Blackbox macro-modeling of the nonlinearity based on Volterra series representation of X-parameters

Volterra series representation is a powerful mathematical model for nonlinear devices. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. This paper proposed a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters for the first time. Then the Vandermonde method is employed to separate different orders of Volterra kernels at the same frequency, which leads to a highly efficient extraction process. The proposed Volterra series representation based on X-parameters is further benchmarked for verification. The proposed new algorithm is very useful for the blackbox macro-modeling of nonlinear devices and systems.