CN105653848A - Method for measuring coupling coil parameters by single-port impendence and sensitivity - Google Patents

Abstract

The invention provides a method for measuring coupling coil parameters by single-port impendence and sensitivity, and belongs to the technical field of measurement. The method firstly uses a simple impedance analyzer and only measures one port in a coupling coil, and the coupling coil can be in a conducting medium or an air medium. A measured item is the equivalent complex impedance of the port under different frequencies. Then, the parameters in the model can be taken as optimizing variables, and the error between the tested impendence and the calculated impendence is taken as a target function to establish an optimal problem mathematical model. The simple method for analyzing the sensitivity is used for calculating the optimizing direction of the calculation function. The minimum value of the target function is searched to distinguish all parameters in a coupling coil model, wherein the parameters comprise model parameters when the conducting medium is in the presence.

Description

A kind of utilize single port impedance and the method for sensitivity measure pickup coil parameter

Technical field

The present invention proposes and a kind of utilize single port impedance and the method for sensitivity measure pickup coil parameter, belong to field of measuring technique.

Background technology

Based on the radio energy transmission system of electromagnetic principle or electromagnetic acoustic principle, and consumption electronic product is with in industry electromechanical equipment, electromagnetic coupled coil is widely applied, and its effect realizes voltage conversion, current transformation, impedance conversion, electrical isolation, transmission ofenergy, signal transmission etc. To when carrying out theoretical analysis or simulation analysis containing electromagnetic coupled coil, it is necessary to set up its model, comprise model structure and model parameter. The method of Modling model, one is according to physical principle, it may also be useful to electromagnetic theory, by calculating model structure and the model parameter of electromagnetic coupled coil. But, due to the complicacy of final condition and the time-varying characteristics of electromagnetic quantities, this kind of Theoretical Calculation is very complicated. Two is use testing tool to measure, such as electric impedance analyzer or network analyzer. Electric impedance analyzer is used for single port and measures, and pickup coil exists the port of two or more; Measure although network analyzer can be used for both-end mouth, but also can cause test inconvenience when tested two ports are apart from each other. In addition, in general, the whole parameters in model can not directly be obtained according to test result, in addition it is also necessary to test result is done further data processing, such as mutual inductance, percentage coupling, alternating current resistance, stray capacitance etc., all can not directly obtain measuring result. When pickup coil is in special medium, such as seawater or ionogen, they form eddy current due to conduction, and vortex phenomenon equivalence can become the virtual coil being made up of inductance and resistance, and at this moment simple measurement is difficult to obtain detailed model parameter especially.

It thus is seen that need to propose a kind of effective ways, simply measure according to several times, it is possible to identification goes out the detail parameters of pickup coil model.

Summary of the invention

The present invention uses simple electric impedance analyzer, is only measured by a port in Multiple coil pickup coil, and this pickup coil can be in conducting medium or in air dielectric, and the project of measurement is this port complex equivalent impedance at different frequencies; Taking the parameter in model as optimizing variable, taking the impedance error of the impedance tested and calculating as objective function, set up optimization problem mathematical model; Utilize the simple method of the sensitivity for analysis that the present invention proposes, the search direction of calculating target function; By finding the minimum value of objective function, identification goes out the whole parameters in pickup coil model, comprises the virtual coil model parameter that conducting medium is corresponding.

The technical scheme that the present invention takes is:

First, electric impedance analyzer is connected on a port of pickup coil, it is preferred to the input port of energy or signal, by other port short circuits, or access known resistance, it is ensured that connect good.

Then, measuring single port complex equivalent impedance at different frequencies, selected frequency to be covered minimum frequency when pickup coil works and most high frequency, and the single port impedance measured has certain distinction. Record these frequencies and corresponding single port complex impedance.

Secondly, according to the structure of pickup coil and medium character, utilize electromagnetism principle, set up the structure of pickup coil model, and determine the character (direct current resistance, alternating current resistance, inductance, electric capacity, mutual inductance) of parameter. If pickup coil is in conducting medium, induced current can be formed in media as well in exchange situation, it is similar to the rotor winding current of induction motor, therefore can by the situation connected and represent in conducting medium of the resistance with the inductance representing electromagnetic induction that represent loss, and there is magnetic coupling between this virtual inductor and other inductance, represent with percentage coupling.

This, taking the whole parameters in above-mentioned model as optimizing variable, set up the mathematical model of optimization problem again. Objective function is two kinds of single port complex impedances Error Absolute Value sums at different frequencies. One is determining under frequency, the complex impedance observed value obtained with electric impedance analyzer; Another kind is based on initial value or iterative value, obtains according to electric network theory, single port complex impedance calculated value under same frequency.

Finally, the simple method of the sensitivity for analysis that the present invention proposes is utilized, the search direction of calculating target function. Through interative computation, after objective function reaches minimum value, the answer of optimizing variable is exactly whole parameter value in pickup coil model. This is a kind of method that surveying and calculating combines.

The invention has the beneficial effects as follows:

(1) using general impedance analyser to measure, cost is low.

(2) only a port Impedance of pickup coil is measured, easy to operate.

(3) model parameter of two or more pickup coil can be measured.

(4) when can there is conducting medium around measuring coupling coil, the model parameter of pickup coil.

(5) with the product of voltage phasor, electric current phasor or square, calculate single port impedance to the sensitivity of parameter, thus eliminate the difficulty determining search direction by derivative operation.

Accompanying drawing explanation

Fig. 1 is the wiring scheme of measuring coupling coil single-ended impedance; (a) conducting medium or air dielectric situation; B () removable or irremovable situation.

Fig. 2 is a kind of circuit model of duplex winding pickup coil.

Fig. 3 is two mouth networks of sensitivity for analysis.

Fig. 4 is with the two mouth network of T-shaped circuitry instead.

Fig. 5 is the situation that two coils exist coupling.

Fig. 6 is the equivalent electrical circuit of Fig. 5 after cancellation mutual inductance.

Specific embodiments

Below in conjunction with Figure of description and technical scheme, specific embodiments is done explanation in detail.

1. single port impedance measurement

The port that electric impedance analyzer is connected to pickup coil, normally the input port of energy or signal, by all the other port short circuits, or connect known resistance, connect and want good, must not open a way, as shown in Fig. 1 (a), (b). Test single port impedance at different frequencies, institute's selected frequency to be covered minimum frequency when pickup coil works and most high frequency, and the single port impedance that measurement obtains has obvious distinction. The frequency that record uses and corresponding single port complex impedance. With

$\tilde{Z}\left({\mathrm{j\ω}}_k\right)=\tilde{R}\left({\mathrm{\ω}}_k\right)+j\tilde{X}\left({\mathrm{\ω}}_k\right),(k=1,2,...m)---\left(1\right)$

Represent the single port complex equivalent impedance obtained m frequency place measurement.

2. set up objective function based on observed value and calculated value

For the purpose of generality, if pickup coil model contains n component parameters, with parameter vector represent for,

P=[P₁,P₂,��,P_n]^T(2)

Wherein P_k(k=1,2 ..., n) can be the parameters such as resistance, inductance, electric capacity, mutual inductance or percentage coupling.It is defined as follows the objective function of n independent variable(s):

$F\left(P\right)=\underset{k=1}{\overset{m}{\Σ}}|Z\left({\mathrm{j\ω}}_k\right)-\tilde{Z}\left({\mathrm{j\ω}}_k\right){|}^2---\left(3\right)$

Wherein, Z (j ��_k)=R (��_k)+jX(��_k) (k=1,2 ... m) it is in the angular frequency corresponding with measurement_kPlace, by certain the group parameter value in iterative process, the single port complex equivalent impedance obtained by Theoretical Calculation. Such as, as shown in Figure 2, this model is because of winding number, medium character, wire character, the factors such as the concern degree of secondary cause is different for a kind of circuit model that Theoretical Calculation is used.

By formula (3) plural number difference mould square, resolve into real part difference square with square sum of imaginary part difference, namely

$F\left(P\right)=\underset{k=1}{\overset{m}{\Σ}}\{{\[R\left({\mathrm{\ω}}_k\right)-\tilde{R}\left({\mathrm{\ω}}_k\right)\]}^2+{\[X\left({\mathrm{\ω}}_k\right)-\tilde{X}\left({\mathrm{\ω}}_k\right)\]}^2\}---\left(4\right)$

The gradient vector G of certain some place objective function, equals objective function F (P) to the partial derivative of parameter vector P, namely

$G=\frac{\∂F\left(P\right)}{\∂P}={\[\frac{\∂F}{\∂P_1},\frac{\∂F}{\∂P_2},...,\frac{\∂F}{\∂P_n}\]}^T---\left(5\right)$

Expression formula (4) according to objective function, gradient i-th (i=1,2 ..., n) individual component is,

$\frac{\∂F}{\∂P_i}=2\underset{k=1}{\overset{m}{\Σ}}\{\[R\left({\mathrm{\ω}}_k\right)-\tilde{R}\left({\mathrm{\ω}}_k\right)\]\frac{\∂R\left({\mathrm{\ω}}_k\right)}{\∂P_i}\}+2\underset{k=1}{\overset{m}{\Σ}}\{\[X\left({\mathrm{\ω}}_k\right)-\tilde{X}\left({\mathrm{\ω}}_k\right)\]\frac{\∂X\left({\mathrm{\ω}}_k\right)}{\∂P_i}\}---\left(6\right)$

It thus is seen that calculateProblem, become calculatingWithProblem. Due to

$\frac{\∂Z\left({\mathrm{j\ω}}_k\right)}{\∂P_i}=\frac{\∂R\left({\mathrm{\ω}}_k\right)}{\∂P_i}+j\frac{\∂X\left({\mathrm{\ω}}_k\right)}{\∂P_i}---\left(7\right)$

So,

$\left\{\begin{array}{c}\frac{\∂R\left({\mathrm{\ω}}_k\right)}{\∂P_i}=\mathrm{Re}\[\frac{\∂Z\left({\mathrm{j\ω}}_k\right)}{\∂P_i}\]\\ \frac{\∂X\left({\mathrm{\ω}}_k\right)}{\∂P_i}=\mathrm{Im}\[\frac{\∂Z\left({\mathrm{j\ω}}_k\right)}{\∂P_i}\]\end{array}\right.---\left(8\right)$

In formula,It is called that single port impedance is to component parameters P_iSensitivity, it be plural number. That is, the gradient problem of calculating target function in the present invention, becomes and calculates single port impedance to the sensitivity problem of component parameters.

3. single port impedance is to the calculating (unitary current source advocate approach) of model parameter sensitivity

For obtaining single port equivalent impedance to the sensitivity of model parameter, so that the search direction of calculating target function, the present invention is by the T-shaped equivalent electrical circuit of two-port network, it is proposed that unitary current source advocate approach. The sensitivity of model parameter is comprised the sensitivity to two-terminal element (resistance, electric capacity, inductance) parameter and the sensitivity to mutual inductance by single port equivalent impedance. Introduced below:

First set the two-terminal element parameter of sensitivity to be asked as complex impedance Z_k, concrete resistance, inductance and electric capacity, it is possible to regard Z as_kSpecial Circumstances. By Z_kTake out from network separately, and take a port. The Impetus of Current Source applied takies another port, namely connects that port of electric impedance analyzer. So just, establish the two-port network model of sensitivity analysis, as shown in Figure 3. Two-port network can come equivalent with T-shaped circuit, as shown in Figure 4.

Z (j ��) can be obtained, and Z (j ��) is to Z by Fig. 4_kPartial derivative, namely Z (j ��) is to impedance parameter Z_kSensitivity,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂Z_k}=\frac{Z_3^2}{{(Z_3+Z_2+Z_k)}^2}---\left(9\right)$

On the other hand, existUnder (unit need not be considered, abstract number) condition, calculate and flow through Z_kElectric current,

${\stackrel{\·}{I}}_{Z_k}=\frac{Z_3{\stackrel{\·}{I}}_1}{Z_2+Z_3+Z_k}=\frac{Z_3}{Z_2+Z_3+Z_k}---\left(10\right)$

Relatively formula (9) obtains following sensitivity formula with (10),

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂Z_k}={\stackrel{\·}{I}}_{Z_k}^2---\left(11\right)$

If Z_kFor resistance, then Z (j ��) is to the sensitivity of resistance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂R_k}={\stackrel{\·}{I}}_{R_k}^2---\left(12\right)$

If Z_kFor conductance, then Z (j ��) is to the sensitivity of conductance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂G_k}=-{\stackrel{\·}{U}}_{G_k}^2---\left(13\right)$

If Z_kFor inductance, then Z (j ��) is to the sensitivity of inductance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_k}=j\mathrm{\ω}{\stackrel{\·}{I}}_{L_k}^2---\left(14\right)$

If Z_kFor electric capacity, then Z (j ��) is to the sensitivity of electric capacity,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂C_k}=-j\mathrm{\ω}{\stackrel{\·}{U}}_{C_k}^2---\left(15\right)$

For the two coil coupling situations that there is public end shown in Fig. 5, utilize cancellation mutual inductance principle, obtain shown in Fig. 6 not containing magnetic-coupled equivalent electrical circuit, formula (11) thus can be used to calculate Z (j ��) to the sensitivity of mutual inductance and self-induction, result is as follows:

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂M_{kl}}=j2\mathrm{\ω}{\stackrel{\·}{I}}_k{\stackrel{\·}{I}}_l,\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_k}=j\mathrm{\ω}{\stackrel{\·}{I}}_k^2,\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_l}=j\mathrm{\ω}{\stackrel{\·}{I}}_l^2---\left(16\right)$

If there is not public end between pickup coil, above-mentioned formula is also correct.

If containing Multiple coil coupling, then there is multiple coefficient of self-induction and multiple mutual inductance. To Multiple coil pickup coil situation, it is possible to two two ground are analyzed.

Utilize percentage coupling and the relation of coefficient of self-induction and mutual inductance, it is also possible to obtain Z (j ��) further to percentage coupling K_klSensitivity:

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂K_{kl}}=j2\mathrm{\ω}{\stackrel{\·}{I}}_k{\stackrel{\·}{I}}_l\×\sqrt{L_k{L}_l}---\left(17\right)$

From above-mentioned each Calculation of Sensitivity formula, in the present invention, by calculating single port impedance to the sensitivity problem of model parameter, the model element electric current phasor and voltage phasor problem that calculate under the phasor effect of unitary current source are melted into it, then use they square or product, just can obtain the sensitivity in strict meaning, it may not be necessary to set up the analytical expression of impedance and model parameter.

3. the acquisition of pickup coil model parameter

Above-mentioned optimization problem obtains a group model parameter value after restraining.Confirm target function value whether enough little (compared with single port impedance magnitude) more further. If enough little, so this group parameter value is exactly the pickup coil model parameter value drawn by measurements and calculations; Otherwise illustrate that objective function does not converge to global minima, now to be changed initial value iteration again, until during convergence, objective function reaches enough little, it is ensured that converge to global minimum.

Claims (4)

1. one kind utilizes sensitivity and the method for single port impedance measurement pickup coil parameter, it is characterised in that,

First, electric impedance analyzer is connected on a port of pickup coil, by other port short circuits or access known resistance;

Then, measuring single port complex equivalent impedance at different frequencies, selected frequency to be covered minimum frequency when pickup coil works and most high frequency, and the single port impedance measured has distinction; Record these frequencies and corresponding single port complex impedance;

Secondly, according to the structure of pickup coil and medium character, utilize electromagnetism principle, set up the structure of pickup coil model, and determine parameter: direct current resistance, alternating current resistance, inductance, electric capacity and mutual inductance; If pickup coil is in conducting medium, induced current is formed in media as well in exchange situation, by the situation connected and represent in conducting medium of the resistance with the inductance representing electromagnetic induction that represent loss, and there is magnetic coupling between this virtual inductor and other inductance, represent with percentage coupling;

Taking the whole parameters in above-mentioned model as optimizing variable, set up the mathematical model of optimization problem; Objective function is two kinds of single port complex impedances Error Absolute Value sums at different frequencies; One is determining under frequency, the complex impedance observed value obtained with electric impedance analyzer; Another kind is based on initial value or iterative value, obtains according to electric network theory, single port complex impedance calculated value under same frequency;

Finally, utilize following single port impedance to the method for calculation of model parameter sensitivity, the search direction of calculating target function; Through interative computation, after objective function reaches minimum value, the answer of optimizing variable is exactly whole parameter value in pickup coil model;

Described single port impedance is as follows to the method for calculation of model parameter sensitivity:

First set the two-terminal element parameter of sensitivity to be asked as complex impedance Z_k, by Z_kTake out from network separately, and take a port; The Impetus of Current Source applied takies another port, namely connects that port of electric impedance analyzer, sets up the two-port network model of sensitivity analysis; Two-port network T-shaped circuit comes equivalent;

Obtain Z (j ��) and Z (j ��) to Z_kPartial derivative, namely Z (j ��) is to impedance parameter Z_kSensitivity,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂Z_k}=\frac{Z_3^2}{{(Z_3+Z_2+Z_k)}^2}---\left(9\right)$

?Under condition, calculate and flow through Z_kElectric current,

${\stackrel{\·}{I}}_{Z_k}=\frac{Z_3{\stackrel{\·}{I}}_1}{Z_2+Z_3+Z_k}=\frac{Z_3}{Z_2+Z_3+Z_k}---\left(10\right)$

Relatively formula (9) obtains following sensitivity formula with (10),

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂Z_k}={\stackrel{\·}{I}}_{Z_k}^2---\left(11\right)$

If Z_kFor resistance, then Z (j ��) is to the sensitivity of resistance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂R_k}={\stackrel{\·}{I}}_{R_k}^2---\left(12\right)$

If Z_kFor conductance, then Z (j ��) is to the sensitivity of conductance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂G_k}=-{\stackrel{\·}{U}}_{G_k}^2---\left(13\right)$

If Z_kFor inductance, then Z (j ��) is to the sensitivity of inductance,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_k}=j\mathrm{\ω}{\stackrel{\·}{I}}_{L_k}^2---\left(14\right)$

If Z_kFor electric capacity, then Z (j ��) is to the sensitivity of electric capacity,

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂C_k}=-j\mathrm{\ω}{\stackrel{\·}{U}}_{C_k}^2---\left(15\right)$

There are two coil coupling situations of public end, utilize cancellation mutual inductance principle, obtain not containing magnetic-coupled equivalent electrical circuit, it may also be useful to formula (11) calculates Z (j ��) to the sensitivity of mutual inductance and self-induction, and result is as follows:

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂M_{kl}}=j2\mathrm{\ω}{\stackrel{\·}{I}}_k{\stackrel{\·}{I}}_l,\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_k}=j\mathrm{\ω}{\stackrel{\·}{I}}_k^2,\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂L_l}=j\mathrm{\ω}{\stackrel{\·}{I}}_l^2---\left(16\right)$

Utilize percentage coupling and the relation of coefficient of self-induction and mutual inductance, obtain Z (j ��) further to percentage coupling K_klSensitivity:

$\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂K_{kl}}=j2\mathrm{\ω}{\stackrel{\·}{I}}_k{\stackrel{\·}{I}}_l\×\sqrt{L_k{L}_l}---\left(17\right).$

2. method according to claim 1, it is characterised in that, described pickup coil is duplex winding or Multiple coil, and surrounding medium is conducting medium or air dielectric.

3. method according to claim 1 and 2, it is characterised in that, described single port impedance, when referring to other port short circuits or access known resistance, from the complex impedance value that energy or signal input port are measured.

4. method according to claim 3, it is characterized in that, described analysis single port impedance is to the method for model parameter sensitivity, refer under unitary current source phasor encourages, calculate voltage phasor and the electric current phasor of element in pickup coil model, again according to the component properties of sensitivity to be asked, by one of following manner: voltage phasor square, electric current phasor square, the product of voltage phasor and electric current phasor, calculate single port impedance to the sensitivity of component parameters, it may also be useful to following formula:

Sensitivity to resistance:

Sensitivity to conductance:

Sensitivity to self-induction:

Sensitivity to electric capacity: $\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂C_k}=-j\mathrm{\ω}{\stackrel{\·}{U}}_{C_k}^2;$

Sensitivity to mutual inductance:

Sensitivity to percentage coupling: $\frac{\∂Z\left(j\mathrm{\ω}\right)}{\∂K_{kl}}=j2\mathrm{\ω}{\stackrel{\·}{I}}_k{\stackrel{\·}{I}}_l\×\sqrt{L_k{L}_l}.$