The describing-function method for the analysis of nonlinear systems with sinusoidal inputs is interpreted as a mean-square quasi-linearization technique and is generalized to apply to random signals.An amplitude-sensitive (or zero-memory) nonlinearity is interpreted as being approximately equivalent to a linear frequency-insensitive device, and a formula is derived for its equivalent gain.A simple rate-limited control system with a Gaussian input is analyzed as a specific application.Approximation of a general nonlinear element (containing memory) is considered next, and a relation between equivalent-system impulse response and the response of the actual nonlinearity is derived.
A hybrid moment methdedge-element method (MMlEEM) is presented. The formulation is quite general; however, the method is applied to two-dimensional scattering problems. Such a hybrid formulation unites the advantages of finite and integral-equation methods and is able to handle unbounded problems in which complex inhomogeneities are present. The edge-element method is easily coupled to the moment method, and it doesn't introduce spurious modes. The equivalence principle is used to divide the original problem into two separate problems: an unbounded homogeneous one in which the moment method is used and a bounded inhomogeneous one in which the edge-element method is used. Several examples involving two-dimensional scattering with TE and TM plane wave excitation are presented. The RCS is computed and compared to results obtained by other numerical techniques.
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