CN-121980796-A - Scattering parameter traceable uncertainty analysis method based on sensitivity inversion

CN121980796ACN 121980796 ACN121980796 ACN 121980796ACN-121980796-A

Abstract

The invention discloses a sensitivity inversion-based scattering parameter traceable uncertainty analysis method which comprises the steps of establishing a metering traceable chain and an uncertainty propagation model integrating TRL and SOLT calibration, tracing coaxial scattering parameter measurement results to the geometric dimension of a standard air medium transmission line, carrying out differential linearization on the TRL eight-term error model, carrying out sensitivity inversion to obtain error coefficient uncertainty, and carrying out joint Monte Carlo sampling to jointly propagate the error coefficient uncertainty and measurement noise to obtain a calibrated scattering parameter uncertainty matrix. The method realizes the full-link uncertainty quantification from the standard air line geometric quantity to the scattering parameter, and is used for evaluating the accuracy and reliability of a high-frequency scattering parameter measurement system.

Inventors

LI HUANXIN
Ren Shuaiqi
CUI XIAOHAI
LI ZIWEI
YUAN WENZE
ZHAO KEJIA
YANG FENGLIN

Assignees

中国计量科学研究院

Dates

Publication Date: 20260505
Application Date: 20260126

Claims (7)

1. The method for analyzing the traceable uncertainty of the scattering parameter based on sensitivity inversion is characterized by comprising the following steps of: Obtaining measured values of the inner diameter of the outer conductor and the outer diameter of the inner conductor of the standard air medium transmission line, and respectively evaluating standard uncertainty of the inner diameter of the outer conductor and the outer diameter of the inner conductor; Calculating the characteristic impedance and uncertainty of the standard air medium transmission line based on the inner diameter of the outer conductor and the outer diameter of the inner conductor; based on the characteristic impedance and the uncertainty thereof, and combining the influence of measurement noise, respectively calculating to obtain a scattering parameter and an uncertainty matrix of a transmission parameter of the standard air medium transmission line; Based on the uncertainty matrix of the transmission parameters, performing linearization processing by using eight error models calibrated by TRL, and obtaining an uncertainty vector of the error coefficient through sensitivity inversion solution; Performing joint sampling on the uncertainty vector of the error coefficient and measurement noise by adopting a Monte Carlo method, repeatedly performing TRL calibration correction on the original scattering parameter of the tested device, and counting and outputting the discreteness to obtain an uncertainty matrix of the scattering parameter of the tested device after TRL calibration; based on the known value and uncertainty of the calibration standard component obtained by TRL calibration, the known value uncertainty of the calibration standard is introduced into SOLT calibration to be transmitted in combination with measurement noise, and a scattering parameter uncertainty matrix of the tested device after SOLT calibration is obtained.
2. The method for analyzing the traceable uncertainty of the scattering parameter based on sensitivity inversion of claim 1, wherein the step of evaluating the standard uncertainty of the inner diameter of the outer conductor and the outer diameter of the inner conductor comprises the steps of identifying uncertainty components of temperature correction, measuring tool calibration and repeatability measurement aiming at an inner diameter and outer diameter measurement process of an air transmission line, and synthesizing the uncertainty components by adopting a square method and a root method to obtain the synthesized standard uncertainty of the inner diameter and the outer diameter measurement.
3. The method of claim 1, wherein calculating uncertainty of the characteristic impedance comprises propagating uncertainty of the inner diameter of the outer conductor and uncertainty of the outer diameter of the inner conductor to the characteristic impedance based on an error propagation law.
4. The method for analyzing the uncertainty of the traceable scattering parameter based on sensitivity inversion of claim 3, wherein the step of calculating the uncertainty of the characteristic impedance uses the following formula: ; Wherein mu and epsilon are the magnetic permeability and the dielectric constant of the air medium respectively.
5. The method for analyzing the traceable uncertainty of the scattering parameter based on the sensitivity inversion according to claim 1, wherein the method for obtaining the uncertainty vector of the error coefficient by the sensitivity inversion solution comprises the following steps: Establishing an error model equation based on TRL calibration, wherein the equation is related to a known transmission matrix of a standard air line, a transmission matrix of a straight-through standard, a corresponding measurement transmission matrix and error coefficients a, b, c, alpha, beta, epsilon, r and rho of eight error models; Carrying out full differential linearization on the error model equation to construct a linear equation set taking uncertainty of an error coefficient as an unknown number; And solving the linear equation set, and inverting to obtain the uncertainty vector of the error coefficient.
6. The method for analyzing the traceable uncertainty of the scattering parameter based on sensitivity inversion according to claim 1, wherein the method for obtaining the uncertainty matrix of the scattering parameter of the device under test after TRL calibration by using the monte carlo method specifically comprises: performing multiple combined random sampling on the error coefficient and the measurement noise according to the uncertainty vector of the error coefficient and the statistical characteristics of the measurement noise; For each sample, performing a complete TRL calibration procedure to correct the original measured scattering parameters of the device under test; and counting the discreteness of output results after the calibration and correction for multiple times to determine an uncertainty matrix of the scattering parameters of the tested device after TRL calibration.
7. The method for analyzing the traceable uncertainty of the scattering parameter based on sensitivity inversion according to claim 1, wherein obtaining the uncertainty matrix of the scattering parameter of the measured device after SOLT calibration specifically comprises: obtaining standard values of short circuit, open circuit and load standard components for SOLT calibration, wherein the standard values and the uncertainty thereof are obtained through TRL calibration and measurement technology; adopting a Monte Carlo method to perform joint propagation analysis on the uncertainty of the standard value of the calibration standard component, the uncertainty introduced by the original measurement noise of the calibration standard component and the uncertainty introduced by the measurement noise of the measured device; and counting the propagation result to obtain an uncertainty matrix of the scattering parameter of the tested device after SOLT calibration.

Description

Scattering parameter traceable uncertainty analysis method based on sensitivity inversion Technical Field The invention relates to the technical field of uncertainty evaluation of measurement of scattering parameters of microwave electronic devices and systems, in particular to a method for analyzing traceable uncertainty of scattering parameters based on sensitivity inversion. Background The scattering parameter is a key performance index of most microwave electronic components and systems, the accurate measurement of the scattering parameter is critical to guaranteeing the quality of devices and systems, and at present, the measurement of the S parameter mainly depends on a vector network analyzer and a calibration algorithm (such as SOLT, TRL and the like) thereof, although the algorithm can correct the inherent error of the system, the measurement error cannot be completely eliminated, and the residual error is often quantized in an uncertainty form, so that the method has important practical significance for accurately and efficiently evaluating the uncertainty of the scattering parameter measured by the VNA. In the existing uncertainty evaluation method, uncertainty propagation is realized by a Monte Carlo method through a large number of random samples, but calculation is time-consuming and an analytic solution cannot be provided, correlation influence among uncertainty sources is ignored by a sensitivity analysis method although random sampling can be avoided, and the uncertainty joint propagation problem caused by noise and non-ideal calibration standards is not solved by a covariance matrix-based method, mainly because of the lack of a corresponding propagation model and decoupling method. Therefore, the invention provides a novel uncertainty analysis method combining sensitivity inversion and Monte Carlo simulation. The sensitivity inversion technique decouples the uncertainty of the known transmission line S parameter from the uncertainty of the error coefficient, and then analyzes the propagation of uncertainty from the error coefficient and measurement noise to the measured device S parameter using a joint monte carlo simulation. Disclosure of Invention The invention aims to provide a method for analyzing traceable uncertainty of scattering parameters by combining sensitivity inversion and Monte Carlo simulation. In order to achieve the above purpose, the invention is implemented according to the following technical scheme: The invention comprises the following steps: Obtaining measured values of the inner diameter of the outer conductor and the outer diameter of the inner conductor of the standard air medium transmission line, and respectively evaluating standard uncertainty of the inner diameter of the outer conductor and the outer diameter of the inner conductor; Calculating the characteristic impedance and uncertainty of the standard air medium transmission line based on the inner diameter of the outer conductor and the outer diameter of the inner conductor; based on the characteristic impedance and the uncertainty thereof, and combining the influence of measurement noise, respectively calculating to obtain a scattering parameter and an uncertainty matrix of a transmission parameter of the standard air medium transmission line; Based on the uncertainty matrix of the transmission parameters, performing linearization processing by using eight error models calibrated by TRL, and obtaining an uncertainty vector of the error coefficient through sensitivity inversion solution; Performing joint sampling on the uncertainty vector of the error coefficient and measurement noise by adopting a Monte Carlo method, repeatedly performing TRL calibration correction on the original scattering parameter of the tested device, and counting and outputting the discreteness to obtain an uncertainty matrix of the scattering parameter of the tested device after TRL calibration; Based on the known value and uncertainty of a calibration standard component obtained by TRL calibration, introducing the known value uncertainty of the calibration standard in SOLT calibration and carrying out joint propagation on measurement noise to obtain a scattering parameter uncertainty matrix of the measured device after SOLT calibration; Further, the step of evaluating the standard uncertainty of the inner diameter of the outer conductor and the outer diameter of the inner conductor comprises the steps of identifying uncertainty components such as temperature correction, measuring tool calibration, repeatability measurement and the like aiming at the inner diameter and outer diameter measurement process of the air transmission line, and synthesizing the uncertainty components by adopting a square and root method to obtain the synthesized standard uncertainty of the inner diameter and outer diameter measurement. Further, the step of calculating the uncertainty of the characteristic impedance includes propagating the uncertainty of t