Second-Order Analytic Extension of Eigenvalues for Fast Frequency Sweep Analysis of RF Circuits

A second-order analytic extension of eigenvalue (AEE) method is presented and investigated for efficiently computing the Z-parameters of passive RF circuits over a wide frequency band with full-wave accuracy. The Z-parameters of an RF circuit are first extracted based on a full-wave simulation on sampling frequencies and then decomposed into eigenmodes, whose eigenvalues are analytically extended to all other frequencies within the frequency band of interest based on functional equations constructed from second-order series and parallel RLC circuits. An eigenvector-eigenvalue identity is adopted to compute the frequency-dependent eigenvectors from the eigenvalues of the submatrices, which are used in the expansion of the Z-parameters. A comparison with full-wave solutions is given for the second-order AEE where four frequencies are employed to accurately approximate the Z-parameters and predict the frequency response over the entire band of interest that goes to much higher frequencies than the first-order AEE. With this, the previously developed first-order AEE for a quasi-static analysis is successfully extended to much higher frequencies. Numerical examples are provided to validate the accuracy and demonstrate the capability of the second-order AEE. It is found that the second-order AEE is very accurate for modeling RF circuits with electrical sizes up to one wavelength that possibly contains resonances, as compared to the first-order AEE, which is applicable only to RF circuits with electrical sizes smaller than one-tenth to one-fifth of a wavelength that contains no resonance.