CN103149410A - Distributed precision resistor with low load coefficient and implementation method thereof - Google Patents

Abstract

The invention provides a distributed precision resistor with a low load coefficient and an implementation method thereof, and belongs to the filed of large-current precision measurement. The distributed precision resistor with the low load coefficient is a chain-shaped circuit and is formed by a group of small-type precision resistor components with the low load coefficients in a parallel connection mode, wherein the small-type precision resistor components are the same in characteristic. A special point is arranged in the chain-type circuit, and the resistance of a connecting guide line of the whole chain-shaped circuit can be ignored at the special point. A current lead of the distributed precision resistor with the low load coefficient is arranged at an input end of the chain-shaped circuit, and a voltage lead is arranged at the position of an input end of a corresponding link of the special point. Through the distributed precision resistor with the low load coefficient and the implementation method thereof, the whole resistor can keep the low load coefficient after the parallel and can keep other good performance of the resistor components which participate in the parallel. When resistors of 20 ohms are under the load of 50 Mw, change of a resistance value is only 10-9 orders of magnitude, and the resistors exceed a standard of domestic and overseas products, wherein the resistors are prepared through the method.

Description

A kind of distributed low load factor precision resistance and its implementation

Technical field

The invention belongs to large electric current precision measurement field, be specifically related to a kind of distributed low load factor precision resistance and its implementation.

Background technology

The Super-Current Measurement technology has widely to be used.In today that power-saving technology is concerned day by day, large electric current Technology of Precision Measurement seems particularly important.The common method of measuring large electric current is to make electric current to be measured by the four-terminal resistance of a low value, measures the voltage drop that electric current produces on this resistance.The resistance value of the voltage drop that records divided by four-terminal resistance, just can obtain the current value of large electric current.Such four-terminal resistance also often is called as " shunt (shunt) ".Improve the accuracy of this method, key is to guarantee the accuracy of four-terminal resistance.

Can generate heat when the characteristics of resistance device are galvanization, resistance value changes along with heating, and namely resistance value can be along with bearing power (I ²R) increase and change.The load effect of Here it is resistance device.The resistance value relative variation that the per unit bearing power causes is called load factor.

Rely on modern Quantum Hall resistance benchmark, being not difficult, it is accurate to 10 that the resistance value of four-terminal resistance is surveyed ^-9The accuracy of magnitude.But this moment, the bearing power of resistance must be very little, the guarantee accuracy of measurement.When the most high measuring resistance was carried out international comparison, when having stipulated to measure, the bearing power of resistance was 2.5mW.

If the power of resistance consumption is W, electric current is I, and ohmically voltage is reduced to When measuring large electric current, if the bearing power W of resistance is limited in very little quantity, ohmically voltage drop V can be very little.When V fell in measuring voltage, the impact of Noise and Interference made the signal to noise ratio (S/N ratio) of measured signal inadequate, and accuracy can not improve.(that is to say if can greatly reduce the load factor of resistance device, even when passing through larger electric current, resistance change is also very little), resistance value R can use greatlyr, and making to have larger voltage drop IR on resistance, thereby has improved signal to noise ratio (S/N ratio) and accuracy of measurement.Therefore, the load factor of reduction resistance device is an effective way that solves accuracy of measurement and sensitivity contradiction.

At present, the method for abroad for reducing resistance load coefficient is that the size of resistance is amplified, and reduces resistance to the thermal resistance of environment, to reduce the temperature rise of resistance device.With the multipotency of such method, load factor is accomplished 10 ^-7Magnitude, and large-sized resistance device uses inconvenient, expensive.

Summary of the invention

The object of the invention is to solve a difficult problem that exists in above-mentioned prior art, a kind of distributed low load factor precision resistance and its implementation are provided, be used for the large electric current of precision measurement.

The present invention is achieved by the following technical solutions:

A kind of distributed low load factor precision resistance, described distributed low load factor precision resistance is a recurrent circuit, is to be formed in parallel by one group of identical low load factor miniature precision resistive element of characteristic; A particular point is arranged in described recurrent circuit, resistance at the connection wire of the whole recurrent circuit in described particular point place can be ignored, the current feed of described distributed low load factor precision resistance is arranged on the input end of described recurrent circuit, and voltage lead is arranged on the input end of link corresponding to this particular point.

A kind of method that realizes described distributed low load factor precision resistance, at first described method is together in parallel one group of identical low load factor miniature precision resistive element of characteristic becomes a recurrent circuit, and described recurrent circuit being converted to the circuit that is formed by one group of symmetrical four terminal network link, described each symmetrical four terminal network is a link of described recurrent circuit; Then utilize Circuit theory to calculate critical value k ₀, this critical value k ₀A particular point in corresponding described recurrent circuit utilizes the characteristic of this point can eliminate the harmful effect of the connection conductor resistance of whole recurrent circuit.At last current feed is arranged on the input end of described recurrent circuit, voltage lead is arranged on the input end of link corresponding to described particular point, form described distributed low load factor precision resistance.

The described Circuit theory of utilizing calculates critical value k ₀Realize by following steps:

(A) network matrix of described symmetrical four terminal network is:

$\left|\begin{array}{cc}A& B\\ C& D\end{array}\right|=\left|\begin{array}{cc}1+{\mathrm{\α}}^2& 2{\mathrm{\α}}^{2}R\\ \frac{1}{2R}(2+{\mathrm{\α}}^2)& 1+{\mathrm{\α}}^2\end{array}\right|---\left(1\right)$

Wherein, R represents by the resistance value of each resistive element of parallel connection,

${\mathrm{\α}}^2=\frac{r_0}{R}---\left(2\right)$

r ₀The resistance of two connection wires between resistive element;

Characterize the characteristic of described symmetrical four terminal network with the linear electrical parameter of equivalence, corresponding wave impedance is:

$Z_C=\sqrt{\frac{B}{C}}=R\frac{2\mathrm{\α}}{\sqrt{2+{\mathrm{\α}}^2}}---\left(3\right)$

Transmission is:

$\mathrm{\Γ}=\ln (A+\sqrt{\mathrm{BC}})=\ln [\sqrt{\mathrm{BC}+1}+\sqrt{\mathrm{BC}}]$

$=\mathrm{Arsh}\sqrt{\mathrm{BC}}=\mathrm{Arshw}---\left(4\right)$

$w=\sqrt{\mathrm{BC}}==\mathrm{\α}(2+{\mathrm{\α}}^2)---\left(5\right)$

(B) n described symmetrical four terminal network linked, this moment, the voltage at top was U ₁, electric current is I ₁, the voltage of terminal is U _n+1, electric current is I _n+1, the input voltage of middle k link is U _k+1, electric current is I _k+1, following relationship is arranged

U _k＝U _n+1ch(n-k+1)Γ-I _n+1Z _Csh(n-k+1)Γ (6)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}+I_{n+1}\mathrm{ch}(n-k+1)\mathrm{\Γ}---\left(7\right)$

k＝1，2，3，......，(n+1) (8)

K represented the input end of first link at 1 o'clock, and k represents the output terminal of last link when being n+1;

If last link back is unloaded, namely

I _n+1＝0 (9)

(6) formula and (7) formula become

U _k＝U _n+1ch(n-k+1)Γ (10)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}---\left(11\right)$

Also can be had by (11) formula

$I_1=\frac{U_{n+1}}{Z_C}\mathrm{shn\Γ}---\left(12\right)$

To have after (12) formula generation time (10) formula

$U_k=I_1{Z}_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(13\right)$

By (13) formula as can be known, as whole recurrent circuit being used as a four-terminal resistance, current feed is arranged on the input end of described recurrent circuit, voltage lead is arranged on the input end of k link, corresponding four-terminal resistance value is:

$R_k=Z_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(14\right)$

(C) in practical situation, when one group of resistive element was together in parallel, line was generally used copper conductor, and between two elements, the resistance value of line much smaller than by the resistance value of parallel resistance element, namely satisfies

r ₀＜＜R (15)

Again by (2) formula as can be known at this moment

α＜＜1 (16)

(3) formula, (4) formula show, Z _C, Γ is the in a small amount function of α;

(14) formula is carried out Taylor expansion, obtain

$R_k=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]{\mathrm{\α}}^2+......\}$

$=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]\frac{r_0}{R}+......\}---\left(17\right)$

What the back in brace was gone suddenly is in a small amount

High-order term;

(17) in formula, first factor on the equation right side

The resistance that expression connects wire is 0, when being superconductor, and the resistance value after the resistance parallel connection that n resistance is R, namely conductor resistance is the desired electrical resistance of 0 o'clock recurrent circuit;

When the connection wire has resistance, the four-terminal resistance value R in (14) formula _kNeed use for a small amount of

Taylor expansion, namely (17) formula represents;

K satisfies one of following two formulas as the link ordinal number:

$k=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(18\right)$

$k=n+1+\sqrt{\frac{{2n}^2+1}{6}}---\left(19\right)$

By single order in (17) formula in a small amount

The coefficient expression formula learn that the coefficient of single order item is 0; But the link ordinal number k of recurrent circuit should be between 1 to n+1, and k＞n+1 that (19) formula provides does not conform to the actual conditions, so do not consider, (18) formula has provided a critical value k ₀:

$k_0=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(20\right)$

Such k ₀Satisfy inequality 1＜k ₀＜n+1, so this critical value is of practical significance;

Work as k=k ₀The time, a small amount of in the expansion of (17) formula

Coefficient be 0, the four-terminal resistance value R that represents of (17) formula at this moment _kWith ideal value

(situation when connecting the wire non-resistance) is very approaching, only differs between the two

Above high-order that is to say to connect the essentially no impact of resistance of wire, the k that obtains like this this moment in a small amount ₀Be described particular point.

Compared with prior art, the invention has the beneficial effects as follows: can be by larger electric current and load factor is very low by a plurality of resistive elements four-terminal resistance that becomes recurrent circuits and form in parallel, and keep participating in other good characteristic of resistive element in parallel; The harmful effect that connects copper conductor is eliminated.The 20 Europe resistance that are developed into according to the method described in the present invention resistance change when the load of 50mW is only 10 ^-9Magnitude has surpassed the level of domestic and international product.

Description of drawings

Fig. 1 is the schematic diagram of the distributed low load precision resistance of the present invention.

Fig. 2 is symmetrical four terminal network of the prior art, and the present invention utilizes this symmetrical four terminal network as a link of recurrent circuit of the present invention.

Fig. 3 is with the recurrent circuit that forms after the link of the link in a plurality of Fig. 2 in the present invention.

Fig. 4 is the simplification circuit of Fig. 3.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The present invention has taked and different both at home and abroad technology paths, not whole resistance to be amplified but employing distributed frame as shown in Figure 1, namely a lot of identical low load factor miniature precision resistive elements of characteristic formation recurrent circuit that is together in parallel, whole as a distributed four-terminal resistance.As to participate in parts number in parallel be N, and each participates in the 1/N that electric current that resistive element in parallel passes through only has total current.Therefore, even the electric current that whole four-terminal resistance passes through is larger, but the electric current that passes through on each resistive element of participation parallel connection is still very little, and the load that namely is distributed on each element is very little, and the heating of element and the variation of resistance value also reduce thereupon greatly.Therefore the load factor of whole four-terminal resistance also becomes very little.

Such idea seems simpler, but the actual comparatively difficulty that realizes.Because need be with connecting copper conductor when resistive element is in parallel, resistive element in parallel be more, and copper conductor is longer.And the resistance of copper conductor can directly affect the resistance value of whole four-terminal resistance, and accuracy is reduced.Simultaneously, copper conductor has very large temperature coefficient, can make the temperature coefficient of whole four-terminal resistance become large, the load factor variation.Element in parallel is more, affects larger.Therefore, can not get good effect with the method for many element parallel connections, be difficult to be applied in practice.

Key point of the present invention is, a lot of identical low load factor miniature precision resistive elements of characteristic are together in parallel become a recurrent circuit, with the circuit of the described recurrent circuit that is formed in parallel (seeing Fig. 1) equivalent transformation for being formed by one group of symmetrical four terminal network chain link, and this circuit integral body is regarded as a four-terminal resistance, current feed is placed on the recurrent circuit input, and voltage lead is placed on certain place a bit in the middle of recurrent circuit.utilize Circuit theory to find and have a particular point (being node corresponding to critical value k described later) in such recurrent circuit, the equipotential line of drawing whole four-terminal resistance at this particular point (has namely judged the position of particular point resistance by calculating, draw the voltage lead of whole four-terminal resistance from this resistance two ends), at this moment, the resistance r of each R in parallel wire used is negligible on the impact of whole four-terminal resistance resistance, the harmful effect that namely connects copper conductor is eliminated, the load factor of whole four-terminal resistance has just greatly reduced, therefore whole resistance can keep the low load factor after parallel connection and other premium properties that participates in single resistive element in parallel.At home and abroad be showed no in document and be the existence of discussing this particular point.

Specific as follows: Fig. 1 is the situation that many resistive elements are connected in parallel with connecting line.Wherein R represents by the resistance value of each resistive element of parallel connection, r ₀The resistance of two connection wires between resistive element.In order to utilize the theory of recurrent circuit in electrotechnics, first investigate circuit shown in Figure 2, this is the four-pole network of a symmetry, and it is used as a link of recurrent circuit.Many such links are linked, just formed appearance shown in Figure 3.Again two adjacent resistance 2R are connected in parallel, become Fig. 4 (low order end of Fig. 4 is not terminal, and the back also has some links, and the resistance of Fig. 4 low order end is only the resistance of intermediate link, by two 2R and be unified into, so be R).Fig. 4 and Fig. 1 are compared, can see, except two resistance of head and the tail, other are the same (Fig. 1 means the schematic diagram of resistance parallel connection, calculates and all carries out according to Fig. 4, implements at last also to carry out according to Fig. 4) all.And the existing ripe formula of recurrent circuit at last, therefore can be the connected mode of Fig. 4 as distributed sample resistance.But it should be noted that in Fig. 4 circuit in fact with Fig. 3 in circuit be the same.

For the performance of circuit in analysis chart 3 or Fig. 4, the recurrent circuit basic link in can first analysis chart 2.This is a symmetrical four terminal network that is made of resistive element, and its network matrix is

$\left|\begin{array}{cc}A& B\\ C& D\end{array}\right|=\left|\begin{array}{cc}1+{\mathrm{\α}}^2& 2{\mathrm{R\α}}^2\\ \frac{1}{2R}(2+{\mathrm{\α}}^2)& 1+{\mathrm{\α}}^2\end{array}\right|---\left(1\right)$

Wherein, R represents that (R does not herein refer in Fig. 2 the resistance value of resistive element in symmetrical four terminal network by the resistance value of each resistive element of parallel connection.In symmetrical four terminal network in Fig. 2, the resistance value of each resistive element is 2R, and computing formula (1) is exactly to calculate according to Fig. 2, and in formula (1), 2R is an integral body.2R is by the twice of the resistance value R of each resistive element in parallel), r ₀The resistance of two connection wires between resistive element,

${\mathrm{\α}}^2=\frac{r_0}{R}---\left(2\right)$

In electrotechnics, such symmetrical four terminal network also can characterize with the linear electrical parameter of equivalence its characteristic.Corresponding wave impedance is

$Z_C=\sqrt{\frac{B}{C}}=R\frac{2\mathrm{\α}}{\sqrt{2+{\mathrm{\α}}^2}}---\left(3\right)$

Transmission is

$=\mathrm{Arsh}\sqrt{\mathrm{BC}}=\mathrm{Arshw}---\left(4\right)$

$w=\sqrt{\mathrm{BC}}==\mathrm{\α}(2+{\mathrm{\α}}^2)---\left(5\right)$

Now the link shown in n Fig. 2 is linked (chained representation is connected together the input end of the output terminal of front link and back link, is not series connection).This moment, the voltage at top was U ₁, electric current is I ₁, the voltage of terminal is U _n+1, electric current is I _n+1The input voltage of middle k link is U _k+1, electric current is I _k+1, following relationship is arranged

U _k＝U _n+1ch(n-k+1)Γ-I _n+1Z _Csh(n-k+1)Γ (6)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}+I_{n+1}\mathrm{ch}(n-k+1)\mathrm{\Γ}---\left(7\right)$

k＝1，2，3，......，(n+1) (8)

K represented the input end of first link at 1 o'clock, and k represents the output terminal of last link when being n+1.

If last link back is unloaded, namely

I _n+1＝0 (9)

(6) and (7) formula become

U _k＝U _n+1ch(n-k+1)Γ (10)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}---\left(11\right)$

Also can be had by (11) formula

$I_1=\frac{U_{n+1}}{Z_C}\mathrm{shn\Γ}---\left(12\right)$

In generation, have after returning (10) formula

$U_k=I_1{Z}_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(13\right)$

By (13) formula as can be known, as whole recurrent circuit being used as a four-terminal resistance, current feed is placed on the input end of recurrent circuit, and voltage lead is placed on the input end of k link, and corresponding four-terminal resistance value is:

$R_k=Z_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(14\right)$

It is comparatively complicated that this expression formula seems, the below analyzes and point out its practical value to it.

In practical situation, when a plurality of resistive elements were together in parallel, line was generally used copper conductor, between two elements the resistance value of line much smaller than by the resistance value of element in parallel, namely satisfied

r ₀＜＜R (15)

Again by (2) formula as can be known at this moment

α＜＜1 (16)

(3), (4) formula shows, Z _C, Γ is the in a small amount function of α.(14) formula is carried out Taylor expansion, can get

$R_k=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]{\mathrm{\α}}^2+......\}$

$=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]\frac{r_0}{R}+......\}---\left(17\right)$

What in brace, the back was gone suddenly is in a small amount

High-order term.

(17) physical significance of formula clearly.First factor on the equation right side

The resistance that expression connects wire is 0, when being superconductor, and the resistance value after the resistance parallel connection that n resistance is R.Be that conductor resistance is the desired electrical resistance of 0 o'clock recurrent circuit.When having resistance, the connection wire (can be seen that by Fig. 1 two is 2r by two between the resistance in parallel resistance that connect wires ₀), the four-terminal resistance value R in (14) formula _kFor a small amount of

Taylor expansion need represent with (17) formula.It should be noted that in (17) formula, single order in a small amount

The coefficient expression formula.K satisfies one of following two formulas as the link ordinal number:

$k=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(18\right)$

$k=n+1+\sqrt{\frac{{2n}^2+1}{6}}---\left(19\right)$

The coefficient of single order item is 0.But the link ordinal number k of recurrent circuit should be between 1 to n+1, and k＞n+1 that (19) formula provides does not conform to the actual conditions, so do not consider.(18) formula has provided a critical value k ₀:

$k_0=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(20\right)$

Such k ₀Satisfy inequality 1＜k ₀＜n+1 is so this critical value is of practical significance.

Work as k=k ₀The time, a small amount of in the expansion of (17) formula

Coefficient be 0, the four-terminal resistance value R that represents of (17) formula at this moment _kWith ideal value

(situation when connecting the wire non-resistance) is very approaching, only differs between the two Above high-order in a small amount.That is to say and connect the essentially no impact of resistance of wire this moment.

An other significant thing is to determine critical value k ₀(20) formula only require a kind of loose constraint condition (15) or (16) formula, for r ₀And the concrete ratio between R is stipulated.Therefore (20) formula has certain ubiquity, can use under multiple concrete occasion.

Analyze effect of the present invention below by the result of several model experiments:

Experiment one: in table 1 be in recurrent circuit link to count n be 10 o'clock R _kExperiment value and the numerical value that calculates with (14) formula.R is the 1k Ω resistive element of accuracy 0.01%, r ₀Be 58m Ω.In general, connect the thicker copper conductor of wire, r ₀For should be more much smaller than 58m Ω.Have a mind to exaggerate the effect that connects conductor resistance in this experiment, used more elongated enameled wire, make r ₀Larger.

Table 1

As can be seen from Table 1, in the scope of resistive element accuracy 0.01% used, experiment value and calculated value are consistent.K be 5 and the minute differences of 11 o'clock be due to evaluation rounds up.

Desired electrical resistance after 10 links link should be 100 Ω.Calculate according to (20) formula, link number n is 10 o'clock, critical value k ₀For

$k_0=10(1-\frac{1}{\sqrt{3}})+1=5.2---\left(21\right)$

But critical value k in fact ₀Answer round numbers.That is to say k ₀Getting at 5 o'clock is optimum value.Get 6 o'clock also relatively good, but slightly more weaker than getting at 5 o'clock.Data acknowledgement in table 1 these conclusions.At k hour, R _kGreater than 100 Ω.When k is larger, R _kLess than 100 Ω.Equal at 5 o'clock at k, R _kNear ideal value 100 Ω.K equals at 6 o'clock, R _kAlso near ideal value, but than k equal 5 o'clock slightly weaker.That is to say, optimum value but is partial to 5 between 5 and 6.This theoretical calculate value with (21) formula is consistent, then current feed is placed on the input end of recurrent circuit, voltage lead is placed on the input end of the 5th link.

Constraint condition (15) or (16) formula are looser.As long as namely satisfied such constraint condition, critical value k ₀Value just provided by (20) formula, and and r ₀And the concrete ratio relation between R is little.In order to confirm this point, done again experiment two.

Experiment two: connect wire in this experiment and changed longer enameled wire into, the resistance that connects wire has enlarged one times of left and right, reaches 110m Ω.Observe R _kExperiment value and the situation of calculated value, result is as shown in table 2.Can see, best k value remains between 5 and 6, but is partial to 5.So just from experimentally having confirmed critical value k ₀Can be determined by (20) formula, with r ₀And the concrete ratio relation between R is little.This is very favourable to practicality.

Table 2

Twice confirmatory experiment explanation shown in table 1 and table 2, theoretical calculating of the present invention is consistent with experiment, that is to say that the method with the low distributed precision resistance of load factor of recurrent circuit realization that the present invention proposes is feasible, can be used as embodiment and use.The back will illustrate concrete effect with embodiment.

Distributed precision resistance of the present invention has many practical occasions.For example when carrying out the high precision measurement of mutual inductance, require 50mA current measurement to 10 ^-8The accuracy of magnitude.If with the very little four-terminal resistance of resistance, the voltage that sampling obtains will be very low, is difficult to reach 10 in order to reduce ohmically load ^-8The accuracy of magnitude.If be 1V but make sampled voltage in order to improve accuracy of measurement, the power consumption on shunt will reach 50mW, the 2.5mW that limits when being much higher than international comparison.The present invention utilizes recurrent circuit to realize the method for distributed four-terminal resistance, has obtained good effect, and the load factor of the resistance of actual measurement is minimum, is 10 ^-9Magnitude.

In experiment, the electric current that distributed precision resistance passes through is 50mA.Obtain the sampled voltage of 1V, the resistance of distributed precision resistance should be 20 Ω.The compact high precision 500 Ω manganese-copper filament resistive elements of customization have been adopted in experiment.Two elements are together in series becomes the assembly of resistance 1000 Ω, then 50 such assemblies are consisted of recurrent circuit with method recited above, has realized the distributed precision resistance of 20 Ω.According to the analysis of front, the voltage lead of this distributed precision resistance is at the optimum value k that satisfies (20) formula ₀Draw, resistive instability and the very large temperature coefficient of the copper wire connection wire that this moment is long can fall very littlely to the performance impact of whole distributed precision resistance.

But, at present will be from experimentally measuring 10 ^-9The resistance load coefficient of magnitude is very difficult, because not yet make the so little commodity resistance of overload coefficient at present both at home and abroad, can be used as the 20 distributed precision resistances of Ω that the standard in investigating checks the present invention to obtain.

In the face of this difficulty, the method that the present invention has designed a kind of " self-verification ", specific as follows: as in order to obtain high-precision load factor experimental result, to have consisted of another distributed resistance with 500 same Ω resistive elements again.4 500 Ω resistive elements to be together in series consist of the assembly of 2000 Ω at this moment.20 2000 same Ω assemblies described method formation recurrent circuit herein, become the distributed resistance of 100 Ω again, voltage lead is also at the optimum value k that satisfies (18) formula ₀Draw at the place.This resistance and the foregoing 20 distributed precision resistances of Ω put into same oil groove with the 6622A type DCC bridge arm ratio of Guildline company than resistance.

Can notice, in the 20 distributed precision resistances of Ω, each assembly is by two 500 Ω resistive element series connection.And in 100 Ω distributed resistance, each assembly is in series by 4 500 Ω resistive elements.On the other hand, during with DCC electric bridge comparison resistance, the voltage on the 20 distributed precision resistances of Ω and 100 Ω distributed resistance all equals the output voltage of electric bridge.Therefore in the 20 distributed precision resistances of Ω and 100 Ω distributed resistance to be compared, although 500 Ω resistive elements used are the same, the voltage on each element is also different.Voltage in voltage ratio 100 Ω distributed resistance in the 20 distributed precision resistances of Ω on each 500 Ω resistive element on each element is twice, large 4 times of power terminations.The load of the whole 20 distributed precision resistances of Ω is also than the load of 100 Ω distributed resistance large 4 times, when bridge output voltage changes, the variation of electric bridge reading is mainly the load effect that has reflected the 20 distributed precision resistances of Ω, so just can reach the purpose of " self-verification ".

Experiment three: the experimental data of " self-verification " is as shown in table 3, the electric bridge reading relative difference when table 3 has provided different temperatures and different bridge output voltage (in the 20 distributed precision resistances of Ω, element load is 4 times of element load in 100 Ω distributed resistance).In order to reduce the impact of reading dispersiveness, adopted repeatedly reading on average to reach symmetrical observation, obtained 10 ^-9The readout resolutions of magnitude.Bridge output voltage is equivalent to the normal load state of the 20 distributed precision resistances of Ω when being 1V.When bridge output voltage is 0.5V, the load of the 20 distributed precision resistances of Ω has dropped to 1/4, and the variation of comparing electric bridge reading in two kinds of situations just can judge the load factor size of the 20 distributed precision resistances of Ω.

Table 3

Can see from table 3, oil sump temperature not simultaneously, load is different for the impact of the 20 distributed precision resistances of Ω.According to measured data, the zero temperature coefficient point of element used is near 24 ℃.The load effect that records when oil sump temperature is 24 ℃ is only 10 ^-9Magnitude, the dispersiveness with experimental data is suitable.When leaving 1 ℃ of zero temperature coefficient point, the impact of load can increase to 10 ^-8Magnitude.And the opposite in sign that in the time of 23 ℃ and 25 ℃ the time, reading changes, this is because near zero temperature coefficient point, the resistance value variation with temperature is parabolic shape, and 23 ℃ and 25 ℃ of these two temperature spots just in time are in the both sides of 24 ℃ of zero temperature coefficient points, and temperature coefficient is opposite.

Analysis according to the front, for the 20 distributed precision resistances of Ω and the 100 Ω distributed resistance that are compared in table 3, the impact of the copper conductor of contact resistance element can be ignored, and the load factor of the 20 distributed precision resistances of Ω of therefore observing in experiment should just equal the load factor of resistive element itself.In order to confirm this point, designed again experiment four.

What experiment four was compared is the 20 distributed precision resistances of Ω and another 100 Ω resistance.This resistance directly just ties together with 5 500 same Ω resistive elements, welds after extension line is stranded, becomes 100 Ω resistance.Namely at all not with additional connection wire, the load factor of measuring is exactly the load factor of element itself.After these direct 100 Ω resistance access comparison bridges in parallel, each is equal to the output voltage of electric bridge by the voltage on 500 Ω resistive elements of parallel connection.On the other hand, the front had said that in the 20 distributed precision resistances of Ω, each assembly was in series by two 500 Ω resistive elements, voltage on each element is only half bridge output voltage, its load be only in 100 Ω resistance directly in parallel element load 1/4.When therefore, in this time experiment, bridge output voltage changes, the variation of electric bridge reading has mainly reflected the load effect of 500 Ω resistive elements in 100 Ω resistance itself.The result of experiment four is as shown in table 4, electric bridge reading relative difference when table 4 has provided different temperatures and different bridge output voltage (in the 20 distributed precision resistances of Ω element load be in 100 Ω resistance element load 1/4), can see by analyzing, basic condition is consistent with table 3, is also to locate the load effect minimum 24 ℃ of the zero temperature coefficient points of element.Locate load at 23 ℃ and 25 ℃ larger in than table 3 on the impact of resistance value, this be because current experiment reflection be the load effect of 500 Ω resistive elements in 100 Ω resistance, and added whole bridge output voltage on each element.And in table 3 reflection be the load effect of the 20 distributed precision resistances of Ω, only added half bridge output voltage in this resistance on each resistive element, load be only in 100 Ω resistance element 1/4, what the impact of load will be than in table 4 is little.It is further noted that in addition, opposite in 23 ℃ and 25 ℃ symbols of locating electric bridge reading difference and table 3 in table 4, this is because the electric bridge reading is the ratio value of two resistance that are compared, and the position of the resistance of responsive to load in ratio value is just in time opposite in twice experiment.In table 3 resistance value of responsive to load is on the denominator of ratio value, in table 4 on molecule.

The situation of comprehensive comparison sheet 3 and twice experiment of table 4 can see that the load effect of the 20 distributed precision resistances of Ω and the load effect of element itself are consistent.That is to say, when consisting of recurrent circuit, the resistance value of the copper conductor of contact resistance element used can be ignored really.The resistive instability of long copper wire connection wire and very large temperature coefficient reduce very littlely to the performance impact of whole resistance.

Table 4

The above is the load factor experimental data of distributed precision resistance.In actual use, the stability in time of this resistance is also a very important index.When distributed precision resistance had just been made, experiment showed that the variable quantity of its every day is 10 ^-8Magnitude.After individual month of time, stability has had obvious improvement.In 15 days, the linear segment of variable quantity only has 1 * 10 ^-7, the resistance value slow drift amount of every day has dropped to 10 ^-9Magnitude.Using for reality, has been goodish performance.

Technique scheme is one embodiment of the present invention, for those skilled in the art, on the basis that the invention discloses application process and principle, be easy to make various types of improvement or distortion, and be not limited only to the described method of the above-mentioned embodiment of the present invention, therefore previously described mode is just preferred, and does not have restrictive meaning.

Claims (3)

1. distributed low load factor precision resistance, it is characterized in that: described distributed low load factor precision resistance is a recurrent circuit, is to be formed in parallel by one group of identical low load factor miniature precision resistive element of characteristic; A particular point is arranged in described recurrent circuit, resistance at the connection wire of the whole recurrent circuit in described particular point place can be ignored, the current feed of described distributed low load factor precision resistance is arranged on the input end of described recurrent circuit, and voltage lead is arranged on the input end of link corresponding to this particular point.

2. method that realizes the described distributed low load factor precision resistance of claim 1, it is characterized in that: at first described method is together in parallel one group of identical low load factor miniature precision resistive element of characteristic becomes a recurrent circuit, and described recurrent circuit being converted to the circuit that is formed by one group of symmetrical four terminal network link, described each symmetrical four terminal network is a link of described recurrent circuit; Then utilize Circuit theory to calculate critical value k ₀, this critical value k ₀A particular point in corresponding described recurrent circuit; At last current feed is arranged on the input end of described recurrent circuit, voltage lead is arranged on the input end of link corresponding to described particular point, form described distributed low load factor precision resistance.

3. the method that realizes distributed low load factor precision resistance according to claim 2, it is characterized in that: the described Circuit theory of utilizing calculates critical value k ₀Realize by following steps:

(A) network matrix of described symmetrical four terminal network is:

$\left|\begin{array}{cc}A& B\\ C& D\end{array}\right|=\left|\begin{array}{cc}1+{\mathrm{\α}}^2& 2{\mathrm{\α}}^{2}R\\ \frac{1}{2R}(2+{\mathrm{\α}}^2)& 1+{\mathrm{\α}}^2\end{array}\right|---\left(1\right)$

Wherein, R represents by the resistance value of each resistive element of parallel connection,

${\mathrm{\α}}^2=\frac{r_0}{R}---\left(2\right)$

r ₀The resistance of two connection wires between resistive element,

Characterize the characteristic of described symmetrical four terminal network with the linear electrical parameter of equivalence, corresponding wave impedance is:

$Z_C=\sqrt{\frac{B}{C}}=R\frac{2\mathrm{\α}}{\sqrt{2+{\mathrm{\α}}^2}}---\left(3\right)$

Transmission is:

$\mathrm{\Γ}=\ln (A+\sqrt{\mathrm{BC}})=\ln [\sqrt{\mathrm{BC}+1}+\sqrt{\mathrm{BC}}]$

$=\mathrm{Arsh}\sqrt{\mathrm{BC}}=\mathrm{Arshw}---\left(4\right)$

$w=\sqrt{\mathrm{BC}}==\mathrm{\α}(2+{\mathrm{\α}}^2)---\left(5\right)$

(B) n described symmetrical four terminal network linked, this moment, the voltage at top was U ₁, electric current is I ₁, the voltage of terminal is U _n+1, electric current is I _n+1, the input voltage of middle k link is U _K+1, electric current is I _k+1, following relationship is arranged

U _k＝U _n+1ch(n-k+1)Γ-I _n+1Z _Csh(n-k+1)Γ (6)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}+I_{n+1}\mathrm{ch}(n-k+1)\mathrm{\Γ}---\left(7\right)$

k＝1，2，3，......，(n+1) (8)

K represented the input end of first link at 1 o'clock, and k represents the output terminal of last link when being n+1;

If last link back is unloaded, namely

I _n+1＝0 (9)

(6) formula and (7) formula become

U _k＝U _n+1ch(n-k+1)Γ (10)

$I_k=\frac{U_{n+1}}{Z_C}\mathrm{sh}(n-k+1)\mathrm{\Γ}---\left(11\right)$

Also can be had by (11) formula

$I_1=\frac{U_{n+1}}{Z_C}\mathrm{shn\Γ}---\left(12\right)$

To have after (12) formula generation time (10) formula

$U_k=I_1{Z}_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(13\right)$

By (13) formula as can be known, as whole recurrent circuit being used as a four-terminal resistance, current feed is arranged on the input end of described recurrent circuit, voltage lead is arranged on the input end of k link, corresponding four-terminal resistance value is:

$R_k=Z_C\frac{\mathrm{ch}(n-k+1)\mathrm{\Γ}}{\mathrm{shn\Γ}}---\left(14\right)$

(C) between two elements, the resistance value of line much smaller than by the resistance value of parallel resistance element, namely satisfies

r ₀＜＜R (15)

Again by (2) formula as can be known at this moment

α＜＜1 (16)

(3) formula, (4) formula show, Z _C, Γ is the in a small amount function of α;

(14) formula is carried out Taylor expansion, obtain

$R_k=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]{\mathrm{\α}}^2+......\}$

$=\frac{R}{n}\{1-\frac{1}{6}\·[k-(n+1-\sqrt{\frac{2n^2+1}{6}})\left]\right[k-(n+1+\sqrt{\frac{2n^2+1}{6}})]\frac{r_0}{R}+......\}---\left(17\right)$

Suspension points in brace represents a small amount of that neglects

High-order term;

(17) in formula, first factor on the equation right side

The resistance that expression connects wire is 0, when being superconductor, and the resistance value after the resistance parallel connection that n resistance is R, namely conductor resistance is the desired electrical resistance of 0 o'clock recurrent circuit;

When the connection wire has resistance, the four-terminal resistance value R in (14) formula _kNeed use for a small amount of

Equal Taylor expansion, namely (17) formula represents;

K satisfies one of following two formulas as the link ordinal number:

$k=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(18\right)$

$k=n+1+\sqrt{\frac{{2n}^2+1}{6}}---\left(19\right)$

By single order in (17) formula in a small amount

The coefficient expression formula learn that the coefficient of single order item is 0; But the link ordinal number k of recurrent circuit should be between 1 to n+1, and k＞n+1 that (19) formula provides does not conform to the actual conditions, so do not consider, (18) formula has provided a critical value k ₀:

$k_0=n+1-\sqrt{\frac{{2n}^2+1}{6}}---\left(20\right)$

Such k ₀Satisfy inequality 1＜k ₀＜n+1, so this critical value is of practical significance;

Work as k=k ₀The time, a small amount of in the expansion of (17) formula

Coefficient be 0, the four-terminal resistance value R that represents of (17) formula at this moment _kWith ideal value

Between only differ Above high-order that is to say that the resistance of the connection wire of whole recurrent circuit this moment is negligible in a small amount.

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