The role of fractional calculus in circuit systems has received increased attention in recent years. In order to evaluate the effectiveness of time-domain calculation methods in the analysis of fractional-order piecewise smooth circuit systems, an experimental prototype is developed and the effects of three typical calculation methods in different test scenarios are compared and studied in this paper. It is proved that Oustaloup’s rational approximation method usually overestimates the peak-to-peak current and brings in pulse-voltage phenomenon in piecewise smooth test scenarios, while the results of two iterative recurrence-form numerical methods are in good agreement with the experimental results. The study results are dedicated to provide a reference for efficiently deploying calculation methods in fractional-order piecewise smooth circuit systems. Some quantitative analysis results are concluded in this paper.

The concepts of fractional calculus and the related techniques have been gaining momentum in circuit system fields, and an increasing body of evidence suggests that fractional-order characteristics are widely distributed in electronic components. In this paper, we consider the fractional characteristics of non-solid aluminum electrolytic capacitors and focus on the nonlinear dynamic characteristics of peak-current-mode controlled (PCMC) dc-dc boost converters with such components. In the work, we establish a piecewise smooth non-commensurate fractional-order model to describe the converter, in which the fractional-order equivalent impedance model of capacitors is adopted and the detailed control loop is considered. In order to analyze the converter, we use the fractional Adams-Bashforth-Moulton typed method (F-ABM) and stroboscopic map technique to obtain the time-domain solutions and the bifurcation diagram. The results of bifurcation diagrams indicate that, with the change of different parameters, the converter enters chaotic state through period doubling bifurcation. In order to provide empirical evidence for the nonlinear dynamic analysis, we consider both circuit-level simulation and experiments in the work, the results of which further confirm the results of theoretical analysis.

Chipless radio frequency identification (RFID) technology is expected to replace barcode technology due to its ability to read in non-line-of-sight (NLOS) situations, long reading range, and low cost. Currently, there is extensive research being conducted on frequency-coded (FC) co-polarized radar cross-section (RCS)-based tags, which are widely used. However, detecting co-polarized chipless RFID tags in cluttered environments is still a challenge, as confirmed by measuring two co-polarized tags in front of a perfect metal reflector (30.5cm×22.5cm). To address this challenge, a realistic mathematical model for a chipless RFID system has been developed that takes into account the characteristics of the reader and the tag, as well as reflections from cluttered objects. This model has been simulated and verified with measurement results by placing a single flat metal reflector behind two co-polarized one-bit designs: a dipole array tag and a square patch tag. The results showed that the interfering signal completely overlaps the ID of the co-polarized tag, severely limiting its detectability. To solve this issue, the proposed solution involves reading the tag in cross-polarization mode by etching a diagonal slot in the square patch tag. This proposed tag provides high immunity to the environment and can be detected in front of both dielectric and metallic objects.