CN102830142A - Method and key circuit for measuring solution conductivity through triangular wave excitation - Google Patents

Abstract

Disclosed is a method for measuring the conductivity of a solution excited by a triangular wave and a key circuit: using a triangular wave voltage signal with an amplitude of U and a period of 2T to excite the electrodes, at two different times t1 in the upper band (or lower band) of the excitation signal and t2 sample the electrode response current i _t1 and i _t2 , use the equation R _x =|2U(t2-t1)/(T(i _t2 -i _t1 ))| to calculate the solution resistance R _x ; or also for the same moment The excitation voltage u _t1 and u _t2 are sampled, and R _x is calculated by the equation R _x =(u _t2 -u _t1 )/(i _t2 -i _t1 ); or the rate of change of the excitation voltage and the current change rate of the electrode response are detected, two Those are divided by phase to get R _x , and then use G=K/R _x to get conductivity, K is the cell constant. This scheme completely eliminates the influence of distributed capacitance.

Description

A method for measuring the conductivity of a solution excited by a triangular wave and its key circuit

technical field

The invention relates to a method for measuring the conductivity or resistivity of a solution, in particular to a method for measuring the conductivity or resistivity of a solution using a triangular wave as an excitation signal.

Background technique

The basic measurement method of the conductivity of the solution is to measure the voltage U _D applied to the two ends of the electrode placed in the solution and the current I flowing through the electrode, and calculate the resistance between the electrodes R=U _D /I, using G=K/ R calculates the conductivity of the solution, where K is the cell constant. However, the electrodes placed in the solution will be polarized after being energized, so that the measured voltage _UD is not actually the voltage across the solution itself, but the electric double layer capacitance applied to the solution resistance series involving the solution/metal electrode interface process The voltage on the two virtual electronic devices, so there is a theoretical error in the formula R=U _D /I; in order to reduce the influence of electrode polarization on the measurement accuracy, the basic method is to apply positive and negative polarity symmetrical alternating current on the electrode, but Under the action of the AC excitation signal, the measured current I is not the current flowing through the solution alone, but the total current flowing through the branch of the solution resistance branch in parallel with the distributed capacitance of the electrodes (including the inter-electrode capacitance and the electrode lead capacitance). Therefore, the use of AC excitation method introduces the influence of electrode distributed capacitance on the measurement while reducing the influence of electrode polarization.

Contents of the invention

The purpose of the present invention is to provide a measurement method that can accurately eliminate the adverse effect of electrode distributed capacitance on measurement and obtain solution conductivity or resistivity.

The technical scheme for realizing the above-mentioned purpose is:

Method: Put the electrode into the solution to be tested, and excite the electrode with an AC symmetrical triangular wave voltage signal with a voltage amplitude of U and a period of 2T, and remove peaks and valleys in the upper or lower band of the excitation voltage signal. Sample the current signal of the electrode response at any two different times t1 and t2, set the sampling values of the two current signals as i _t1 and i _t2 respectively, and use the expression R _x =|2U(t2-t1)/(T(i _t2 -i _t1 ))|Obtain the resistance value R _x of the solution to be measured; or, also sample the excitation voltage signals at time t1 and t2, set the sampling values of the two voltage signals as u _t1 and u _t2 respectively, use The expression R _x =(u _t2 -u _t1 )/(i _t2 -i _t1 ) obtains the resistance value R _x of the solution to be measured; or, the rate of change of the excitation voltage signal and the current signal of the electrode response Perform detection, divide the two to obtain the resistance value _Rx of the solution to be measured; on the basis of _Rx obtained by one of the above three methods, use the formula G=K/ _Rx to obtain the conductivity of the solution to be measured, K is the cell constant.

Key circuit: the detection circuit of the rate of change of the triangular wave excitation voltage signal u and the rate of change of the electrode response current i of the present invention is composed of a conductivity cell, an operational amplifier 1, an operational amplifier 2, an operational amplifier 3, a capacitor C1, a capacitor C2, a resistor Composed of R1, resistor R2, resistor R3, resistor R4, resistor R5 and resistor R6. One end of the conductivity cell is connected to the triangular wave excitation voltage signal u, and the other end is connected to the inverting input end of the op amp 1; Connect to the signal ground through resistor R6, the output terminal Ur of op amp 1 is connected to the inverting input terminal of op amp 2 through capacitor C2; the inverting input terminal of op amp 2 is connected to the output terminal Ui through resistor R3, and the op amp The same input terminal of 2 is connected to the signal ground through the resistor R4, and the output terminal Ui of the operational amplifier 2 is connected to the subsequent processing circuit; the reverse input terminal of the operational amplifier 3 is connected to the triangular wave excitation voltage signal u through the capacitor C1, and the output terminal of the operational amplifier 3 The same input terminal is connected to the signal ground through the resistor R2, the inverting input terminal of the operational amplifier 3 is connected to the output terminal Uv through the resistor R1, and the output terminal Uv of the operational amplifier 3 is connected to the subsequent processing circuit.

The working principle of the circuit is analyzed as follows: the resistance values of resistor R5 and resistor R6 are the same as 1 ohm, the resistance values of resistors R1, R2, R3, and R4 are the same as Rd, and the capacitance values of capacitors C1 and C2 are equal as Cd, then according to Electronics principle Ur=-R5·i, Ui=-Rd·Cd·dUr/dt=R5·Rd·Cd·di/dt=Rd·Cd·di/dt, indicating that Ui is equal to the rate of change of the electrode response current i di/dt is amplified by Rd·Cd times; Uv=-Rd·Cd·du/dt, indicating that Uv is equal to the rate of change of the triangular wave excitation voltage signal u, that is, du/dt is amplified by -Rd·Cd times; the same multiple is enlarged between the two , but after passing through the detection circuit, the polarity of the change rate of the excitation voltage signal u becomes reversed, as long as the sign is corrected in the subsequent processing; or the change of the electrode response current i is detected in the upper band of the triangular wave excitation voltage signal u rate, and the rate of change of the excitation voltage signal u is detected in the lower band of the triangular wave excitation voltage signal u, so that the two are amplified with the same sign and value, and the ratio of the two is kept unchanged by the subsequent processing. The circuit takes out the rate of change of the excitation voltage signal u and the rate of change of the electrode response current i detected by the circuit of this scheme, and divides the two to obtain the resistance of the measured solution. The role of resistors R2, R4 and R6 in the circuit is to make the input impedance of the same and reverse input terminals of the op amp equal, making the op amp circuit more symmetrical and reducing the zero offset.

In the above technical solution, the AC symmetrical triangular wave means that the polarity of the peak and the trough of the triangular wave are opposite, the amplitude is equal, and the absolute values of the slopes of the upper band and the lower band are equal.

Compared with the existing measuring method, the measuring method and key circuit of a kind of triangular wave excitation of the present invention have the following beneficial effects: the excitation signal is simple, and the triangular wave AC voltage signal of a single frequency is used for excitation, and the electrode distributed capacitance flows through The current is alternating and constant, and the influence of electrode distributed capacitance can be completely eliminated. The measurement and calculation methods involved in the technical solution of the invention are simple and the calculation amount is small.

Description of drawings

Figure 1 is an equivalent physical model diagram of a conductivity cell.

Figure 2 is a detection circuit for the rate of change of the triangular wave excitation voltage signal u and the rate of change of the electrode response current i.

Fig. 3 is a triangular wave AC excitation voltage signal and a waveform diagram related to the electrode response current signal.

Detailed ways

The principle and implementation steps of the technical solution of the present invention are further described below in conjunction with the accompanying drawings:

Under the condition that the frequency of the AC excitation signal applied to the electrodes is high enough, the polarization effect can be ignored, so the circuit model of the conductivity cell can be represented by Figure 1, and this model is in most cases where the accuracy requirements are not particularly strict. Appropriately, R _x in Fig. 1 represents the resistance of the solution to be measured; C _p represents the electrode distribution capacitance (including electrode plate capacitance, wire capacitance, capacitance caused by solution concentration polarization); _ix represents the capacitance flowing through the solution to be measured Current, the reference direction is from left to right; _ip represents the current flowing through the electrode distributed capacitance C _p , the reference direction is from left to right; i is the confluence of i _x and _ip , the reference direction is from left to right, and then In this paper, i is referred to as the electrode response current; u is the excitation voltage signal, which is an AC symmetrical triangular wave (hereinafter referred to as triangular wave, "symmetrical" means that the amplitude of the peak and trough of the triangular wave is equal, and the absolute value of the slope of the upper band and the lower band is equal), its The reference direction is left positive and right negative, the duration of the upper and lower bands of the triangular wave is T, the period of the triangular wave is 2T, the amplitude of the peak and the trough are both U, the waveform diagram of the excitation voltage signal u is shown in Figure 3 a Show.

According _to the principle of physics, the current ip flowing through the electrode distributed capacitance C _p satisfies the following formula

i _p =C _p du/dt…………………………………………………………(1)

The triangular wave excitation voltage signal u is not derivable at the two peaks and troughs, but can be derived everywhere in the upper and lower bands. Due to its piecewise linearity, du/dt is constant in the upper and lower bands, respectively are 2U/T and -2U/T, so during the upper band,

i _p =C _p ·2U/T

During the lower band of the triangular wave excitation voltage signal u,

i _p =-C _p 2U/T………………………………………………………(3)

The waveform diagram of i _p is shown in b in Figure 3, which is a bipolar AC square wave with a period of 2T;

The current i _x flowing through the solution to be measured obeys Ohm's law

i _x =u/R _x ……………………………………………………………(4)

The waveform of i _x is shown in c in Figure 3, and its waveform is similar to that of the triangular wave excitation voltage signal u but the slope may be different;

The electrode response current i is a current that can be directly measured. According to Kirchhoff's current law,

i=i _x +i _p ……………………………………………………………(5)

The waveform of i is shown in d in Figure 3, which is a double-edged sawtooth wave with a period of 2T;

In the upper band of the triangular wave excitation voltage signal u, two moments t1 and t2 are arbitrarily taken except for the peak and trough, and at these two moments, the values of the triangular wave excitation voltage signal u are u _t1 and u _t2 , and the electrode response current i Set the values of i _t1 and _it2 , the values of the current i _x flowing through the solution to be tested are set i _xt1 and i _xt2 , the values of the current i _p flowing through the electrode distributed capacitance C _p are set i _pt1 and i _pt2 , Obviously according to formula (2),

i _pt1 =i _pt2 ……………………………………………………………(6)

According to formula (4),

i _xt1 =u _t1 /R _x ……………………………………………………………(7)

i _xt2 =u _t2 /R _x …………………………………………………………(8)

According to formula (5),

i _t1 =i _xt1 +i _pt1 ……………………………………………………(9)

i _t2 =i _xt2 +i _pt2 ………………………………………………………(10)

Subtract the two sides of (10) and (9) respectively to get

i _t2 -i _t1 =(i _xt2 +i _pt2 )-(i _xt1 +i _pt1 )=(i _xt2 -i _xt1 )+(i _pt2 -i _pt1 )………(11)

Substitute (6), (7), (8) into (11) and get

i _t2 -i _t1 =u _t2 /R _x -u _t1 /R _x =(u _t2 -u _t1 )/R _x ………………………(12)

Arranging (12) to get

R _x =(u _t2 -u _t1 )/(i _t2 -i _t1 )…………………………………………(13)

The formula (13) shows that as long as the values u t1 and u t2 of the triangular wave excitation voltage signal u and the values i _t1 and i _t2 of the electrode response current i are measured at the time _t1 and _t2 , the measured solution can be calculated according to the formula (13) resistance R _x ; because of the segmental linearity of the triangular wave excitation voltage signal u, referring to a in Figure 3, it is obvious that during the upper band there is

du/dt=(u _t2 -u _t1 )/(t2-t1)=2U/T………………………………(14)

Arranging (14) to get

u _t2 -u _t1 = (t2-t1) 2U/T…………………………………………………………………………………………………………………(15)

Substitute (15) into (13) to get

R _x =2U(t2-t1)/(T(i _t2 -i _t1 ))…………………………………………(16)

Similarly, in the lower band of the triangular wave excitation voltage signal u, any two moments t1 and t2 except the peak and trough can be deduced

R _x =-2U(t2-t1)/(T(i _t2 -i _t1 ))………………………………………………(17)

Combining (16) and (17) to get

R _x =|2U(t2-t1)/(T(i _t2 -i _t1 ))|……………………………………(18)

Equation (18) shows that as long as two moments t1 and t2 except the peak and trough are randomly selected in the upper or lower band of the triangular wave excitation voltage signal u, the electrode response currents i _t1 and i _t2 at these two moments can be measured , calculate the time difference t2-t1 between the two moments and the difference _it2 -i _t1 between the electrode response currents at the two moments, respectively substituting them into (18) to calculate the resistance R _x of the solution to be tested.

Formula (13) can also be adjusted as follows

R _x =(u _t2 -u _t1 )/(i _t2 -i _t1 )=[(u _t2 -u _t1 )/(t2-t1)]/[(i _t2 -i _t1 )/(t2-t1)]

……………………………………(19)

Equation (19) shows that R _x is equal to the rate of change of the triangular wave excitation voltage signal u divided by the rate of change of the electrode response current i, so the rate of change of the triangular wave excitation voltage signal u and the rate of change of the electrode response current i are detected. Division equals R _x .

In Figure 2, the triangular wave excitation voltage signal u is composed of conductivity cell, operational amplifier 1, operational amplifier 2, operational amplifier 3, capacitor C1, capacitor C2, resistor R1, resistor R2, resistor R3, resistor R4, resistor R5 and resistor R6. The detection circuit of the rate of change and the rate of change of the electrode response current i.

In Fig. 3, a is the waveform of the triangular wave AC excitation voltage signal u applied at both ends of the electrodes of the conductivity cell, its amplitude is U, and the period is _2T ; b is the waveform of the current ip flowing through the electrode distributed capacitance C _p , It is an AC square wave with a period of 2T; c is the waveform of the current _ix flowing through the solution to be tested; d is the waveform of the electrode response current i, which is the superposition of the waveform of _ip and the waveform of _ix , which is a double-edged sawtooth wave .

According to the method and circuit of the present invention, a detection system is built.

Example 1

When testing, place the electrode in the solution to be tested, and use an AC symmetrical triangular wave voltage signal with a voltage amplitude of U and a period of 2T to excite the electrode, and remove the peaks and troughs in the upper or lower band of the excitation voltage signal. Sampling the current signal of the electrode response at any two different times t1 and t2, the two current signal sampling values are i _t1 and i _t2 respectively, using the expression R _x =|2U(t2-t1)/(T(i _t2 -i _t1 ))| Obtain the resistance value Rx of the solution to be measured.

Example 2

When testing, place the electrode in the solution to be tested, and use an AC symmetrical triangular wave voltage signal with a voltage amplitude of U and a period of 2T to excite the electrode, and remove the peaks and troughs in the upper or lower band of the excitation voltage signal. Sample the current signal of the electrode response at any two different moments t1 and t2, and the sampling values of the two current signals are i _t1 and i _t2 respectively; the excitation voltage signals at the time t1 and t2 are also sampled, and the two voltage signals are sampled The values are u _t1 and u _t2 respectively, using the expression R _x =(u _t2 -u _t1 )/(i _t2 -i _t1 ) to obtain the resistance value R _x of the solution to be measured.

Example 3

During detection, put the electrode into the solution to be tested, and use an AC symmetrical triangular wave voltage signal with a voltage amplitude of U and a period of 2T to excite the electrode. The rate of change of the current signal is detected, and the rate of change of the excitation voltage signal is divided by the rate of change of the electrode response current signal with a subsequent circuit to obtain the resistance value R _x of the solution to be measured;

In the above embodiments, the AC symmetrical triangular wave used refers to a triangular wave in which the peaks and troughs of the triangular wave have opposite polarities, equal amplitudes, and the absolute values of the slopes of the upper and lower bands are equal.

Claims (5)

1. a method for measuring and key circuit of the solution conductivity of triangular wave excitation, it is characterized in that: 1) method Use an AC symmetrical triangular wave voltage signal with a voltage amplitude of U and a period of 2T to excite the electrode, and respond to the electrode at any two different times t1 and t2 except for the peak and trough within the upper or lower band of the excitation voltage signal. The current signal is sampled, and the two current signal sampling values are i _t1 and _it2 respectively, and the required measurement is obtained by the expression R _x =|2U(t2-t1)/(T(i _t2 -i _t1 ))| The resistance value R _x of the solution; or, in the upper band or lower band of the excitation voltage signal, any two different moments t1 and t2 except the peak and trough are sampled for the current signal of the electrode response, and two current signals The sampling values are i _t1 and i _t2 respectively, and the excitation voltage signals at time t1 and t2 are sampled, and the sampling values of the two voltage signals are respectively u _t1 and u _t2 , using the expression R _x =(u _t2 -u _t1 ) /(i _t2 -i _t1 ) to obtain the resistance value R _x of the solution to be measured; or, use the following key circuit to detect the rate of change of the excitation voltage signal and the rate of change of the electrode response current signal, and divide the two That is, the resistance value R _x of the solution to be measured is obtained; on the basis of R _x obtained by one of the above three methods, the formula G=K/R _x is used to obtain the conductivity G of the solution to be measured, and K is the electrode constant; 2) Key circuits The detection circuit of the rate of change of the triangular wave excitation voltage signal u and the rate of change of the electrode response current i consists of a conductivity cell, an operational amplifier 1, an operational amplifier 2, an operational amplifier 3, a capacitor C1, a capacitor C2, a resistor R1, a resistor R2, a resistor R3, Composed of resistor R4, resistor R5 and resistor R6, one end of the conductivity cell is connected to the triangular wave excitation voltage signal u, and the other end is connected to the inverting input terminal of op amp 1; the inverting input terminal of op amp 1 and the output terminal Ur are connected by resistor R5 Connected, the same input terminal of op amp 1 is connected to the signal ground through resistor R6, the output terminal Ur of op amp 1 is connected to the inverting input terminal of op amp 2 through capacitor C2; the inverting input terminal of op amp 2 and the output terminal Ui are connected through resistor R3, the same input terminal of operational amplifier 2 is connected to the signal ground through resistor R4, the output terminal Ui of operational amplifier 2 is connected to the subsequent processing circuit; the inverting input terminal of operational amplifier 3 is connected to the triangle wave through capacitor C1 Excitation voltage signal u, at the same time, the same input terminal of operational amplifier 3 is connected to the signal ground through resistor R2, the reverse input terminal of operational amplifier 3 is connected to the output terminal Uv through resistor R1, and the output terminal Uv of operational amplifier 3 is connected to the subsequent processing circuit. 2. the measuring method and key circuit of the solution conductivity of a kind of triangular wave excitation as claimed in claim 1, it is characterized in that: described alternating current symmetrical triangular wave refers to the crest of triangular wave and the opposite polarity of wave trough, equal amplitude, upper The absolute values of the slopes of the band and the lower band are equal. 3. The method and key circuit for measuring the conductivity of a solution excited by a triangular wave as claimed in claim 1, characterized in that: the resistance values of the resistors R1, R2, R3, and R4 are equal. 4. The method and key circuit for measuring the conductivity of a solution excited by a triangular wave as claimed in claim 1, characterized in that: the capacitance values of the capacitors C1 and C2 are equal. 5. The method and key circuit for measuring the conductivity of a solution excited by a triangular wave as claimed in claim 1, wherein the resistance values of the resistors R5 and R6 are the same as 1 ohm.

Images