CN106570209A - AC resistance voltage divider correction method for error model established based on equivalence principle - Google Patents

Abstract

The invention discloses an AC resistance voltage divider correction method for an error model established based on an equivalence principle. The method comprises the following steps that a frequency error equivalent model of the AC resistance voltage divider is built, and errors of the voltage divider are respectively expressed as a formula 6 and a formula 7 simply; and Kf and Kt can be obtained by calculating according to the formula 6 and the formula 7, and the calibration of the AC resistance voltage divider in a full frequency range can be completed. The invention accurately proposes a frequency error model of a precise AC resistance voltage divider; capacitive errors generated due to various reasons are controlled in the design of the precise AC resistance voltage divider; the correction of continuous spectrum ratio error and angle error of 50 Hz to 100 kHz is realized by adopting a one-point correction method; the direction and magnitude of screen potential compensating capacitive errors are researched; and besides, the invention proposes that an important feature p factor of the voltage divider is independent of the frequency and an equivalent capacitance value, and solves the problem of phase correction of harmonic power measurement.

Description

The AC resistance divider bearing calibration of error model is set up based on einstem's equialency principle

Technical field

The present invention relates to a kind of AC resistance divider bearing calibration that error model is set up based on einstem's equialency principle.

Background technology

AC resistance divider is widely used in various voltage gradation measurements, due to the frequency characteristic of electric resistance partial pressure ratio There is easily realization compared with electromagnetic transformer, using accurate alternating current generally under audio frequency or electric harmonic measuring condition Resistance divider, higher voltage is measured for low-voltage, and due to the growing demand of harmonic power measurement, essence Close resitstance voltage divider requires strict control phase shift.It is 3kHz to 60 subharmonic that accurate harmonic measure frequency range covers power frequency, Audio power measurement is then up to 100kHz, how to reduce the capacitive leakage produced over the ground and to shielding due to resistance connection, resistance Affect, how to set up harmonic wave metering theory and source tracing correction method, it has also become the urgent task of electrical measurement worker.Improve resistance Divider precision can generally adopt following methods：

(1) voltage divider arrangement based on equal potential screening technique, document [1]《It is a kind of for industrial frequency harmonic power measurement Wideband resitstance voltage divider》:The project realizes equivalent potential screen using major-minor divider branch road, solves resistance and connects to circuit Distribution capacity leakage around the leakage of plate and resistance.Provide method of testing of tracing to the source：Resistance alternating voltage ratio traces direct current Voltage ratio, phase error traces two-channel digital voltmeter, is employed herein " step-up " i.e. by low-voltage to high voltage Method, the project has been used in national industrial frequency harmonic standard.Existing problems：Divider phase error is raised with frequency and increasing makes The measurement of harmonic power brings trouble；With normative reference, pointwise correction error is clearly difficulty under various complicated harmonic wave operating modes 's.

(2) document [2]《Inductive voltage divider is the voltage coefficient with reference to evaluation high voltage ac/dc converter》：The project is adopted Twin-stage and single-stage equipotential inductive voltage divider are the high voltage measuring that normative reference covers power frequency to 100kHz measurement frequency scopes, And concatenated with thermocouple by spreading resistance and reach AC trace source in direct current, it is proposed that fixed mask and mobile shielding compensation side Method.Existing problems：Because the intervention of thermocouple makes tested voltage-phase to measure；Mobile shielding compensation leakage does not provide mould Type.

For problem like above, the present invention is proposed：The equivalent model and error of AC resistance divider is with frequency The rule of change；Disclose the frequency consistency essence of AC resistance voltage divider arrangement parameter；Innovation proposes adjustment shielding electricity The method of optimum compensation of position；Give the Precise Representation formula of harmonic wave digital compensation.

The content of the invention

The technical problem to be solved is：A kind of alternating current that error model is set up based on einstem's equialency principle is provided Resistance divider bearing calibration.

Above-mentioned technical problem is solved, the technical solution adopted in the present invention is as follows：

A kind of AC resistance divider bearing calibration that error model is set up based on einstem's equialency principle, including：

Set up the frequency error equivalent model of the AC resistance divider：

T=C × (R₁₂+R₂₁)…………………(1)

ω=2 π f ... ... ... ... (3)

Wherein：

T is time constant；

K is resitstance voltage divider intrinsic standoff ratio；

ω is angular frequency (rad), and f is divider frequency input signal (Hz)；

Consider the actual intrinsic standoff ratio and the resitstance voltage divider intrinsic standoff ratio expression after " Δ-Y " abbreviation under communicational aspects：

, there is implicit important judgement factor p in K (ω) expression formula in the Jing strict mathematical derivations of equation：

P=R₂₁×R₁₁-R₂₂×R₁₂…………·(5)

Further substitute into the parameters simulations such as resistance, the equivalent capacity of divider to calculate：

As p=0, either how frequency changes with equivalent capacity, and the proportional error and angular difference of divider are zero；

Work as p<When 0, the proportional error of divider for just and absolute value to raise with frequency be in ω²Relation becomes big；Angular difference is negative And absolute value is raised with frequency and becomes big in ω relations；

Work as p>When 0, it is in ω that the proportional error of divider is raised for negative and absolute value with frequency²Relation becomes big；Angular difference is for just And absolute value is raised with frequency and becomes big in ω relations；

The derivation of equation：

Make a=T²×R₂₂, b=T × R₂₁, c=T²×(R₁₁+R₂₂), d=T × (R₂₁+R₂₂), then：

Because the imaginary numbers very little in above formula, contrast differences calculate negligible,

Divider is than poor f_cExpression：

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

Then

Divider angular difference δ_cExpression：

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

Then

Thus, the error of divider brief respectively can be expressed as：

Divider ratio is poor：

f_c=ω²×K_f…………(6)

Divider angular difference：

δ_c=ω × K_t…………(7)

In formula：

K_fDimension is second square (s²),

K_tDimension is the second (s),

K_fValue is about 1 × 10^-15, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not with frequency The constant of change, reduced form (6), formula (7) are about 1 × 10 with the calculating goodness of fit of accurate formula (4) in the range of 50Hz-3kHz^-20；

K_tValue is about 1 × 10^-7, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not become with frequency The constant of change, the goodness of fit is about 1 × 10 in the calculating of reduced form (6), formula (7) with accurate formula (4) in the range of 50Hz-3kHz^-14；

Thus, divider error function can be simplified shown as：

f_i=ω_i ²×K_f... ... ... ... ... ... (formula 8-1)

δ_i=j ω_i×K_t... ... ... ... ... ... (formula 8-2)

Section 1 is divider ratio poor (formula 8-1) in formula 8, and Section 2 is divider angular difference (formula 8-2), f_iAnd δ_iRepresent model Enclose the ratio difference and angular difference of interior arbitrary frequency, ω_iRepresent frequency, K_f、K_tConstant can be by any one frequency under normative reference Measurement can obtain K than difference and angular difference by formula 6 and the simple computation of formula 7_fAnd K_t, complete the divider calibration of all frequency range.

Compared with prior art, the invention has the advantages that：

First, the present invention proposes exactly the frequency error model of accurate AC resistance divider.

Second, the capacitive error produced because of a variety of causes is controlled in the design of accurate AC resistance divider.

3rd, the amendment poorer than declinate of the continuous frequency spectrum of 50Hz-100kHz is realized using some bearing calibrations.

4th, have studied direction, value that screen potential compensates capacitive error.

5th, it is proposed that the divider key character p factors have independence with frequency and equivalent capacity value.

6th, solve a phase only pupil filter difficult problem for harmonic power measurement.

Description of the drawings

Below in conjunction with the accompanying drawings the present invention is described in further detail with specific embodiment：

Fig. 1 is the circuit theory diagrams of the accurate AC resistance divider frequency error equivalent model of the present invention；

In Fig. 1：PBK is metal shielding, and R is auxiliary divider resistance；

R1-divider resistance 1；

R2-divider resistance 2；

C-equivalent leakage capacitance；

The equivalent upper resistance of R11-divider resistance 1；

The equivalent lower resistance of R12-divider resistance 1；

The equivalent upper resistance of R21-divider resistance 2；

The equivalent lower resistance of R22-divider resistance 2；

Fig. 2 is the 50Hz-3000Hz amplitude-versus-frequency curve figures that 120V/0.8V selects optimal parameter matching；

Fig. 3 is the 50Hz-3000Hz phase-frequency characteristic curve maps that 120V/0.8V selects optimal parameter matching.

Specific embodiment

1. accurate AC resistance divider frequency error equivalent model

As shown in figure 1, setting up the frequency error equivalent model of the accurate AC resistance divider：

Here, the electrical structures such as auxiliary-voltage divider branch road and equivalent potential screen are simplified, while by R₁、R₂Regard ideal as (i.e. Resistance is nominal value, noninductive) single resistance and be segmented into the needs that two arbitrary portions are analyses, usual R₁Resistance is number Hundred k Ω, equivalent leakage capacitance be tens of pF, basic reference of the above parameter as following qualitative analyses.

T=C × (R₁₂+R₂₁)…………………(1)

ω=2 π f ... ... ... ... (3)

Wherein：

T is time constant；

K is resitstance voltage divider intrinsic standoff ratio；

ω is angular frequency (rad), and f is divider frequency input signal (Hz)；

Consider the actual intrinsic standoff ratio and the resitstance voltage divider intrinsic standoff ratio expression after " Δ-Y " abbreviation under communicational aspects：

, there is implicit important judgement factor p in K (ω) expression formula in the Jing strict mathematical derivations of equation：

P=R₂₁×R₁₁-R₂₂×R₁₂…………(5)

Further substitute into the parameters simulations such as resistance, the equivalent capacity of divider to calculate：

As p=0, either how frequency changes with equivalent capacity, and the proportional error and angular difference of divider are zero.

Work as p<When 0, the proportional error of divider for just and absolute value to raise with frequency be in ω²Relation becomes big.Angular difference is negative And absolute value is raised with frequency and becomes big in ω relations.

Work as p>When 0, it is in ω that the proportional error of divider is raised for negative and absolute value with frequency²Relation becomes big.Angular difference is for just And absolute value is raised with frequency and becomes big in ω relations.

The derivation of equation：

Make a=T²×R₂₂, b=T × R₂₁, c=T²×(R₁₁+R₂₂), d=T × (R₂₁+R₂₂), then：

Because the imaginary numbers very little in above formula, contrast differences calculate negligible,

Divider is than poor f_cExpression：

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

Then

Divider angular difference δ_cExpression：

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

Then

Thus, the error of divider brief respectively can be expressed as：

Divider ratio is poor：

f_c=ω²×K_f…………(6)

Divider angular difference：

δ_c=ω × K_t…………(7)

In formula：

K_fDimension is second square (s²),

K_tDimension is the second (s),

K_fValue is about 1 × 10^-15, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not with frequency The constant of change, reduced form (6), formula (7) are about 1 × 10 with the calculating goodness of fit of accurate formula (4) in the range of 50Hz-3kHz^-20。

K_tValue is about 1 × 10^-7, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not become with frequency The constant of change, the goodness of fit is about 1 × 10 in the calculating of reduced form (6), formula (7) with accurate formula (4) in the range of 50Hz-3kHz^-14。

Thus, divider error function can be simplified shown as：

f_i=ω_i ²×K_f... ... ... ... ... ... (formula 8-1)

δ_i=j ω_i×K_t... ... ... ... ... ... (formula 8-2)

Section 1 is divider ratio poor (formula 8-1) in formula 8, and Section 2 is divider angular difference (formula 8-2), f_iAnd δ_iRepresent model Enclose the ratio difference and angular difference of interior arbitrary frequency, ω_iRepresent frequency, K_f、K_tConstant can be by any one frequency under normative reference Measurement can obtain K than difference and angular difference by formula 6 and the simple computation of formula 7_fAnd K_t, complete the divider calibration of all frequency range.

2. the checking of divider error model

The angular difference measurement data such as table 1 of [1] six divider of citation.

The angular difference measurement data of [1] six divider of document of table 1

K is carried out to the data in table 1 using Mathematical Modeling of the present invention_tValue is calculated, and it the results are shown in Table 2.

Table 2 calculates the K of [1] six divider of document using Mathematical Modeling of the present invention_tValue

Consider that resitstance voltage divider emphasis needs to pay close attention to 1kHz and with super band, therefore only K is made to 1kHz and above frequency_tPrimary system Meter analysis, it the results are shown in Table 3 (if actually starting result of calculation from power frequency has same order).

3 1kHz of table～3kHz calculates K_tValue analysis

Checking example 1：

For 120V/0.8V, after emulation is matched with parameter, R₁=298K, R₂=2K, equivalent capacity is 30pF, R₁₂=0, R₂₁=1735 Ω, R₂₂=265 Ω, K_t=4.49 × 10^-8, the angular difference of each frequency is calculated, and compared with actual test value, knot Fruit is shown in Table 4.As can be seen from the table, fit like a glove with angular difference actual measurement data (table 3), be only document [1] step-up phase places Error Tracing ＆ process generates the deviation of very little.

The 120V/0.8V of table 4 is according to K_tValue calculates angular difference and compares with measured value

Carry out further emulation to 120V/0.8V again to match with parameter, equivalent capacity is 30pF, R₁₂=1000, R₂₁=10 Ω、R₂₂=1990 Ω K_t=4.95 × 10^-11, the angular difference of each frequency is calculated, and compared with actual test value, 5 are the results are shown in Table, , it is obvious that little about three magnitudes of angular difference data that error ratio document [1] is provided.

120V/0.8V is according to K after the fine match of table 5_tValue calculates angular difference and compares with measured value

Checking example 2：

After 480V/0.8V emulation is matched with parameter, R₁=599k, R₂=1k, equivalent capacity is 10pF, R₁₂=54k, R₂₁= 0、R₂₂=1000 Ω, K_t=-4.86 × 10^-8It coincide with direct statistics, now the emulation data correspondence of 480V/0.8V (50～3000) Hz angular differences are respectively -15.3 × 10^-6Rad, -153 × 10^-6Rad, -305 × 10^-6Rad, -458 × 10^{- 6}Rad, -610 × 10^-6Rad, -763 × 10^-6Rad and -916 × 10^-6Rad, control above angular difference measurement data is kissed completely Close, be only deviation that document [1] the step-up phase error processes of tracing to the source generate very little.

Carry out further emulation to 480V/0.8V again to match with parameter, equivalent capacity is 10pF, R₁₂=54k, R₂₁=90 Ω、R₂₂=910 Ω K_t=-8.11 × 10^-11, now the emulation data of 480V/0.8V correspondingly distinguish by (50～3000) H angular differences For -0.026 × 10^-6Rad, -0.255 × 10^-6Rad, -0.510 × 10^-6Rad, -0.764 × 10^-6Rad, -1.02 × 10^-6Rad, -1.27 × 10^-6Rad and -1.530 × 10^-6Rad, little 2 amounts of the angular difference data that error ratio document [1] is provided It is more than level.

Extension tri- l-G simulation test points of 5kHz, 10kHz, 100kHz, 120V/0.8V K_t=4.49 × 10^-8In the case of：Than Difference is respectively -2.29 × 10^-6, -9.15 × 10^-6With -914 × 10^-6, angular difference is respectively 1400 × 10^-6rad、2820×10^-6Rad and 28200 × 10^-6Rad, i.e., the 120V/0.8V divider proportional error that now document [1] is provided will can not ignore, angle Difference also becomes very big.Demonstrate frequency it is higher when can not again with document [1] DC partial voltage ratio trace to the source calibration AC potentiometer ratio Example method.

3. the design of precision voltage divider and aligning step

3.1 select suitable shielding construction and R by test₁、R₂Parameter makes judgement factor p value as little as possible.Such as document [1] 480V divider R₁=599k, R₂=1k, K_tIt is negative to be worth, 240V divider R₁=598k, R₂=2k, K_tIt is worth just, to choose and closing Suitable R₁、R₂Cooperation obtains less K_tValue design, with K_tIt is worth and is because usual K to adjust target_fValue compares K_tValue wants little 4-5 numbers Magnitude, as long as K_tValue choose after because p value is little can be while obtaining less K_fValue.

3.2 after shielding construction and resistance parameter are selected, and the resistance for finely tuning auxiliary branch causes screen potential to reduction p value Move in direction.When p value is moved up for timing, move down when p value is to bear.

After the completion of 3.3 two above steps, or because other reasons cause that resistance parameter and shielding construction can not be selected else, Can digital amendment be carried out to divider.

● divider output should access operational amplifier by strict shielding protection, and operational amplifier should be broadband and pass through frequency Rate rectification building-out, obtains simultaneously in other words K_tCompensate, but should be noted that the ratio declinate difference frequency characteristic of amplifier is basic It is same magnitude, tool difference substantially, equally exists RC constants compared with divider inside amplifier.

● with reference to equipotential inductive voltage divider, suitable frequency such as 1kHz is chosen, carry out selected voltage ratio such as 120V/ 0.8V measurements are obtained than aberration measurements f_c, angular difference measured value δ_c, by formula 6 and formula 7 K is calculated_f、K_t, by K_f、K_tSubstitution formula 8-1 and Formula 8-2 can calculate any frequency ω_iError (including calibration point 1kHz itself), complete frequency continuous to 50Hz-100kHz That what is composed calibrates for error.

Under 3.4 Harmonic Conditions, either single-frequency or multifrequency operating mode, can obtain any frequency of resitstance voltage divider using the present invention Point ω_iError.The error that Kt values calculate in the present inventive method each correspondence frequency, its result are obtained according to the angular difference data of table 1 Such as table 6：

Table 6 obtains K according to document [1] angular difference measurement data_tThe divider error that value is calculated

The data of contrast table 1 can be seen that the divider error obtained using the method for the present invention and kiss completely with actual test Close, it was demonstrated that the correctness of this method.

From Fig. 2 and Fig. 3 it is also seen that divider is signal frequency quadratic behavior curved line relation than difference, angular difference is signal frequency Rate linear relationship, is hypothesized here in optimal compensation match parameter operating mode.

Compared with prior art, the invention has the advantages that：

7th, the present invention proposes exactly the frequency error model of accurate AC resistance divider.

8th, the capacitive error produced because of a variety of causes is controlled in the design of accurate AC resistance divider.

9th, the amendment poorer than declinate of the continuous frequency spectrum of 50Hz-100kHz is realized using some bearing calibrations.

Tenth, have studied direction, value that screen potential compensates capacitive error.

11st, it is proposed that the divider key character p factors have independence with frequency and equivalent capacity value.

12nd, solve a phase only pupil filter difficult problem for harmonic power measurement.

The present invention is not limited to above-mentioned specific embodiment, according to the above, according to the ordinary technical knowledge of this area And customary means, under the premise of without departing from above-mentioned basic fundamental thought of the invention, the present invention can also make other various ways Equivalent modifications, replace or change, among all falling within protection scope of the present invention.

Claims (1)

1. a kind of AC resistance divider bearing calibration that error model is set up based on einstem's equialency principle, including：

Set up the frequency error equivalent model of the AC resistance divider：

T=C × (R₁₂+R₂₁)......................(1)

$K=\frac{R_2}{(R_1+R_2)}...\left(2\right)$

ω=2 π f...................... (3)

Wherein：

T is time constant；

K is resitstance voltage divider intrinsic standoff ratio；

ω is angular frequency (rad), and f is divider frequency input signal (Hz)；

Consider the actual intrinsic standoff ratio and the resitstance voltage divider intrinsic standoff ratio expression after " Δ-Y " abbreviation under communicational aspects：

$K\left(\mathrm{\&omega;}\right)=\frac{{\mathrm{\&omega;}}^2\&times;T^2\&times;R_{22}+R_2+R_{21}\&times;j\mathrm{\&omega;}T}{{\mathrm{\&omega;}}^2\&times;T^2\&times;(R_{11}+R_{22})+R_1+R_2+(R_{12}+R_{21})\&times;j\mathrm{\&omega;}T}...\left(4\right)$

, there is implicit important judgement factor p in K (ω) expression formula in the Jing strict mathematical derivations of equation：

P=R₂₁×R₁₁-R₂₂×R₁₂.............(5)

Further substitute into the parameters simulations such as resistance, the equivalent capacity of divider to calculate：

As p=0, either how frequency changes with equivalent capacity, and the proportional error and angular difference of divider are zero；

Work as p<When 0, the proportional error of divider for just and absolute value to raise with frequency be in ω²Relation becomes big；Angular difference is negative and absolute Value is raised with frequency and becomes big in ω relations；

Work as p>When 0, it is in ω that the proportional error of divider is raised for negative and absolute value with frequency²Relation becomes big；Angular difference is for just and definitely Value is raised with frequency and becomes big in ω relations；

The derivation of equation：

Make a=T²×R₂₂, b=T × R₂₁, c=T²×(R₁₁+R₂₂), d=T × (R₂₁+R₂₂), then：

$\begin{array}{c}K\left(\mathrm{\&omega;}\right)=\frac{{\mathrm{\&omega;}}^2\&times;a+R_2+j\mathrm{\&omega;}b}{{\mathrm{\&omega;}}^2\&times;c+R_1+R_2+j\mathrm{\&omega;}d}\\ =\frac{\left({\mathrm{\&omega;}}^{2}a+R_2\right)\&times;\left({\mathrm{\&omega;}}^{2}c+R_1+R_2\right)+{\mathrm{\&omega;}}^{2}bd+j\left(\mathrm{\&omega;}b\left({\mathrm{\&omega;}}^{2}c+R_1+R_2\right)-\left({\mathrm{\&omega;}}^{2}a+R_2\right)\&times;\mathrm{\&omega;}d\right)}{{\left({\mathrm{\&omega;}}^{2}c+R_1+R_2\right)}^2+{\mathrm{\&omega;}}^2{d}^2}\end{array}$

Because the imaginary numbers very little in above formula, contrast differences calculate negligible,

Divider is than poor f_cExpression：

$\begin{array}{c}{f}_c=\frac{\mathrm{Re}\left(K\left(\mathrm{\&omega;}\right)\right)-K}{K}\\ =\frac{(R_1+R_2)\&times;\left(\right({\mathrm{\&omega;}}^{2}a+R_2)\&times;({\mathrm{\&omega;}}^{2}c+R_1+R_2)+{\mathrm{\&omega;}}^{2}bd)-R_2\&times;({\left({\mathrm{\&omega;}}^{2}c+R_1+R_2\right)}^2+{\mathrm{\&omega;}}^2{d}^2)}{R_2\&times;({\left({\mathrm{\&omega;}}^{2}c+R_1+R_2\right)}^2+{\mathrm{\&omega;}}^2{d}^2)}\end{array}$

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

$f_c=\frac{-{\mathrm{\&omega;}}^2{T}^2\&times;p\&times;(R_{11}+R_{22})}{R_2\&times;{(R_1+R_2)}^2}$

Then

$K_f=\frac{-T^2\&times;p\&times;(R_{11}+R_{22})}{R_2\&times;{(R_1+R_2)}^2}$

Divider angular difference δ_cExpression：

${\mathrm{\&delta;}}_c=\frac{\mathrm{\&omega;}b\&times;({\mathrm{\&omega;}}^{2}c+R_1+R_2)-({\mathrm{\&omega;}}^{2}a+R_2)\&times;\mathrm{\&omega;}d}{({\mathrm{\&omega;}}^{2}a+R_2)\&times;({\mathrm{\&omega;}}^{2}c+R_1+R_2)+{\mathrm{\&omega;}}^{2}bd}$

Ignore higher order term error and a, b, c, d are substituted into into final result, and abbreviation is obtained：

$\begin{array}{c}{\mathrm{\&delta;}}_c=\frac{\mathrm{\&omega;}T\&times;\left(R_{21}\&times;R_{11}-R_{22}\&times;R_{12}\right)}{R_2\&times;(R_1+R_2)}\\ =\frac{\mathrm{\&omega;}\&times;T\&times;p}{R_2\&times;(R_1+R_2)}\end{array}$

Then

$K_t=\frac{T\&times;p}{R_2\&times;(R_1+R_2)}$

Thus, the error of divider brief respectively can be expressed as：

Divider ratio is poor：

f_c=ω²×K_f.............(6)

Divider angular difference：

δ_c=ω × K_t.............(7)

In formula：

K_fDimension is second square (s²),

K_tDimension is the second (s),

K_fValue is about 1 × 10^-15, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not change with frequency Constant, reduced form (6), formula (7) are about 1 × 10 with the calculating goodness of fit of accurate formula (4) in the range of 50Hz-3kHz^-20；

K_tValue is about 1 × 10^-7, determined by resistance parameter, shielding construction parameter and air dielectric etc., it is not change with frequency Constant, the goodness of fit is about 1 × 10 in the calculating of reduced form (6), formula (7) with accurate formula (4) in the range of 50Hz-3kHz^-14；

Thus, divider error function can be simplified shown as：

f_i=ω_i ²×K_f... ... ... ... ... .... (formula 8-1)

δ_i=j ω_i×K_t... ... ... ... ... ... (formula 8-2)

Section 1 is divider ratio poor (formula 8-1) in formula 8, and Section 2 is divider angular difference (formula 8-2), f_iAnd δ_iIn the range of expression The ratio difference of arbitrary frequency and angular difference, ω_iRepresent frequency, K_f、K_tConstant can be by any one frequency measurement under normative reference Than difference and angular difference, K can be obtained by formula 6 and the simple computation of formula 7_fAnd K_t, complete the divider calibration of all frequency range.