This paper presents two discrete circuit solutions for realizing passive, electronically adjustable constant-phase elements, specifically half-order capacitors with a -45° phase shift. Fractional-order capacitors with electronically adjustable pseudocapacitance are especially useful for designing tunable filters and oscillators. The ability to adjust pseudocapacitance electronically and continuously is a major improvement over traditional passive solutions. Their pseudocapacitance can be controlled by a DC voltage, allowing key parameters like the cut-off or oscillation frequency to be tuned. Two presented design approaches differ in accuracy, tuning range, and signal-handling capability. Both solutions maintain a constant phase over one frequency decade, with a phase ripple within ± 2°. The tuning range spans from hundreds of Hz to several MHz. Presented solutions allow pseudocapacitance tuning in range of hundreds of nano F/sec0.5 (with varicaps) and tens of micro F/sec0.5 (with MOSFETs). The MOS-based circuit offers a tuning ratio of 7 but shows a 19% deviation between simulation and measurement. It also suffers from notable nonlinearity, with undistorted operation limited to signal levels up to 20 mV peak-to-peak. The varicap-based solution achieves a tuning ratio of 5, with high accuracy (up to 6% error), and handles input signals in the hundreds of mV with acceptable distortion. PSpice simulations and laboratory measurements confirm the performance of both designs.

Department of Electrical and Computer Engineering The University of Alabama Box 870286 Tuscaloosa 35487 USA

Department of Electrical Engineering Faculty of Military Technology University of Defence Sumavska 4 Brno 602 00 Czech Republic

Faculty of Electrical Engineering and Communication Brno University of Technology Technicka 3082 12 Brno 616 00 Czech Republic

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