A figure of merit for Transit-Time-Limited time-derivative electromagnetic field sensors

This note derives a sensitivity-bandwidth figure of merit for comparing the performance of sensors designed to measure the time derivative of D or B. This figure of merit is a dimensionless number combining sensitivity and upper frequency response (bandwidth) in a form equivalent area times the square of bandwidth. The larger the figure of merit A, the more efficient is the design. This figure of merit is appropriate where sensor size is not a factor, but sensitivity and bandwidth are of primary concern.