CN110850165B - Direct current point solving and frequency band expanding method suitable for vector network time domain function - Google Patents

Direct current point solving and frequency band expanding method suitable for vector network time domain function Download PDF

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CN110850165B
CN110850165B CN201911186367.6A CN201911186367A CN110850165B CN 110850165 B CN110850165 B CN 110850165B CN 201911186367 A CN201911186367 A CN 201911186367A CN 110850165 B CN110850165 B CN 110850165B
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袁国平
刘丹
年夫顺
杨明飞
庄志远
李明太
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Abstract

The invention discloses a direct current point solving and frequency band expanding method suitable for a vector network time domain function, and belongs to the field of electronic measurement. The method comprises the steps of obtaining a group of direct current points by using a vector fitting technology, processing original frequency domain test data by using interpolation to obtain another group of direct current points, and carrying out weighted average on the two direct current points to obtain a final direct current point; the accuracy of the direct current point is improved, and the test precision of the time domain function is further improved; the frequency band extension method suitable for the vector network time domain function can effectively improve the time domain resolution of the time domain function, does not need to purchase a vector network with a wider frequency band, and reduces the test cost; the invention provides a frequency resampling and time domain characteristic solving technology of network parameters, which can obtain time domain response of any time length of a measured object.

Description

Direct current point solving and frequency band expanding method suitable for vector network time domain function
Technical Field
The invention belongs to the field, and particularly relates to a direct current point obtaining and frequency band expanding method suitable for a vector network time domain function.
Background
Traditionally, a vector network analyzer (hereinafter referred to as "vector network") is a frequency domain test instrument, obtains the frequency domain network parameter characteristics of a tested object, and obtains a time domain function which is an expansion function of the vector network. At present, the time domain function of the vector network does not have the functions of frequency band extension and frequency point resampling test, and meanwhile, the direct current test point is simply obtained by adopting an interpolation mode.
The vector network time domain function has a very wide application range, typically, for example, fault point judgment of a cable, voltage distribution of the cable along the axial length can be obtained through the time domain function, and capacitive type, inductive type or mixed type faults can be further judged according to the change trend of the voltage.
With the rapid advance of 5G mobile communication, under the drive of the mobile internet and the internet of things, the requirement of a user on the speed of high-speed data transmission is higher and higher, a digital circuit develops to high bandwidth and high speed, and the vector network time domain function is widely used for designing the high-speed digital circuit and analyzing the signal integrity problems such as time domain reflection, crosstalk and jitter. Among them, the time domain reflectometry impedance test is a common method for estimating a transmission line by using a time domain reflectometry oscilloscope. The time domain reflection impedance test based on the vector network time domain function is used as a substitute method for the time domain analysis, has the advantages of large dynamic range, small test error and the like, and is more and more concerned by people.
At present, the network parameter testing technology with time domain function is relatively mature, and German technology company, Luode and Schwarz company and Anli company, and domestic China Central and electronic instruments and meters company all provide commercialized products. However, with the development of the test scenario, two core indexes of the time domain function of the vector network are: the requirements for test length and time domain resolution are higher and higher. The test length is inversely proportional to the interval between the vector network test frequency points, and the time domain resolution is proportional to the maximum bandwidth of the vector network test. In addition, the current vector network cannot directly acquire the test data of the direct current point of the tested piece, and needs to be acquired through low-frequency point interpolation, and if the interpolation value is inaccurate, the final time domain test precision is affected.
At present, time domain functions of vector network analyzer manufacturers at home and abroad do not have the functions of frequency band expansion and frequency point resampling in testing, and meanwhile, a direct current test point is simply obtained by adopting an interpolation mode.
If a larger test length or a higher time domain resolution is to be obtained, only the vector network with a wider frequency band can be purchased for completion, but the frequency band of the current vector network is limited and the cost for purchasing the vector network with the wider frequency band is also greatly increased.
The direct current point is obtained by adopting an interpolation mode, and is easily influenced by the noise of originally adopted data, and further the time domain response precision obtained by the vector network time domain function is also influenced.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a direct current point acquisition and frequency band expansion method suitable for the vector network time domain function, which is reasonable in design, overcomes the defects of the prior art and has a good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a direct current point solving and frequency band expanding method suitable for a vector network time domain function comprises the following steps:
step 1: the S parameter of the discrete frequency point of the tested piece is obtained through a vector network analyzer, and the specific form is shown as formula (1):
Figure GDA0003287970700000021
wherein,
Figure GDA0003287970700000022
representing vectors of discrete frequency point components, f1,f2…fNRepresents discrete frequency points, N represents the number of parameters of the discrete frequency points,
Figure GDA0003287970700000023
representing vectors, S, formed by S parameters corresponding to different discrete frequency points1,s2,…sNRepresenting S parameter values of different discrete frequency points;
step 2: and fitting the S parameter by adopting a vector matching algorithm to obtain an analytical expression of the scattering characteristic of the measured piece, wherein the analytical expression is shown as the formula (2):
Figure GDA0003287970700000024
wherein g(s) represents an analytical expression of scattering characteristics of the measured piece, s ═ j2 π f represents a Laplace variable, cnRepresents the nth value of residue, anRepresents the nth pole, d represents the steady state response value, N1Representing the number of total poles;
and step 3: the time length of time domain test of the vector network analyzer is inversely proportional to the discrete frequency point interval of the S parameter, the time domain resolution is inversely proportional to the coverage frequency width of the S parameter, and the required discrete frequency point interval delta f and frequency width f are obtained according to the time length and time domain resolution set by a userspanAnd obtaining the required value of the discrete frequency point according to the two values, as shown in formula (3):
Figure GDA0003287970700000025
wherein f isext1＝Δf，fext2＝2Δf，fspan＝N2Δf；
And 4, step 4: substituting the value of the discrete frequency point obtained in the step 3 into the formula (1), and resampling the scattering characteristic of the measured piece to obtain the S parameter of a group of discrete frequency points, wherein the S parameter is specifically shown as the formula (4):
Figure GDA0003287970700000026
wherein s isext0＝g(0)，sext1＝g(j2πΔf)，sextN2＝g(j2πN2Δf)；
And 5: according to the stepsF of the raw data in step (1)1、f2、s1And s2Processing the original frequency domain test data by using a least square method to solve the interpolation s of the direct current point0Then comparing with the DC value s obtained in step 4ext0Carrying out weighted average to obtain a final direct current point value sfinal0And substituting the S parameter into a formula (4) to obtain the S parameter of the discrete frequency point, which is specifically shown in a formula (5):
Figure GDA0003287970700000031
step 6: and (5) obtaining the time domain response of the tested piece by utilizing an inverse Fourier transform algorithm, and further obtaining the step response after integration.
The invention has the following beneficial technical effects:
1) the invention provides a direct current point expansion method suitable for a vector network time domain function, which comprises the steps of obtaining a group of direct current points by utilizing a vector fitting technology, simultaneously processing original frequency domain test data by utilizing interpolation to obtain another group of direct current points, and carrying out weighted average on the two direct current points to obtain final direct current points; the accuracy of the direct current point is improved, and the test precision of the time domain function is further improved.
2) The frequency band extension method suitable for the vector network time domain function can effectively improve the time domain resolution of the time domain function, does not need to purchase a vector network with a wider frequency band, and reduces the test cost.
3) The invention provides a frequency resampling and time domain characteristic solving technology of network parameters, which can obtain time domain response of any time length of a measured object.
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FIG. 1 is a process diagram of the implementation of the method of the present invention.
FIG. 2 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
as shown in fig. 1 and fig. 2, a method for direct current point calculation and frequency band extension suitable for a vector network time domain function includes the following steps:
step 1: the S parameter of the discrete frequency point of the tested piece is obtained through a vector network analyzer, and the specific form is shown as formula (1):
Figure GDA0003287970700000032
wherein,
Figure GDA0003287970700000033
representing vectors of discrete frequency point components, f1,f2…fNRepresents discrete frequency points, N represents the number of parameters of the discrete frequency points,
Figure GDA0003287970700000034
representing vectors, S, formed by S parameters corresponding to different discrete frequency points1,s2,…sNRepresenting S parameter values of different discrete frequency points;
step 2: and fitting the S parameter by adopting a vector matching algorithm to obtain an analytical expression of the scattering characteristic of the measured piece, wherein the analytical expression is shown as the formula (2):
Figure GDA0003287970700000041
wherein g(s) represents an analytical expression of scattering characteristics of the measured piece, s ═ j2 π f represents a Laplace variable, cnRepresents the nth value of residue, anRepresents the nth pole, d represents the steady state response value, N1Representing the number of total poles;
and step 3: the time length of time domain test of the vector network analyzer is inversely proportional to the discrete frequency point interval of the S parameter, the time domain resolution is inversely proportional to the coverage frequency width of the S parameter, and the required discrete frequency point interval delta f and frequency width f are obtained according to the time length and time domain resolution set by a userspanThe required discrete frequency point value is obtained according to the two values, as shown in formula (3)The following steps:
Figure GDA0003287970700000042
wherein f isext1＝Δf，fext2＝2Δf，fspan＝N2Δf；
And 4, step 4: substituting the value of the discrete frequency point obtained in the step 3 into the formula (1), and resampling the scattering characteristic of the measured piece to obtain the S parameter of a group of discrete frequency points, wherein the S parameter is specifically shown as the formula (4):
Figure GDA0003287970700000043
wherein s isext0＝g(0)，sext1＝g(j2πΔf)，sextN2＝g(j2πN2Δf)；
And 5: f according to the original data in step (1)1、f2、s1And s2Processing the original frequency domain test data by using a least square method to solve the interpolation s of the direct current point0Then comparing with the DC value s obtained in step 4ext0Carrying out weighted average to obtain a final direct current point value sfinal0And substituting the S parameter into a formula (4) to obtain the S parameter of the discrete frequency point, which is specifically shown in a formula (5):
Figure GDA0003287970700000044
step 6: and (5) obtaining the time domain response of the tested piece by utilizing an inverse Fourier transform algorithm, and further obtaining the step response after integration.
Key points and protection points of the invention:
1) implementation of the technology. The invention provides a direct current point and frequency band expanding method suitable for a vector network time domain function, which is different from the traditional vector network time domain function, and mainly comprises the steps of utilizing a vector fitting technology to carry out transfer function fitting on frequency domain data obtained by vector network testing to obtain an analytic expression of the characteristics of a tested object about frequency, solving a direct current point through the transfer function of the tested object, simultaneously utilizing interpolation to process original frequency domain test data to obtain another group of direct current points, and carrying out weighted average on the two direct current points to obtain a final direct current point; for frequency band expansion, the transfer function of the object to be measured is also utilized, and the network parameter value of the required frequency point is obtained according to the requirement of time domain resolution.
2) Frequency resampling and time domain characteristic solving technology of network parameters. According to the requirements of testing time length and inverse Fourier transform, network parameter discrete frequency point distribution is obtained according to equidistant frequency intervals, the frequency points are substituted into a transfer function of a tested object to obtain discrete point network parameter values, mirror image transformation is carried out on the discrete point network parameters by taking direct current points as a central axis, inverse Fourier transform is carried out on data after the mirror image transformation to obtain time domain impact response of the tested object, integration is further carried out on the impact response, and time domain unit step response is obtained.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (1)

1. A direct current point solving and frequency band expanding method suitable for a vector network time domain function is characterized by comprising the following steps: the method comprises the following steps:
step 1: the S parameter of the discrete frequency point of the tested piece is obtained through a vector network analyzer, and the specific form is shown as formula (1):
Figure FDA0003287970690000011
wherein,
Figure FDA0003287970690000012
representing vectors of discrete frequency point components, f1,f2…fNRepresents discrete frequency points, N represents the number of parameters of the discrete frequency points,
Figure FDA0003287970690000013
representing vectors, S, formed by S parameters corresponding to different discrete frequency points1,s2,…sNRepresenting S parameter values of different discrete frequency points;
step 2: and fitting the S parameter by adopting a vector matching algorithm to obtain an analytical expression of the scattering characteristic of the measured piece, wherein the analytical expression is shown as the formula (2):
Figure FDA0003287970690000014
wherein g(s) represents an analytical expression of scattering characteristics of the measured piece, s ═ j2 π f represents a Laplace variable, cnRepresents the nth value of residue, anRepresents the nth pole, d represents the steady state response value, N1Representing the number of total poles;
and step 3: the time length of time domain test of the vector network analyzer is inversely proportional to the discrete frequency point interval of the S parameter, the time domain resolution is inversely proportional to the coverage frequency width of the S parameter, and the required discrete frequency point interval delta f and frequency width f are obtained according to the time length and time domain resolution set by a userspanAnd obtaining the required value of the discrete frequency point according to the two values, as shown in formula (3):
Figure FDA0003287970690000015
wherein f isext1＝Δf，fext2＝2Δf，fspan＝N2Δf；
And 4, step 4: substituting the value of the discrete frequency point obtained in the step 3 into the formula (1), and resampling the scattering characteristic of the measured piece to obtain the S parameter of a group of discrete frequency points, wherein the S parameter is specifically shown as the formula (4):
Figure FDA0003287970690000016
wherein s isext0＝g(0)，sext1＝g(j2πΔf)，
Figure FDA0003287970690000017
And 5: f according to the original data in step (1)1、f2、s1And s2Processing the original frequency domain test data by using a least square method to solve the interpolation s of the direct current point0Then comparing with the DC value s obtained in step 4ext0Carrying out weighted average to obtain a final direct current point value sfinal0And substituting the S parameter into a formula (4) to obtain the S parameter of the discrete frequency point, which is specifically shown in a formula (5):
Figure FDA0003287970690000021
step 6: and (5) obtaining the time domain response of the tested piece by utilizing an inverse Fourier transform algorithm, and further obtaining the step response after integration.
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