Characteristics of the capacitively loaded flux gate sensor

Starting with a variational principle (through Lagrange's equation), a new and simpler form of the equations for reactively loaded flux gate elements has been developed. Apart from the simplicity of the derivation, the result offers the advantage that it is expressed in terms of easily measurable parameters. By capacitively loading the flux gate there may be obtained through parametric amplification sensitivity increases of two or more orders of magnitude without additional noise-producing components. In order to make optimal use of parameteric amplification, it is necessary to be able to predict the effect of component selection on operating point and on overall performance. Some unfortunate choices of components and operating points can lead to extreme sensitivity to component values, and other combinations can lead to oscillation. The theory of Fluoquet [1], as presented in Nayfeh and Mook [2], has been adapted to predict the stability of the solutions. We present plots showing the growth with time of currents and charge in typical unstable modes. Typical maps showing regions of stability and instability also are presented. The results agree with our laboratory observations. They provide a basis on which to make preferred design choices for practical instruments.