Analysis of the Moebius Loop Magnetic Field Sensor

An analysis of the Moebius loop which provides the relationship between magnetic field and output voltage is presented. This analysis accounts for all of the loop electrical phenomena involved over the broad range of frequencies encountered in measurement of fast pulses; specifically, from dc to frequencies corresponding to a loop electrical diameter of from about 6.4 degrees to 12.8 degrees. In the usual application, the loop is small, so that this corresponds to high (typically much greater than 100 MHz) frequencies. It is found that the relationship given is valid up to the stated 6.4 degrees limit for any loop coax and connecting balanced line impedance combination, but that the validity of extensions above this limit depend on the relationship between these impedances. Loop response as a function of frequency is deduced, from which useful approximations are derived, one of which is that below a certain frequency, which is defined here, loop output voltage is proportional to the derivative of the field. Finally, a detailed numerical example is given.