Treatment of extremely low frequency magnetic and electric field sensors via the rules of electromagnetic duality

This work deals with extremely low frequency (ELF) electric and magnetic sensors. The discussion emphasizes the similarity existing between the two families and attempts to exploit this similarity in studying the performance of such devices. The new approach is not based merely on similarity. We show that the two families of devices are in fact mutually related by the strict rules of electromagnetic duality. It is known that a small loop antenna serves as a magnetic dual for the short electric dipole. This duality is usually demonstrated by the far fields behaviors and the radiation resistances. By introducing an appropriate ferromagnetic core into the loop, the detailed duality relationship can be extended to the immediate vicinity of the sensors as well. The latter means that sensors of both families process the near vicinity fields in a similar way in converting them to the measured signals. The existence of duality is assessed by showing that for geometrically similar structures, the reactances of the two entities are correctly related. It is also shown that the electromagnetic duality manifested by the fields conforms also with the rules of duality in circuit theory. The latter is demonstrated by dealing in both cases with circuit models of the sensors, which are derived by considering similar circuit models that are common in antenna theory. The presently investigated sensors possess practical implications. It is well established that short electric dipoles are employed as sensors in the field of electromagnetic interference (EMI) and also as ELF electric field sensors aboard spacecrafts. Cored search coils are employed as ELF and even as ultra low frequency (ULF) magnetometers in geophysical and space research. They were even considered as possible antennas for ELF communications. The paper is concluded by showing that the present duality considerations of ac sensors can be even extended to deal with dc field sensors magnetic and electric.