Circuit analogue of relativistic aberration of light using low-cost, low-complexity operational amplifier-based all-pass filters

We propose, simulate, and experimentally demonstrate a circuit analogue of a special relativity phenomenon known as relativistic aberration of light (RAL) by using a surprisingly simple, low-cost, and easily accessible electronic circuit-based all-pass filter. This work is useful for two audiences: (i) physicists who are interested in research on circuit analogues; and (ii) physics educators who are interested in using the research results to raise interest among students by incorporating analogue-based learning into undergraduate physics lecture and laboratory courses. For the first type of audience, we present a rigorous theoretical framework describing this RAL-on-an-electronic-chip analogy. We show by (i) analytical modelling, (ii) commercial circuit software simulation, and (iii) experiment that the electrical phase shift phi of the output signal is analogous to the RAL angle, psi. This parameter opens up a path among researchers to model the effects of other relativistic phenomena with electronic circuits. For the second type of audience, we discuss the potential role of RAL-on-an-electronic-chip in physics education (both in lectures and laboratory) that combines students' learnings of both physics and electronic circuits, at the same time. We also explore briefly its relevance to engineering education.