Circuits, Systems, and Signal Processing https://doi.org/10.1007/s00034-018-0944-z Practical Design of RC Approximants of Constant Phase Elements and Their Implementation in Fractional-Order PID Regulators Using CMOS Voltage Differencing Current Conveyors Ondrej Domansky 1 · Roman Sotner 1 · Lukas Langhammer 1 · Jan Jerabek 2 · Costas Psychalinos 3 · Georgia Tsirimokou 3 Received: 5 March 2018 / Revised: 12 September 2018 / Accepted: 14 September 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper brings a practical and straightforward view on the design of circuit elements described by fractional-order dynamics known as the constant phase element (CPE) and their implementation in a novel structure of a PI α D β (or PI λ D μ in some literature) regulator based on fabricated CMOS voltage differencing current conveyors. Compar- ison of presented topology with known solutions indicates significant improvements regarding overall simplification, simpler electronic controllability of time constants, and having all passive elements in grounded form. Step-by-step design of the CPE as well as the PI α D β regulator is supported by experiments with active devices fabricated using the C07 I2T100 0.7 μm CMOS process (ON Semiconductor). Laboratory tests in frequency and time domain confirm the correct operation of the designed application and the accuracy of the derived results in comparison with the theoretical expectations. Keywords Constant phase element (CPE) · Differentiator · Fractional-order circuit · Integrator · Proportional branch · Proportional integrational and differential controller (PID) · Voltage differencing current conveyor (VDCC) 1 Introduction In recent years, fractional elements [43] have attracted increasing attention of researchers because of their interesting behavior in both the time and frequency domain. Fractional calculus has been well known in the mathematical domain for decades, but its potential in electronic circuits with lumped parameters has not been fully explored in detail. Practical implementation of these elements (such as two ter- B Ondrej Domansky domansky@phd.feec.vutbr.cz Extended author information available on the last page of the article