass filters in a single topology with high input and low output impedance. This is particularly useful for voltage-mode circuits. The filter’s pole frequency can be controlled electronically. The filter was used to implement a new quadrature oscillator to confirm its advantages. The multiple-input was applied to bulk-driven differential pairs operating in weak inversion; therefore, the proposed circuit operated from a supply voltage of 0.3 V and consumed 357.4 nW. The circuit was designed in the Cadence program using $0.13~\mu \text{m}$ UMC CMOS technology. The performance and robustness of the design was validated by intensive simulations, including Monte Carlo and Process, Voltage and Temperature corner analyses.

Non-integer order filters can be derived from a generalized structure presented in this work. More specifically, fractional-order and power-law filters of single- or double-order are special cases of non-integer order filters with three degrees of freedom and can be implemented using a Current Feedback Operational Amplifier as the active element. The transfer function is formed as a ratio of two impedances which can be synthesized using Foster or Cauer RC networks. A curve-fitting based technique is employed for approximating the magnitude and phase of each impedance. The behavior of the presented structures is evaluated through simulation results, using the OrCAD design suite and, also, through experimental results.

Complex-order controllers are a generalized version of conventional integer-order controllers and are known to offer greater flexibility, better robustness, and improved system performance. This paper discusses the design of complex-order PI/PID controllers to control the speed of an induction motor drive and an electric vehicle. The speed-tracking performance of the complex-order controllers is compared with fractional-order controllers and conventional integer-order controllers. Implementing complex-order controllers is challenging due to commercial complex-order fractance element unavailability. Hence, it is carried out by approximating the complex-order controller transfer function using an integer-order rational function with a curve-fitting approach, namely the Sanathanan Koener (SK) iterative method. This method is quite simple and can fit the required frequency range compared to the conventional Matsuda and Oustaloup approaches. The approximated controller transfer function can easily be realized by employing the AN231E04 Field Programmable Analog Array (FPAA). Simulation and experimental results highlight that the controller behaviour is in good agreement with the theoretical expectations.

This paper describes the design of analog pseudo-differential fractional frequency filter with the order of $(2+\alpha)$ , where $0 < \alpha < 1$ . The filter operates in a mixed-transadmittance mode (voltage input, current output) and provides a low-pass frequency response according to Butterworth approximation. General formulas to determine the required transfer function coefficients for desired value of fractional order $\alpha $ are also introduced. The designed filter provides the beneficial features of fully-differential solutions but with a less complex circuit topology. It is canonical, i.e. it employs a minimum number of passive elements, whereas all are grounded, and current conveyors as active elements. The proposed structure offers high input impedance, high output impedance, and high common-mode rejection ratio. By simple modification, voltage response can also be obtained. The performance of the proposed frequency filter is verified both by simulations and experimental measurements proving the validity of theory and the advantageous features of the filter.

This paper presents a new multiple-input single −output voltage-mode universal biquad filter based on multiple−input operational transconductance amplifiers (MI-OTA). This work demonstrates that the multiple-input OTA−based universal filter can provide more filtering responses and other benefits, compared to conventional OTA−based one. The filter provides electronic and orthogonal control of the natural frequency and the quality factor. Furthermore, a two-phase quadrature oscillator can be obtained by slightly modifying the proposed universal filter while the condition and frequency of oscillation can be controlled orthogonally and electronically. The performance of the proposed circuit is evaluated in Cadence environment using the TSMC $0.18~\mu \text{m}$ CMOS technology. The voltage supply is 1.2 V and the power dissipation of the MI−OTA is $24~\mu \text{W}$ . For 1% third intermodulation distortion (IMD3) the dynamic range of the band−pass filter is 78.6 dB. In addition, the proposed filter and oscillator are investigated through experiment tests using LM13700 commercially available OTA.

Low-pass and high-pass non-integer order shelving filter designs, which are suitable for acoustic applications, are presented in this work. A first design is based on a standard fractional-order bilinear transfer function, while a second one is based on the transposition of the integer-order transfer function into its power-law counterpart. Both transfer functions are approximated using the Oustaloup approximation tool, while the implementation in the case of the power-law filters is performed through the employment of the concept of driving-point impedance synthesis. An attractive benefit is the extra degree of freedom, resulting from the variable order of both fractional-order and power-law filters, which allows improved design flexibility compared to the case of integer-order filters. From the implementation point of view, only one building block is required to realize both filter types, thanks to the employment of the Voltage Conveyor.

A generalized structure for implementing fractional-order controllers is introduced in this paper. This is achieved thanks to the consideration of the controller transfer function as a ratio of integer and non-integer impedances. The non-integer order impedance is implemented using RC networks, such as the Foster and Cauer networks. The main offered benefit, with regards to the corresponding convectional implementations, is the reduced active and, also, passive component count. To demonstrate the versatility of the proposed concept, a controller suitable for implementing a cardiac pacemaker control system is designed. The evaluation of the performance of the system is performed through circuit simulation results, using a second-generation voltage conveyor as the active element.

A generalized structure that is capable of implementing power-law filters derived from 1st and 2nd-order mother filter functions is presented in this work. This is achieved thanks to the employment of Operational Transconductance Amplifiers (OTAs) as active elements, because of the electronic tuning capability of their transconductance parameter. Appropriate design examples are provided and the performance of the introduced structure is evaluated through simulation results using the Cadence Integrated Circuits (IC) design suite and Metal Oxide Semiconductor (MOS) transistors models available from the Austria Mikro Systeme (AMS) 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process.

A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the introduced concept deals with the consideration of this function as a whole, with its approximation being performed using a curve-fitting-based technique. Compared to the conventional procedure, where each fractional-order Laplace operator of the transfer function is individually approximated, the main offered benefit is the significant reduction in the order of the resulting rational function. Experimental results, obtained using a field-programmable analog array device, verify the validity of this concept.

An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved accuracy compared to the Oustaloup and Padé methods. As a design example, a lead compensator intended for usage in car suspension systems is realized. The open-loop and closed-loop behavior of the system is evaluated by post-layout simulation results obtained using the Cadence IC design suite and the Metal Oxide Semiconductor (MOS) transistor models provided by the Austria Mikro Systeme 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process. The derived results verify the efficient performance of the introduced implementation.

Fractional-order controllers have gained significant research interest in various practical applications due to the additional degrees of freedom offered in their tuning process. The main contribution of this work is the analog implementation, for the first time in the literature, of a fractional-order controller with a transfer function that is not directly constructed from terms of the fractional-order Laplacian operator. This is achieved using Padé approximation, and the resulting integer-order transfer function is implemented using operational transconductance amplifiers as active elements. Post-layout simulation results verify the validity of the introduced procedure.

The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with simulation results verifying the validity of the introduced procedure.

The fractional-order lung impedance model of the human respiratory tree is implemented in this paper, using Operational Transconductance Amplifiers. The employment of such active element offers electronic adjustment of the impedance characteristics in terms of both elements values and orders. As the MOS transistors in OTAs are biased in the weak inversion region, the power dissipation and the dc bias voltage of operation are also minimized. In addition, the partial fraction expansion tool has been utilized, in order to achieve reduction of the spread of the required time-constants and scaling factors. The performance of the proposed scheme has been evaluated, at post-layout level, using MOS transistors models provided by the 0.35 μ m Austria Mikro Systeme technology CMOS process, and the Cadence IC design suite.

An ultra-low voltage sixth-order low pass filter topology, suitable for sensing the T-wave signal in an electrocardiogram (ECG), is presented in this paper. This is realized using a cascade connection of second-order building blocks constructed from a sinh-domain two-integrator loop. The performance of the filter has been evaluated using the Cadence Analog Design Environment and the design kit provided by the Austria Mikro Systeme (AMS) 0.35-µm CMOS process. The power consumption of filters was 7.21 nW, while a total harmonic distortion (THD) level of 4% was observed for an input signal of 220 pA. The RMS value of the input referred noise was 0.43 pA, and the simulated value of the dynamic range (DR) was 51.1 dB. A comparison with already published counterparts shows that the proposed topology offers the benefits of 0.5-V supply voltage operation and significantly improved power efficiency.