Theory of operation of direct string magnetic gradiometer with proportional and integral feedback

A quantitative theory of operation of a novel device, namely Direct String Magnetic Gradiometer (DSMG), is presented. The paper provides a detailed analysis of DSMG basic functions and measured quantities, represented in terms of physical parameters that are known either a priori or can be experimentally determined. It leaves a reasonable degree of freedom to further investigate some of the finer detail of this new instrument based on experimental results coming both from the laboratory environment and from field trials. The analysis also allows us to quantitatively evaluate the error budget for an optimised DSMG.