Steady-state characteristics of the capacitively loaded flux gate sensor

An analytical derivation of the transient response of the capacitively loaded flux gate sensor has been presented in a previous paper [1]. Here the analysis is extended to include steady-state periodic solutions. The characteristic differential equation for the flux gate presented in [1] is used as a starting point. An equivalent circuit corresponding exactly to this equation is presented, avoiding the pitfalls associated with many saturable-core descriptions. This equivalence provides a means of obtaining an intuitive understanding of the flux gate which is quite different from conventional representations. The flux gate can be represented exactly as a current transducer in the form of a time-varying inductor L(t) loading a current source proportional to an ambient magnetic field H. We have extended the theory of Floquet, as presented by Nayfeh and Mook [2], to provide complete steady-state solutions to complement the transient solutions presented in [1] and can thus predict flux gate absolute sensitivity, parametric gain, and bandwidth. Further our description is based upon easily measured or observed properties, namely, sense-winding inductances with or without a permeable core, and real or equivalent circulating currents. Typical maps showing absolute sensitivity, parametric gain and dominating eigenvalues are also presented. The results agree well with our laboratory observations. They provide a basis for the design of practical instruments.