Practical design of variable fractional-order capacitors with a single tuning feature using field effect transistors and variable capacitance diodes.

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/sec (with varicaps) and tens of micro F/sec (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.