CN109510734A - A kind of measurement method of group delay - Google Patents

A kind of measurement method of group delay Download PDF

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Publication number
CN109510734A
CN109510734A CN201811383728.1A CN201811383728A CN109510734A CN 109510734 A CN109510734 A CN 109510734A CN 201811383728 A CN201811383728 A CN 201811383728A CN 109510734 A CN109510734 A CN 109510734A
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phase
group delay
function
measurement
measurement method
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CN109510734B (en
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李凌云
骆睿
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Shanghai Institute of Microsystem and Information Technology of CAS
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Shanghai Institute of Microsystem and Information Technology of CAS
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L43/00—Arrangements for monitoring or testing data switching networks
    • H04L43/08—Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
    • H04L43/0852—Delays
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters

Abstract

The present invention provides a kind of measurement method of group delay, comprising: under certain frequency step interval, using phase of the measuring device measurement examining system in different frequency point, obtains Frequency point, phase measurement and phase noise level parameter；According to Frequency point and phase measurement segmented construction phase function, Tikhonov Regularization is carried out to phase function, its undetermined coefficient is solved, obtains phase function expression formula；Group delay value is calculated using the phase function solved.The measurement method of group delay of the invention obtains the phase noise level parameter of Frequency point, phase value and measuring device in measurement, using smooth Cubic Spline Functions Fitting phase value, carries out Tikhonov Regularization to fitting function, obtains the value of group delay.Overcome that traditional measurement method noise resisting ability is poor, the low problem of resolution ratio can effectively improve measurement accuracy.

Description

A kind of measurement method of group delay
Technical field
The present invention relates to Microwave Measurement Technique fields, more particularly to a kind of measurement method of group delay.
Background technique
Group delay is the physical quantity for describing the phase-frequency characteristic of signal transmission system, is the importance of signal transmission system One of energy index.Group delay not only determines the size of signal transmission system propagation delay time, also reflects signal and passes by entire The distortion level of defeated system.Therefore, correct measurement signal transmission system different frequency point group delay parameter, it is entire to determination The performance indicator of signal transmission system is of great significance.
In the building process of high stability system, such as satellite navigation, the fields such as International Atomic Time comparison, to time synchronization Required precision it is higher and higher.The Group Delay Ripple of amplifier, frequency mixer and radio-frequency cable in system has become time synchronization Main error, how critically to measure the problem of group delay has become urgent need to resolve in high stable system building process.
Existing Group Delay Measurement method is the phase value diagonal frequencies differential using difference coefficient method to measurement, and this method exists The contradiction between resolution ratio and precision, in the case where phase measurement error is certain, improve frequency resolution reduce frequency steps It is long, it will increase the calculating error of group delay.
Although existing Group Delay Measurement system can be using the method for increasing sampling interval, such as
“KEYSIGHT TECHN-OLOGIES.Understanding the Fundamental Principles of Vector Network Analysis,”
Https: //literaturecdnkeysightcom/litweb/pdf/59657707Epdf, 2017, to reduce Influence of the measurement error to group delay value, but this method also reduces frequency resolution simultaneously, still remains resolution ratio and essence The contradiction of degree.
In view of this situation, it is necessary to use new Group Delay Measurement method, enhance noise resisting ability, reduce measurement error The influence calculated group delay value is selected with step-length.
Summary of the invention
The present invention is intended to provide a kind of measurement method of the group delay based on Tikhonov regularization, to realize high resolution And the Group Delay Measurement that accuracy is high.
To achieve the goals above, the present invention provides a kind of measurement methods of group delay, comprising:
S1: taking frequency step Δ f as the interval of two neighboring Frequency point, using measuring device measurement examining system in difference Phase on Frequency point, and the phase noise level parameter δ of the measuring device is obtained, obtain Frequency point fi, phase measurementAnd phase noise level parameter δ, i=0,1, L, n-1；
S2: the Frequency point f obtained according to step S1iAnd phase measurementSegmented construction phase function g (f), to phase Bit function carries out Tikhonov Regularization, solves the undetermined coefficient of phase function, obtains complete phase function expression formula； The phase function g (f) constructed is the Tikhonov Regularization function based on cubic spline function；
S3: the group delay value of examining system is calculated using the undetermined coefficient of the S2 phase function solved.
Preferably, the measuring device is vector network analyzer.
Preferably, the frequency step Δ f is less than 10MHz.
Preferably, the experimental temperature of the measurement method of the group delay is set as steady temperature.
Preferably, the S1 further include: dual-port calibration is carried out to measuring device before measurement every time.
Preferably, the phase noise level parameter δ is defined as:
Wherein,For phase measurement,For the truth-function of phase；δ is phase noise level parameter.
Preferably, the phase function g (f) constructed are as follows:
In formula,For the undetermined coefficient of phase function.
It is wherein, described that Tikhonov Regularization is carried out to phase function, comprising:
Following constraint condition is arranged to the phase function constructed:
And meets following cost functional and obtains minimum value:
Wherein,For the truth-function of phase；λ is regularization coefficient, λ=k δ2, the value range of k is 10-5~10-10。
Preferably, the group delay value of the examining system are as follows:
Wherein,For the undetermined coefficient of the S2 phase function g (f) solved.
The measurement method of group delay of the invention considers phase noise, and the phase noise of measuring device is obtained in measurement Horizontal parameters, while by smooth Cubic Spline Functions Fitting phase function, using the derivative of cubic spline function come approximate The value for solving group delay, overcomes the contradiction between prior art intermediate-resolution and precision, in the case where keeping high-resolution Improve the precision of Group Delay Measurement.
Detailed description of the invention
The comparison for the phase curve that Fig. 1 is the phase curve of difference coefficient method and the measurement method of group delay of the invention is constructed Result figure.
Fig. 2 is the group delay value that the measurement method of the obtained group delay value of traditional difference coefficient method and group delay of the invention obtains Comparing result figure.
Specific embodiment
Below in conjunction with specific embodiment, the present invention will be further described.It should be understood that following embodiment is merely to illustrate this The range of invention and is not intended to limit the present invention.
The present invention provides a kind of measurement methods of group delay comprising:
Step S1: using frequency step Δ f as the interval of two neighboring Frequency point, examining system is measured using measuring device Phase in different frequency point, and obtain the phase noise level parameter δ of the measuring device wherein, phase noise level parameter δ can be obtained by inquiring from the technical manual of measuring device.Obtain Frequency point fi, phase measurementAnd phase Noise level parameter δ, i=0,1, L, n-1；
The phase noise level parameter δ's is defined as:
Wherein,For phase measurement,For the truth-function of phase；δ is phase noise level parameter.
In the present embodiment, the measuring device is vector network analyzer, and precision is 0.1 °, the measuring device The higher the better for precision；The frequency range of measurement is that 1.5~1.52GHz is not wanted in addition, frequency range can take arbitrary value It asks.And the frequency step Δ f should be less than 10MHz, because frequency resolution is too low for 10MHz or more, can not achieve High-resolution purpose is kept while improving the precision of Group Delay Measurement.In the present embodiment, frequency step Δ f= 100KHz；The experimental temperature of the measurement method of the group delay is set as steady temperature, preferably 25 DEG C, because under different temperatures Measured piece group delay can be different, as a result, by the way that by temperature control, when some steady temperature is to guarantee measurement, group delay value will not It changes.Phase noise level parameter δ is determined by test macro, illustrates the range of uncertainty of measurement.
In addition, the S1, which can also include: that each measurement is preceding, carries out dual-port calibration to measuring device.
Step S2: the Frequency point f obtained according to step S1iAnd phase measurementSegmented construction phase function g (f), Tikhonov Regularization is carried out to phase function g (f), the undetermined coefficient of phase function g (f) is solved, obtains complete phase Bit function expression formula, specifically includes:
The phase function g (f) constructed is to correspond respectively to the n-1 in n-1 section based on changing on cubic spline function Become the Tikhonov Regularization function that partially restrained condition obtains, expression formula are as follows:
In formula,For the undetermined coefficient of phase function g (f).
It is wherein, described that Tikhonov Regularization is carried out to phase function g (f), comprising:
Following constraint condition is arranged to the phase function g (f) constructed:
And meets following cost functional and obtains minimum value:
Wherein, λ is regularization coefficient, λ=k δ2, k is constant；K is an additional proportionality coefficient, generally rule of thumb Value, the value range of k are 10-5~10-10。
The cost functional obtains minimum value, can be calculated by following formula:
Wherein,For phase measurement, g(3)(f) three order derivatives for being phase function g (f), λ is regularization coefficient.
The undetermined coefficient of phase function g (f) can be acquired using above-mentioned constraint conditionValue, obtain complete phase letter Number expression formula.
Step S3: the group delay value of examining system is calculated using the undetermined coefficient of the S2 phase function g (f) solved.
Wherein, the group delay value of the examining system are as follows:
Wherein,For the undetermined coefficient of the S2 phase function g (f) solved, direct physical meaning is just It is the group delay value of each frequency, superscript is exactly frequency serial number.
In order to prove the validity of this method in actual measurement, by phase data collected in vector network analyzer The group delay value handled using the high-resolution Group Delay Measurement method based on Tikhonov regularization in the present invention It is compared with difference coefficient method obtains in vector network analyzer group delay value.
As depicted in figs. 1 and 2, the group delay value comparison that the group delay value obtained for the method for the present invention is obtained with difference coefficient method Image, as can be observed from Figure, the group delay value dispersion that the present invention obtains are small.Table 1 is the group that two kinds of processing methods obtain The comparison of the average and standard deviation of time delay result overcomes as it can be seen from table 1 the method standard difference that the present invention uses is small Contradiction between conventional method resolution ratio and accuracy, result verification the method for the present invention are feasible for actual experiment analysis Property and validity.
Group delay Comparative result when 1 frequency step 100KHz of table
Above-described, only presently preferred embodiments of the present invention, the range being not intended to limit the invention, of the invention is upper Stating embodiment can also make a variety of changes, for example, test equipment can also be not limited only to vector network analyzer.It is i.e. all according to Simple, equivalent changes and modifications made by claims and description according to the present patent application are fallen within of the invention special The claims of benefit.The not detailed description of the present invention is routine techniques content.

Claims (9)

1. a kind of measurement method of group delay characterized by comprising
Step S1: taking frequency step Δ f as the interval of two neighboring Frequency point, using measuring device measurement examining system in difference Phase on Frequency point, and the phase noise level parameter δ of the measuring device is obtained, obtain Frequency point fi, phase measurementAnd phase noise level parameter δ, i=0,1, L, n-1；
Step S2: the Frequency point f obtained according to step S1iAnd phase measurementSegmented construction phase function g (f), to phase Bit function carries out Tikhonov Regularization, solves the undetermined coefficient of phase function, obtains complete phase function expression formula； The phase function g (f) constructed is the Tikhonov Regularization function based on cubic spline function；
Step S3: the group delay value of examining system is calculated using the undetermined coefficient of the S2 phase function solved.
2. the measurement method of group delay according to claim 1, which is characterized in that the measuring device includes vector network Analyzer.
3. the measurement method of group delay according to claim 1, which is characterized in that the frequency step Δ f is less than 10MHz。
4. the measurement method of group delay according to claim 1, which is characterized in that the reality of the measurement method of the group delay Testing temperature setting is steady temperature.
5. the measurement method of group delay according to claim 1, which is characterized in that the S1 further include: every time before measurement Dual-port calibration is carried out to measuring device.
6. the measurement method of group delay according to claim 1, which is characterized in that the phase noise level parameter δ's Is defined as:
Wherein,For phase measurement,For the truth-function of phase；δ is phase noise level parameter.
7. the measurement method of group delay according to claim 1, which is characterized in that the phase function g (f) constructed are as follows:
In formula,For the undetermined coefficient of phase function.
8. the measurement method of group delay according to claim 7, which is characterized in that described to be carried out to phase function Tikhonov Regularization, comprising:
Following constraint condition is arranged to the phase function constructed:
And meets following cost functional and obtains minimum value:
Wherein,For the truth-function of phase；λ is regularization coefficient, λ=k δ2, the value range of k is 10-5~10-10。
9. the measurement method of group delay according to claim 1, which is characterized in that the group delay value of the examining system Are as follows:
Wherein,For the undetermined coefficient of the S2 phase function g (f) solved.
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Cited By (1)

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Publication number Priority date Publication date Assignee Title
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US20100078576A1 (en) * 2007-04-06 2010-04-01 The General Hospital Corporation Systems and Methods for Optical Imaging Using Early Arriving Photons
CN107610102A (en) * 2017-08-24 2018-01-19 东南大学 A kind of Displacement measuring method based on Tikhonov regularizations

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Cited By (2)

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Publication number Priority date Publication date Assignee Title
CN111580137A (en) * 2020-05-18 2020-08-25 中国人民解放军国防科技大学 Fitting method for time characteristics of radio frequency channel group of high-precision navigation receiver
CN111580137B (en) * 2020-05-18 2022-04-22 中国人民解放军国防科技大学 Fitting method for high-precision navigation receiver radio frequency channel group delay characteristics

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