CN101713791A - Correction method of nonlinear output of DC low-voltage standard source - Google Patents

Abstract

In order to solve the problem of low output voltage accuracy caused by nonlinear output of the DC low-voltage standard source, the invention provides a correction method of nonlinear output of a DC low-voltage standard source, which is realized in a way that: in the correlation formula for the output voltage of the DC low-voltage standard source, Vo is the output voltage of the DC low-voltage standard source, and Vi is the input voltage of the DC low-voltage standard source. The correction method of the invention can be used for obtaining expected output voltage by adjusting the input voltage of the resistance divider.

Description

The modification method of the non-linear output of DC low-voltage standard source

Technical field

The present invention relates to a kind of method that the output voltage of DC low-voltage standard source is revised

Background technology

DC low-voltage standard source is usually used in the calibration to high sensitivity testing instruments such as digital nV table, photoelectricity galvanometer and small signal amplifiers.The general resitstance voltage divider mode output LOW voltage that adopts as shown in Figure 1 of DC low-voltage standard source, U among Fig. 1 _iBe the input voltage of DC low-voltage standard source, U ₀Output voltage for DC low-voltage standard source.

Because DC low-voltage standard source is used for the high sensitivity testing instrument is calibrated, so the DC low-voltage standard source output voltage should have quite high accuracy.And find that in actual application between DC low-voltage standard source output voltage and the input voltage be not highly to meet theoretic linear relationship, present nonlinear relationship (being designated hereinafter simply as the non-linear output of DC low-voltage standard source), this has caused the uncertainty of DC low-voltage standard source output, and this uncertainty can not satisfy the high sensitivity testing instrument is calibrated needed accuracy.After having got rid of the influence of input voltage and environment temperature, determined that resitstance voltage divider is the main cause that causes the non-linear output of DC low-voltage standard source to the non-linear output of DC low-voltage standard source.

Summary of the invention

The low problem of output voltage accuracy that causes for the non-linear output that solves the DC low-voltage standard source existence, the invention provides the modification method of the non-linear output of a kind of DC low-voltage standard source, the method according to this invention can be determined the relation between DC low-voltage standard source input voltage and the output voltage, thereby has realized purpose of the present invention.

Technical scheme of the present invention is as follows:

The modification method of the non-linear output of DC low-voltage standard source, DC low-voltage standard source adopt the electric resistance partial pressure mode to export, and comprise the steps:

The correction formula of DC low-voltage standard source output voltage is V _o=aV _i ²+ bV _i+ c, wherein V _oBe the output voltage of DC low-voltage standard source, V _iInput voltage for DC low-voltage standard source; C=V _O1, V _O1It is the output voltage values of DC low-voltage standard source when the input voltage of DC low-voltage standard source is 0; $a=\frac{V_{o2}+V_{o3}-2V_{o1}}{2V_m^2},$ $b=\frac{V_{o2}-V_{o3}}{2V_m},$ V _mBe a direct current low-voltage standard source input voltage value, V _O2Be the DC low-voltage standard source output voltage values when the Vi=Vm, V _O3Be the DC low-voltage standard source output voltage values when the Vi=-Vm;

According to the input voltage of described correction formula adjustment DC low-voltage standard source, obtain the output voltage of expectation.

Resitstance voltage divider is in the working environment that steady temperature is T in the DC low-voltage standard source when obtaining a, b and c value; When utilizing described correction formula correction in the DC low-voltage standard source resitstance voltage divider also be in the working environment of steady temperature for T.

Technique effect of the present invention:

The present invention has provided the relational expression more accurately between DC low-voltage standard source input voltage and the output voltage, can adjust the input voltage value of DC low-voltage standard source in view of the above, to obtain the DC low-voltage standard source output voltage values of expectation, realize purpose of the present invention.

Description of drawings

Fig. 1 is the schematic diagram of resitstance voltage divider.

Fig. 2 has indicated each node for resitstance voltage divider and has had the synoptic diagram of thermoelectrical potential.

Embodiment

Through the analysis of background technology part as can be known, the non-linear output of DC low-voltage standard source is that mainly there is non-linear output in resitstance voltage divider, therefore below with reference to accompanying drawing the resitstance voltage divider of DC low-voltage standard source is analyzed and is illustrated.

As shown in Figure 2, the bleeder circuit of resitstance voltage divider has a plurality of nodes (pad between resistance and the lead), all there is the thermoelectrical potential (definition of thermoelectrical potential: when two kinds of different metals are in contact with one another in each node, if the temperature of its contact jaw and noncontact end is unequal, and then the potential difference (PD) that produces between two kinds of metals is called thermoelectrical potential).The size of thermoelectrical potential and temperature, material are relevant, finish in case the circuit of resitstance voltage divider connects, and material just determines therefore have only temperature directly to influence the size of thermoelectrical potential.Because the pin material of resistor is identical, the conductor material that connects resistor is identical, among Fig. 2, and thermoelectrical potential e ₁And e ₂, e ₃And e ₅, e ₄And e ₆Polarity is opposite, can offset a part.And consider thermoelectrical potential e ₁And e ₂, e ₃And e ₅With input voltage U _iThe end series connection, after each is cancelled each other to thermoelectrical potential, its difference size and U _i(1～10V) compares and can ignore that (relative error that causes is 10 ^-6The order of magnitude).

Under the isoperibol condition, the environment temperature of resitstance voltage divider is constant relatively, and the material of node does not change yet, the thermoelectrical potential relative fixed of each node.When the electric current by voltage divider changed, the variation of resistor consumed power caused the variation of thermal value, and temperature causes the thermoelectrical potential of each node to change along with change.

When the intrinsic standoff ratio of the input of resitstance voltage divider and output hour, R ₂Compare R ₁Much bigger, all on R2, R2 integral body produces heat to main power consumption, the pin temperature at R2 two ends is approaching, and the variation of e4 and e6 at this moment is approaching, because polarity is almost offset on the contrary, therefore, when intrinsic standoff ratio when not being very big, the thermoelectrical potential that the resistor power consumption causes is very little to the influence of output.This also is the reason that people do not notice the non-linear output problem of resitstance voltage divider.

When the intrinsic standoff ratio of the input of resitstance voltage divider and output is big, (, reach 10 as in DC low-voltage standard source ⁵: 2), owing to equate by the electric current of two resistance, in resistance R ₁On power consumption compare R ₂On power consumption much bigger, R ₂On power consumption can ignore.Because R ₁Power consumption make R ₁Produce heat, R ₁With R ₂Connect by conductor, make R by heat conduction ₂With R ₁The node (being designated hereinafter simply as node s) and the R that connect ₁Temperature very approaching, node s constantly obtains heat energy raises its temperature, with R ₂Another node (being another pin) forms certain temperature difference, so the difference generation significant change between e4 and the e6, directly influences the variation of resitstance voltage divider output voltage.

Resistance R ₁(the resistance value R in the following formula ₁Also with representing) power consumption be converted to heat energy, resistance R ₁Obtain the heat energy input continuously together with node s, its power is:

P＝I ²R ₁……………………………………(1)

Resistance R ₁Distribute heat energy together with node s by conduction and radiation.The surface conductive heat is:

Φ _c＝h _c·ΔT·A……………………………………………(2)

In the formula, Φ c is conduction heat, W/m ²

A is resistance with node and is connected the surface area of lead, m ²

h _cBe transmissibility factor, W/ (m ²K)

Δ T is temperature rise, K.

Resistance R ₁With node s and the surface emissivity heat that is connected lead be:

$\mathrm{\Φr}=C[{\left(\frac{T+\mathrm{\ΔT}}{100}\right)}^4-{\left(\frac{T}{100}\right)}^4]\·A...\left(3\right)$

In the formula, Φ _rBe radiations heat energy, W;

A is resistance with node and is connected the surface area of lead, m ²

C is a radiation coefficient, W/ (m ²K ⁴)

T is an environment temperature, K;

Δ T is temperature rise, K.

When resistance consumption power was very little, temperature rise was very little, and Δ T → 0 can be got after ignoring the higher order term of Δ T by formula (3):

$\mathrm{\Φr}\≈C\frac{3T^3\mathrm{\ΔT}}{{\left(100\right)}^4}A...\left(4\right)$

Because under isoperibol, can think that T is a constant, formula (4) is expressed as:

Φr≈h _r·ΔT·A………………………………………(5)

In the formula, $h_r\≈C\frac{3T^3}{{\left(100\right)}^4},$ Constant, W/ (m ²K).

When system reaches balance, have:

(h _c+h _r)·ΔT·A＝I ²R ₁………………………………………(6)

In a single day resistance device installs, and surface area A and transmissibility factor and radiative chain number average are fixed, and formula (6) is reduced to:

ΔT＝k ₁I ²R ₁………………………………………(7)

The thermoelectrical potential of node, relevant with material and temperature, when temperature variation, being changed to of thermoelectrical potential:

ε＝C _h×10 ^-6×ΔT………………………………………(8)

In the formula, ε tie point thermoelectrical potential, V;

C _hBe Seebeck coefficient, μ V/K;

Δ T is temperature rise, K.

Resistive element is after circuit board is installed, and material is just definite, therefore, and Seebeck coefficient C _hRemain unchanged, be constant.Can draw according to formula (7) and (8), when electric current flows through voltage divider resistance, being changed to of thermoelectrical potential:

ε＝C _h×10 ^-6×k ₁I ²R ₁………………………………………(9)

With synthetic one of every coefficient, be:

ε＝kI ²R ₁………………………………………(10)

Therefore, for the bigger resitstance voltage divider of intrinsic standoff ratio, output voltage can be expressed as:

$V_o=\frac{R_2}{R_1+R_2}{V}_i+e+{\mathrm{kI}}^2{R}_1$ …………………………………(11)

$=k\frac{R_1}{{(R_1+R_2)}^2}{V}_i^2+\frac{R_2}{R_1+R_2}{V}_i+e$

In the formula, V _oBe resitstance voltage divider output voltage, V;

V _iBe resitstance voltage divider input voltage, V;

E is the thermoelectrical potential output when the resitstance voltage divider input voltage is zero, V.

First on formula (11) equal sign the right is the nonlinearity erron item; Second is the normal partial pressure item, i.e. the output voltage standard value; The 3rd is the output of zero current thermoelectrical potential.

Formula (11) is a quafric curve function, and this is the basic reason that causes the non-linear output of resitstance voltage divider.

Table 1 has been listed the test findings of verifying above-mentioned formula.

Table 1

Range	??Vi(V)	??R 1(Ω)	??R 2(Ω)	??P	??ΔT(℃)	??ε
							??10μV	??10	??500000	??10	??0.2mW	??5×10 -3	??15nV
??100μV	??10	??50000	??10	??2.0mW	??5×10 -2	??148nV
							??1mV	??10	??5000	??10	??20.0mW	??0.5	??1.43μV
??10mV	??10	??5000	??100	??19.6mW	??0.49	??1.39μV

ε is a measurement result in the table 1, and conforms to by formula (8) result of calculation.

Observation type (11) as can be known, when Vi further improved, thermoelectrical potential rose rapidly.In the reality, because the heat radiation in the formula (3) is risen with biquadratic, just, when electric current constantly increased, temperature rise came not obvious more.And, big current voltage distribution device considers that power problem all adopts good cooling measure, and heat conduction also makes temperature rise ease up, at this moment, the Vi quadratic component of formula (11) tends towards stability and merges with zero current thermoelectrical potential e, and the non-linear output of resitstance voltage divider clearly is not difficult for being found.

Formula (11) is simplified to:

V _o＝a·V _i ²+b·V _i+c…………………………………(12)

The input voltage of putting resitstance voltage divider is zero, i.e. V _i=0, measuring resistance voltage divider output voltage values V _O1Be c, that is:

V _o1＝c…………………………………(13)

The input voltage of putting resitstance voltage divider is a magnitude of voltage Vm, i.e. Vi=Vm has:

$V_{o2}=a\·V_m^2+b\·V_m+V_{o1}...\left(14\right)$

The input voltage of putting resitstance voltage divider is-Vm, i.e. Vi=-Vm has:

$V_{o3}=a\·V_m^2-b\·V_m+V_{o1}...\left(15\right)$

Can get from formula (14) and formula (15):

$a=\frac{V_{o2}+V_{o3}-2V_{o1}}{2V_m^2}...\left(16\right)$

$b=\frac{V_{o2}-V_{o3}}{2V_m}...\left(17\right)$

A, b that formula (13) (16) and (17) are tried to achieve and the value substitution formula (12) of c, obtain the correction formula of the non-linear output of resitstance voltage divider, Shu Chu voltage Vo calculates the input voltage modified value as required, can realize the correction to the non-linear output of resitstance voltage divider.

In order to make method of the present invention more accurate, the environment temperature of the resitstance voltage divider that the environment temperature of resitstance voltage divider and the value of using this a, b and c are revised during the value of a that tries to achieve, b and c is identical.

Below by two experiments the present invention is verified.

The method of experiment is connect to go up the input standard source to DC low-voltage standard source, and described input standard source adopts the multi-functional standard source of Fluke 5725A, be used to export 0～± 10V standard DC voltage; The output terminal of DC low-voltage standard source be linked in sequence Keithlei 1801 low noise amplifiers and 2002 digital multimeters are used to measure the DC low-voltage of voltage divider output, show resolving power 1pV, and actual resolving power can reach 0.1nV.The environmental baseline of two experiments is as follows:

Environment temperature: 20 ± 0.1 ℃

Relative humidity: 55%.

First experimental subjects is 1 resitstance voltage divider that maximum output voltage is 20 μ V.

At first, adjust the input voltage Vi of resitstance voltage divider, obtain the result of table 2 for the value that obtains a, b and c.

Table 2

??Vi(V)	Measured value
		??0	??1.50E-08
??10	??2.00316E-05
		??-10	??-1.99677E-05

And then obtain the value of a, b and c, see Table 3.

Table 3

??c	??1.50E-08
		??a	??1.695E-10
??b	??1.99997E-06

Table 4 is an experimental result.

Table 4

??Vi(V)	Measured value	Calculated value	Deviation
				??10	??20.0316	??2.00316E-05	??0.00E+00
??9	??18.0279	??1.80284E-05	??-5.15E-10
				??8	??16.0250	??1.60256E-05	??-5.68E-10
??7	??14.0228	??1.40231E-05	??-2.61E-10

??Vi(V)	Measured value	Calculated value	Deviation
				??6	??12.0215	??1.20209E-05	??6.08E-10
??5	??10.0193	??1.00191E-05	??2.37E-10
				??4	??8.0172	??8.01757E-06	??-3.72E-10
??3	??6.0162	??6.01642E-06	??-2.20E-10
				??2	??4.0153	??4.01561E-06	??-3.08E-10
??1	??2.0151	??2.01513E-06	??-3.45E-11
				??0	??0.0150	??1.50000E-08	??0.00E+00
??-1	??-1.9844	??-1.98480E-06	??3.96E-10
				??-2	??-3.9840	??-3.98425E-06	??2.52E-10
??-3	??-5.9836	??-5.98337E-06	??-2.30E-10
				??-4	??-7.9822	??-7.98215E-06	??-5.20E-11
??-5	??-9.9810	??-9.98059E-06	??-4.13E-10
				??-6	??-11.9785	??-1.19787E-05	??1.88E-10
??-7	??-13.9761	??-1.39764E-05	??3.49E-10
				??-8	??-15.9736	??-1.59739E-05	??2.72E-10
??-9	??-17.9712	??-1.79710E-05	??-2.44E-10
				??-10	??-19.9677	??-1.99677E-05	??0.00E+00

Second experimental subjects is 1 resitstance voltage divider that maximum output voltage is 100 μ V.

At first, adjust the input voltage Vi of resitstance voltage divider, obtain the result of table 5 for the value that obtains a, b and c.

Table 5

??Vi(V)	Measured value
		??0	??1.63000E-08
??10	??2.00163E-04
		??-10	??-1.99840E-04

And then obtain the value of a, b and c, see Table 6.

Table 6

??c	??1.63E-08
		??a	??1.452E-09
??b	??2.00002E-05

Table 7 is an experimental result.

Table 7

??Vi(V)	Measured value	Calculated value	Deviation
				??10	??200.163	??2.00163E-04	??0.00E+00
??9	??180.135	??1.80135E-04	??-2.62E-10
				??8	??160.110	??1.60110E-04	??-4.28E-10
??7	??140.089	??1.40088E-04	??5.02E-10
				??6	??120.070	??1.20069E-04	??5.28E-10
??5	??100.053	??1.00053E-04	??-3.50E-10
				??4	??80.0410	??8.00401E-05	??8.68E-10
??3	??60.0295	??6.00298E-05	??-3.18E-10
				??2	??40.0220	??4.00224E-05	??-4.08E-10
??1	??20.0172	??2.00179E-05	??-7.02E-10

??Vi(V)	Measured value	Calculated value	Deviation
				??0	??0.0163	??1.63000E-08	??0.00E+00
??-1	??-19.9821	??-1.99824E-05	??2.98E-10
				??-2	??-39.9788	??-3.99782E-05	??-6.08E-10
??-3	??-59.9716	??-5.99711E-05	??-5.18E-10
				??-4	??-79.9615	??-7.99611E-05	??-4.32E-10
??-5	??-99.9482	??-9.99482E-05	??-5.00E-11
				??-6	??-119.932	??-1.19932E-04	??3.28E-10
??-7	??-139.914	??-1.39914E-04	??-3.98E-10
				??-8	??-159.891	??-1.59892E-04	??9.72E-10
??-9	??-179.867	??-1.79867E-04	??4.38E-10
				??-10	??-199.840	??-1.99840E-04	??0.00E+00

Claims (2)

1. the modification method of the non-linear output of DC low-voltage standard source, DC low-voltage standard source adopt the electric resistance partial pressure mode to export, and it is characterized in that comprising the steps:

The correction formula of DC low-voltage standard source output voltage is $V_o=a\·V_i^2+b\·V_i+c,$ V wherein _oBe the output voltage of DC low-voltage standard source, V _iInput voltage for DC low-voltage standard source; C=V _O1, V _O1It is the output voltage values of DC low-voltage standard source when the input voltage of DC low-voltage standard source is 0; $a=\frac{V_{o2}+V_{o3}-2V_{o1}}{2V_m^2},$ $b=\frac{V_{o2}-V_{o3}}{2V_m},$ V _mBe a direct current low-voltage standard source input voltage value, V _O2Be the DC low-voltage standard source output voltage values when the Vi=Vm, V _O3Be the DC low-voltage standard source output voltage values when the Vi=-Vm;

According to the input voltage of described correction formula adjustment DC low-voltage standard source, obtain the output voltage of expectation.

2. according to the modification method of the non-linear output of the described DC low-voltage standard source of claim 1, it is characterized in that when obtaining a, b and c value resitstance voltage divider is in the working environment that steady temperature is T in the DC low-voltage standard source; When utilizing described correction formula correction in the DC low-voltage standard source resitstance voltage divider also be in the working environment of steady temperature for T.

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