Research On Surface Differential Equation For Electromagnetic Scattering

This thesis mainly studies the theory of Maxwell circuit(MC),which is a new theory to solve the problem of electromagnetic scattering.Different from the traditional numerical method,MC theory combines the both theories of "field" and " circuit ".The research shows that the theory has the advantages of high accuracy,low resource consumption and wide-band characteristics.At present,MC theory mainly studies the electromagnetic scattering of linear conductors,but there are few researches on the electromagnetic scattering of objects of other shapes.In this thesis,MC theory is applied for the first time to deal with the electromagnetic scattering problem of conductor flat plate.This thesis first introduces the existence theorem,uniqueness theorem and the basic principle of MC theory,the derivation of MC equation and the Metron method for solving MC equation.The existence and uniqueness theorem describes the transformation relationship between differential equation and integral equation,which is the fundmentals of MC theory.MC theory contains two forms of "field" and " circuit ",so it can be used to analyze both circuit problems and electromagnetic problems.In this thesis,the assumed form of test current and its distribution period are analyzed,so that the induced current and its phase distribution on the linear scatterer can be accurately calculated.In this thesis,the MC equation of the conductor plate is derived for the first time,and the solution process of the MC equation of the conductor plate is described in detail.The specific steps to solve the MC equation include setting the test current,calculating the electric field distribution of the test current on the scatterer,solving the MC coefficients,using the discrete MC equation as linear algebraic equations,and finally solving the induced current.The MC form of scatterers of different structures is different,and the number of MC coefficient is also different.The MC equation of linear conductor contains three coefficients,and only three sets of test current to determine the MC equation.The MC equation of flat conductor contains six coefficient and six sets of test current to determine the MC equation.Numerical examples show that the induced current distribution solved by Maxwell circuit theory is in good agreement with the results obtained by moment method.