Intelligent inversion and calibration parameter uncertainty quantification method for microwave probe S parameters

Abstract

With the rapid development of microwave and radio frequency technology, precise on-chip S-parameter measurement is constrained by non ideal standard components, probe crosstalk, and residual nonlinear errors in the millimeter wave frequency band. A intrinsic on-chip calibration process has been proposed. This process combines an open/short circuit de embedding model for crosstalk perception, a backpropagation neural network for residual error inversion, and a semi naive Bayesian network for probabilistic error compensation. The Bayesian stage generates a posterior distribution on the discretized residual error categories. The posterior mean is used for continuous compensation, while the posterior quantile provides the prediction interval. On the independent test set, the amplitude mean absolute error of the complete process reached 0.061 ± 0.003 dB, and the phase root mean square error was 1.43 ± 0.07°, while the traditional open/short circuit de embedding methods were 0.105 ± 0.005 dB and 3.46 ± 0.12°, respectively. For the nominal 90% interval, the predicted interval coverage probability is 91.2%, and the expected calibration error is 0.024. In 500 engineering evaluations, the average end-to-end inference time was 0.91 ms per sample. The contribution lies in the system level integration of physically driven de embedding, nonlinear inversion, and probability compensation.