CN102830143A - Method and key circuit for measuring solution conductivity through triangular wave excitation and integral processing - Google Patents

Method and key circuit for measuring solution conductivity through triangular wave excitation and integral processing Download PDF

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CN102830143A
CN102830143A CN201210305745XA CN201210305745A CN102830143A CN 102830143 A CN102830143 A CN 102830143A CN 201210305745X A CN201210305745X A CN 201210305745XA CN 201210305745 A CN201210305745 A CN 201210305745A CN 102830143 A CN102830143 A CN 102830143A
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resistance
amplifier
triangular wave
integral
input end
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CN102830143B (en
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廖晓东
洪亲
陈由甲
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Fujian Normal University
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Abstract

The invention discloses a method and a key circuit for measuring solution conductivity through triangular wave excitation and integral processing. The method comprises the following steps of: exciting an electrode by using a triangular wave voltage signal with amplitude U and period 2T, integrating excitation voltage and electrode response current at two integral intervals of [t1, tm] and [t1, t2] at any two different moments t1 and t2 and a middle moment tm of the two moments of an upper band or a lower band of the excitation signal, and calculating solution resistance Rx according to one of two formulas shown in the specification; or solving the conductivity by using G=K/Rx, wherein K is electrode constant. According to the technical scheme, a circuit for integrating an excitation voltage signal and a current signal responded by the electrode is also provided. According to the scheme, the influence of distributed capacitance of the electrode is completely eliminated, influence of random interference on a measuring accuracy can be eliminated, and the measuring stability is high.

Description

The electrical conductivity of solution measuring method and the Key Circuit of triangular wave excitation and integral processing
Technical field
The present invention relates to the measuring method of electrical conductivity of solution or resistivity, relating in particular to and adopting triangular wave is the measuring method of pumping signal, is the electrical conductivity of solution or the resistivity measurement method of accurately evading the distribution of electrodes capacitive effect.
Background technology
The fundamental method of measurement of electrical conductivity of solution is the voltage U of measuring on the two ends that are applied to the electrode of inserting solution DWith the electric current I that flows through electrode, calculate the resistance R=U between the electrode D/ I, with the conductivity of G=K/R calculating solution, wherein K is an electrode constant again.But the electrode of inserting in the solution can produce polarization after energising, make the voltage U that records DNot the voltage at the two ends of solution own in fact, but be applied to the voltage on two virtual electronic devices of electric double layer capacitance that one of solution resistance series connection relates to solution/metal electrode interface process, so formula R=U DThere is theoretical error in/I; In order to reduce the influence of electrode polarization to accuracy of measurement; Basic skills is the ac-excited signal that on electrode, applies the positive-negative polarity symmetry; But under ac-excited signal effect; The electric current I that records not is the electric current that flows through solution merely; But flow through the total current of solution resistance branch road parallel connection distribution of electrodes electric capacity (comprising electrode interelectrode capacity and contact conductor electric capacity) branch road, therefore use ac-excited method when reducing the electrode polarization influence, but to introduce of the influence of distribution of electrodes electric capacity to measurement.
Summary of the invention
The purpose of this invention is to provide a kind of adverse effect that can accurately eliminate distribution of electrodes electric capacity to measurement, obtain the measuring method of electrical conductivity of solution or resistivity.
The technical scheme that realizes above-mentioned purpose is:
Method: electrode is inserted in the detected solution; The employing voltage magnitude is U, cycle to be that the interchange symmetric triangular wave voltage signal of 2T encourages electrode, on the driving voltage signal wave band or down wave band get two different t1 and t2 constantly in the period arbitrarily, calculate t1 and t2 in the middle of moment tm; At [t1; Tm] and [t1, t2] two integrating ranges driving voltage and electrode response electric current are carried out integration, calculate the solution resistance value R that obtains required mensuration by one of following two formulas x
R x = U 2 T | ( t 2 - t 1 ) 2 ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt | Or R x = | ∫ t 1 t 2 Udt - 2 ∫ t 1 Tm Udt ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt |
Utilize formula G=K/R again xObtain the conductivity of solution to be measured, K is an electrode constant.
Key Circuit: the integrating circuit to the current signal of the integration of driving voltage signal and electrode response is made up of conductance cell, amplifier 1, amplifier 2, amplifier 3, capacitor C 1, capacitor C 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, resistance R 5 and resistance R 6.One termination triangular wave driving voltage signal u of conductance cell, the reverse input end of another termination amplifier 1; Link to each other through resistance R 5 between the reverse input end of amplifier 1 and the output terminal Ur, the input end in the same way of amplifier 1 is connected to signal ground through resistance R 6, and the output terminal Ur of amplifier 1 is connected to the reverse input end of amplifier 2 through resistance R 3; Link to each other through capacitor C 2 between the reverse input end of amplifier 2 and the output terminal Ui, the input end in the same way of amplifier 2 is connected to signal ground through resistance R 4, and the output terminal Ui of amplifier 2 is exactly the integration of electrode response current i, connects subsequent process circuit; The reverse input end of amplifier 3 links to each other through capacitor C 1 with output terminal Uv; The reverse input end of amplifier 3 is connected to triangular wave driving voltage signal u through resistance R 1; The input end in the same way of amplifier 3 is connected to signal ground through resistance R 2; The output terminal Uv of amplifier 3 is exactly the integration of triangular wave driving voltage signal u, connects subsequent process circuit.
In the technique scheme, the crest that described interchange symmetric triangular ripple is meant triangular wave is opposite with the polarity of trough, amplitude equates, go up wave band equates with the slope absolute value of following wave band.Described driving voltage and electrode response electric current are carried out integration, integration method adopts numerical integration or mimic channel integration.
The electrical conductivity of solution measuring method of triangular wave excitation of the present invention and integral processing and Key Circuit are compared existing measuring method and had following beneficial effect: pumping signal is simple; Adopt the triangular wave ac voltage signal of single-frequency to encourage; The electric current that flows through distribution of electrodes electric capacity is the constant current that alternately commutates, and the influence of distribution of electrodes electric capacity can be eliminated fully, and the measurements and calculations method is succinct; Operand is few, and measurement stability is high.
Description of drawings
Fig. 1 is the equivalent physical model figure of conductance cell.
Fig. 2 is the integrating circuit to triangular wave driving voltage signal u and electrode response current i.
Fig. 3 is ac-excited voltage signal of triangular wave and electrode response current signal waveform correlation figure
Fig. 4 is that the derivation of equation is auxiliary with figure, and the figure bend is represented electrode response electric current variation relation in time.
Embodiment
Further describe below in conjunction with the principle and the implementation step of accompanying drawing technical scheme of the present invention:
Principle of the present invention is:
Under the sufficiently high condition of the frequency of the ac-excited signal that puts on electrode; The polarization influence can be ignored; Therefore the circuit model of conductance cell can be represented with Fig. 1, and this model is not to be suitable under harsh especially most of situations for accuracy requirement, R among Fig. 1 xThe resistance of representing solution to be measured; C pExpression distribution of electrodes electric capacity (comprising the electric capacity that electrode pad electric capacity, lead capacitance, solution concentration polarization cause); i xThe flow through electric current of solution to be measured of expression, reference direction is for from left to right; i pThe distribution of electrodes capacitor C is flow through in expression pElectric current, reference direction is for from left to right; I is i xWith i pThe interflow, reference direction is for from left to right, it is the electrode response electric current that the back literary composition is called for short i; U representes the driving voltage signal; Be to exchange symmetric triangular ripple (the back literary composition is called for short triangular wave, and " symmetry " refers to that the crest of triangular wave equates, goes up wave band and equates with the slope absolute value of following wave band with the amplitude of trough), its reference direction is that a left side is positive right negative; The last wave band of triangular wave is T with the duration of following wave band; Triangle wave period is 2T, and the amplitude of crest and trough is U, and the oscillogram of driving voltage signal u is shown in a among Fig. 3.
According to physics principle, flow through the distribution of electrodes capacitor C pCurrent i pSatisfy following formula
i p=C pdu/dt…………………………………………………………………(1)
Triangular wave driving voltage signal u except locate at crest and 2 in trough can not differentiate, can lead at last wave band and following wave band, owing to its piecewise linear characteristics everywhere; Du/dt is constant at last wave band and following wave band; Be respectively 2U/T and-2U/T, so during last wave band
i p=C p·2U/T………………………………………………………………(2)
During the following wave band of triangular wave driving voltage signal u,
i p=-C p·2U/T…………………………………………………………………(3)
i pOscillogram see the b among Fig. 3, be that cycle is the bipolarity ac square wave of 2T;
Flow through the current i of solution to be measured xObey Ohm law
i x=u/R x………………………………………………………………(4)
i xWaveform see the c among Fig. 3, its waveform is with the similar of triangular wave driving voltage signal u but slope maybe be different;
The electrode response current i is the electric current that can directly measure, according to Kirchhoff's current law (KCL),
i=i x+i p……………………………………………………………………(5)
The waveform of i is seen the d among Fig. 3, is that a cycle is the twolip sawtooth wave of 2T;
On triangular wave driving voltage signal u, appoint in the wave band and get two t1 and t2 constantly, be located at this two moment, the value of triangular wave driving voltage signal u is u T1And u T2, the value of electrode response current i is made as i T1And i T2, flow through the current i of solution to be measured xValue be made as i Xt1And i Xt2, flow through the distribution of electrodes capacitor C pCurrent i pValue be made as i Pt1And i Pt2, obviously according to (2) formula,
i pt1=i pt2………………………………………………………………………(6)
According to (4) formula,
i xt1=u t1/R x……………………………………………………………(7)
i xt2=u t2/R x…………………………………………………………………(8)
According to (5) formula,
i t1=i xt1+i pt1………………………………………………………………(9)
i t2=i xt2+i pt2……………………………………………………………(10)
(10) subtract each other respectively on formula and (9) formula both sides
i t2-i t1=(i xt2+i pt2)-(i xt1+i pt1)=(i xt2-i xt1)+(i pt2-i pt1)……………(11)
Also get with (6), (7), (8) formula substitution (11) formula
i t2-i t1=u t2/R x-u t1/R x=(u t2-u t1)/R x……………………………(12)
Arrangement (12) formula gets
R x=(u t2-u t1)/(i t2-i t1)…………………………………………………(13)
(13) formula shows: as long as measure the value u of triangular wave driving voltage signal u constantly at t1 and t2 T1And u T2And the value i of electrode response current i T1And i T2, just can be according to the resistance R of (13) formula calculating detected solution xBecause the piecewise linear characteristics of triangular wave driving voltage signal u with reference to a among the figure 3, obviously have during last wave band
du/dt=(u t2-u t1)/(t2-t1)=2U/T…………………………………………(14)
Arrangement (14) formula gets
u t2-u t1=(t2-t1)·2U/T…………………………………………………(15)
Get with (15) formula substitution (13) formula
R x=2U(t2-t1)/(T(i t2-i t1))……………………………………………(16)
In like manner, appoint at the following wave band of triangular wave driving voltage signal u and to get two constantly t1 and t2, can release
R x=-2U(t2-t1)/(T(i t2-i t1))……………………………………………(17)
Comprehensively (16) and (17) two formulas get
R x=|2U(t2-t1)/(T(i t2-i t1))|……………………………………………(18)
(18) formula shows, if on triangular wave driving voltage signal u wave band or down wave band appoint and get two t1 and t2 constantly, measure electrode response current i in these two moment T1And i T2, calculate the mistiming t2-t1 in two moment and the electrode response difference between currents i in two moment T2-i T1, substitution (18) formula can calculate the resistance R of solution to be measured respectively x
Calculate the resistance R of solution to be measured according to (13) formula or (18) formula xRequirement detects the instantaneous value of the voltage and current in changing, and stability, anti-interference and the precise digitization etc. of testing circuit are had relatively high expectations, and increases circuit cost.Can be out of shape (13) formula or (18) formula to this problem, convert into the form of electric current and voltage integrating meter is found the solution again, to the distortion of (18) formula, specific as follows:
R x = | 2 U ( t 2 - t 1 ) / ( T ( i t 2 - i t 1 ) ) | = 2 U T | ( t 2 - t 1 ) 2 ( i t 2 - i t 1 ) ( t 2 - t 1 ) | . . . ( 19 )
With reference to figure 4; Oblique line among the figure representes that the electrode response current i concerns over time; T1 and t2 are any two moment in the last wave band of triangular wave driving voltage signal u, the vertical line of making t axle (time shaft) constantly at t1 hand over the t axle in P, hand over oblique line in A, the vertical line of making the t axle constantly at t2 hand over the t axle in Q, hand over oblique line in C; The mean value of t1 and t2 promptly (t1+t2)/2=tm vertical line of making the t axle constantly hand over the t axle in M, hand over oblique line in N; Cross the A point do the parallel lines of t axle hand over the MN line in D, hand over the QC line in B, cross parallel lines friendship QC line that N point makes the t axle in E, obviously have the area of △ ADE to equal the area of △ NEC; The △ ADE area that the area of square DBEN equals 2 times; The area of rectangle APMD equals the area of rectangle DMQB, and then the area that can the find out quadrilateral APQC area that deducts 2 times quadrilateral APMN equals the area of square DBEN, (i in (19) formula T2-i T1) the △ ABC area that equals 2 times of value (t2-t1), also equal the area of 4 times square DBEN, therefore (i in (19) formula T2-i T1) (t2-t1) the value area that the equals quadrilateral APQC area gained difference that deducts 2 times quadrilateral APMN takes advantage of 4, the area of quadrilateral APQC equals the electrode response electric current in [t1, t2] interval integrated value, is designated as The area of quadrilateral APMN equals the electrode response electric current in [t1, tm] interval integrated value, is designated as (19) formula can be rewritten as in view of the above:
R x = U 2 T | ( t 2 - t 1 ) 2 ∫ t 1 t 2 idt - 2 ∫ t 1 tm idt | . . . ( 20 )
T1 and t2 are at a distance of big more; It is more little to measure the error of calculation; Typically get t2-t1=T, even t1 is in the interior starting point (trough) of last wave band of triangular wave driving voltage signal u, t2 is in the interior terminal point (crest) of last wave band of triangular wave driving voltage signal u; Tm then is the intermediate point of the last wave band of triangular wave driving voltage signal u, and (20) formula abbreviation again is:
R x = 1 2 | UT ∫ t 1 t 2 idt - 2 ∫ t 1 tm idt | . . . ( 21 )
Otherwise; Make t1 be in the interior starting point (crest) of following wave band of triangular wave driving voltage signal u; T2 is in the interior terminal point (trough) of following wave band of triangular wave driving voltage signal u, and tm is that the intermediate point of the following wave band of triangular wave driving voltage signal u also can be derived (21) formula.If t1 and t2 are interior any two moment of following wave band of triangular wave driving voltage signal u, also can in like manner derive (20) formula.
In like manner (13) formula is done same integral transformation, and it is constant to establish the definition of t1, t2, tm, can push away so:
R x = | ∫ t 1 t 2 udt - 2 ∫ t 1 tm udt ∫ t 1 t 2 idt - 2 ∫ t 1 tm idt | . . . ( 22 )
(20), (21), (22) formula comprise integral operation, integral operation can be adopted numerical integration, the precision of numerical integration and sampling frequency, it is relevant with the number of significant digit of numerical evaluation etc. that numerical value stores, integral operation also can be adopted Realization of Analog Circuit.
The integral operation of triangular wave driving voltage signal u and the integrating circuit of electrode response current i are seen Fig. 4, are made up of conductance cell, amplifier 1, amplifier 2, amplifier 3, capacitor C 1, capacitor C 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, resistance R 5 and resistance R 6.One termination triangular wave driving voltage signal u of conductance cell, the reverse input end of another termination amplifier 1; Link to each other through resistance R 5 between the reverse input end of amplifier 1 and the output terminal Ur, the input end in the same way of amplifier 1 is connected to signal ground through resistance R 6, and the output terminal Ur of amplifier 1 is connected to the reverse input end of amplifier 2 through resistance R 3; Link to each other through capacitor C 2 between the reverse input end of amplifier 2 and the output terminal Ui, the input end in the same way of amplifier 2 is connected to signal ground through resistance R 4, and the output terminal Ui of amplifier 2 is exactly the integration of electrode response current i, connects subsequent process circuit; The reverse input end of amplifier 3 links to each other through capacitor C 1 with output terminal Uv; The reverse input end of amplifier 3 is connected to triangular wave driving voltage signal u through resistance R 1; The input end in the same way of amplifier 3 is connected to signal ground through resistance R 2; The output terminal Uv of amplifier 3 is exactly the integration of triangular wave driving voltage signal u, connects subsequent process circuit.
The circuit working principle analysis is following: the resistance of resistance R 5 and resistance R 6 is identical all to be 1 ohm; The identical Rs that is made as of the resistance of resistance R 1, R2, R3, R4; The capacitance of capacitor C 1 and C2 equates to be made as Cs; So according to electronics principle Ur=-R5i=-i, Ui=-∫ Ur/R3 dt/C2=-∫ Ur/Rs dt/Cs=∫ idt/ (RsCs) explains that the integration that Ui equals the electrode response current i is that ∫ idt dwindles RsCs doubly; Uv=-∫ u/R1 dt/C1=-∫ u/Rs dt/Cs=-∫ u dt/ (RsCs), explain integration that Uv equals triangular wave driving voltage signal u be ∫ u dt dwindle-RsCs doubly; Dwindled same multiple between the two, just through behind the integrating circuit, the symbol changeabout of the integrated value of triangular wave driving voltage signal u, as long as in subsequent treatment, correct symbol; Perhaps wave band carries out integration to the electrode response current i on triangular wave driving voltage signal u; And driving voltage signal u is carried out integration at the following wave band of triangular wave driving voltage signal u; The two has promptly dwindled with value with symbol like this; Substitution (22) formula computing will keep the ratio of actual value after the integration of driving voltage signal u and electrode response current i dwindles with value, carry out R as adopting (20) or (21) formula xFind the solution, then need amplify RsCs doubly to operation result.The effect of resistance R 2, resistance R 4 and resistance R 6 is make amplifier equal with the input impedance of reverse input end in the same way in the circuit, makes discharge circuit symmetry more, reduces zero migration.
Embodiment one
Based on the foregoing invention principle, draw the electrical conductivity of solution measuring method and the Key Circuit of triangular wave excitation and integral processing, comprise following method and core circuit:
1) method:
Electrode is inserted in the detected solution; The employing voltage magnitude is U, cycle to be that the interchange symmetric triangular wave voltage signal of 2T encourages electrode, on the driving voltage signal wave band or down wave band get two different t1 and t2 constantly in the period arbitrarily, calculate t1 and t2 in the middle of moment tm; At [t1; Tm] and [t1, t2] two integrating ranges driving voltage and electrode response electric current are carried out integration, calculate the solution resistance value R that obtains required mensuration by one of following two formulas x
R x = U 2 T | ( t 2 - t 1 ) 2 ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt | Or R x = | ∫ t 1 t 2 Udt - 2 ∫ t 1 Tm Udt ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt |
Utilize formula G=K/R again xObtain the conductivity of solution to be measured, K is an electrode constant.The crest that above-mentioned interchange symmetric triangular ripple is meant triangular wave is opposite with the polarity of trough, amplitude equates, go up wave band equates with the slope absolute value of following wave band.Described driving voltage and electrode response electric current are carried out integration, integration method adopts numerical integration or mimic channel integration.
2) Key Circuit
Integrating circuit to the current signal of driving voltage signal and electrode response is made up of conductance cell, amplifier 1, amplifier 2, amplifier 3, capacitor C 1, capacitor C 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, resistance R 5 and resistance R 6.One termination triangular wave driving voltage signal u of conductance cell, the reverse input end of another termination amplifier 1; Link to each other through resistance R 5 between the reverse input end of amplifier 1 and the output terminal Ur, the input end in the same way of amplifier 1 is connected to signal ground through resistance R 6, and the output terminal Ur of amplifier 1 is connected to the reverse input end of amplifier 2 through resistance R 3; Link to each other through capacitor C 2 between the reverse input end of amplifier 2 and the output terminal Ui, the input end in the same way of amplifier 2 is connected to signal ground through resistance R 4, and the output terminal Ui of amplifier 2 is exactly the integration of electrode response current i, connects subsequent process circuit; The reverse input end of amplifier 3 links to each other through capacitor C 1 with output terminal Uv; The reverse input end of amplifier 3 is connected to triangular wave driving voltage signal u through resistance R 1; The input end in the same way of amplifier 3 is connected to signal ground through resistance R 2; The output terminal Uv of amplifier 3 is exactly the integration of triangular wave driving voltage signal u, connects subsequent process circuit.

Claims (6)

1. triangular wave encourages also the electrical conductivity of solution measuring method and the Key Circuit of integral processing, it is characterized in that:
1) method
The employing voltage magnitude is U, cycle to be that the interchange symmetric triangular wave voltage signal of 2T encourages electrode; Wave band or following wave band are got two different t1 and t2 constantly arbitrarily in the period on the driving voltage signal; Calculate the middle tm constantly of t1 and t2, at [t1, tm] and [t1; T2] two integrating ranges carry out integration to driving voltage and electrode response electric current, calculate the solution resistance value R that obtains required mensuration by one of following two formulas x
R x = U 2 T | ( t 2 - t 1 ) 2 ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt | Or R x = | ∫ t 1 t 2 Udt - 2 ∫ t 1 Tm Udt ∫ t 1 t 2 Idt - 2 ∫ t 1 Tm Idt |
Utilize formula G=K/R again xObtain the conductivity of solution to be measured, K is an electrode constant.
2) Key Circuit
Integrating circuit to the current signal of driving voltage signal and electrode response is made up of conductance cell, amplifier 1, amplifier 2, amplifier 3, capacitor C 1, capacitor C 2, resistance R 1, resistance R 2, resistance R 3, resistance R 4, resistance R 5 and resistance R 6.One termination triangular wave driving voltage signal u of conductance cell, the reverse input end of another termination amplifier 1; Link to each other through resistance R 5 between the reverse input end of amplifier 1 and the output terminal Ur, the input end in the same way of amplifier 1 is connected to signal ground through resistance R 6, and the output terminal Ur of amplifier 1 is connected to the reverse input end of amplifier 2 through resistance R 3; Link to each other through capacitor C 2 between the reverse input end of amplifier 2 and the output terminal Ui, the input end in the same way of amplifier 2 is connected to signal ground through resistance R 4, and the output terminal Ui of amplifier 2 is exactly the integration of electrode response current i, connects subsequent process circuit; The reverse input end of amplifier 3 links to each other through capacitor C 1 with output terminal Uv; The reverse input end of amplifier 3 is connected to triangular wave driving voltage signal u through resistance R 1; The input end in the same way of amplifier 3 is connected to signal ground through resistance R 2; The output terminal Uv of amplifier 3 is exactly the integration of triangular wave driving voltage signal u, connects subsequent process circuit.
2. the electrical conductivity of solution measuring method and the Key Circuit of triangular wave as claimed in claim 1 excitation and integral processing is characterized in that: the crest that described interchange symmetric triangular ripple is meant triangular wave is opposite with the polarity of trough, amplitude equates, last wave band equates with the slope absolute value of following wave band.
3. the electrical conductivity of solution measuring method and the Key Circuit of triangular wave as claimed in claim 1 excitation and integral processing is characterized in that: describedly driving voltage and electrode response electric current are carried out integration, integration method employing numerical integration or mimic channel integration.
4. the electrical conductivity of solution measuring method and the Key Circuit of triangular wave as claimed in claim 1 excitation and integral processing is characterized in that: the resistance of described resistance R 1, R2, R3, R4 equates.
5. the electrical conductivity of solution measuring method and the Key Circuit of triangular wave excitation as claimed in claim 1 and integral processing is characterized in that: the capacitance of described capacitor C 1 and C2 equates.
6. the electrical conductivity of solution measuring method and the Key Circuit of triangular wave excitation as claimed in claim 1 and integral processing, it is characterized in that: the resistance of described resistance R 5 and resistance R 6 is identical all to be 1 ohm.
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