GB2307753A

GB2307753A - Determining electrical impedance

Info

Publication number: GB2307753A
Application number: GB9524338A
Authority: GB
Inventors: James Hambleton
Original assignee: SYCOPEL SCIENT Ltd
Current assignee: SYCOPEL SCIENT Ltd
Priority date: 1995-11-29
Filing date: 1995-11-29
Publication date: 1997-06-04
Anticipated expiration: 2015-11-29
Also published as: WO1997020220A1; GB2307753B; GB9524338D0

Abstract

A method of determining electrical impedance in an electro chemical cell 2 is disclosed. The electro chemical cell 2 is connected in series with a first limb 4 of a current mirror circuit 3 and a reference impedance 6 is connected in series with a second limb 7 of the current lower circuit 3 such that the current in the first limb 4 is substantially proportional to the current of the second limb 7. A potential difference is determined in the object 2 and the potential different across the reference impedance 6 is measured.

Description

METHOD AND APPARATUS FOR DETERMINING ELECTRICAL IMPEDANCE The present invention relates to a method and apparatus for determining electrical impedance, and relates particularly, but not exclusively, to a method and apparatus for determining electrical impedance in electro chemical cells.

Electro chemical cells have a wide variety of uses, for example to determine the corrosion properties of a material forming one of the electrodes of the electro chemical cell.

The electrical impedance between a working electrode and a reference electrode of the electro chemical cell provides a measure of the electro chemical properties of materials forming one or more electrodes of the cell.

Existing methods of determining the electrical impedance in an electro chemical cell generally involve the measurement of a potential difference between the working and reference electrodes of the cell by means of a differential amplifier, and a determination of the current flowing through the cell by means of a current-to-voltage converter. Such existing techniques involve the disadvantage that the current-to-voltage converter circuitry is completely different from the circuitry used for effecting direct voltage measurements using a straightforward amplifier or a differential amplifier, and the variation in behaviour of the two different types of circuitry with frequency is generally not the same.

Another existing technique is to use two substantially identical differential amplifier circuits, one to measure potential directly between the reference and working electrodes, and one to measure current flowing through the cell by connecting the amplifier across a suitable resistance in series with the working electrode. This technique however suffers from the disadvantage that there is serious deterioration of the high frequency performance as a result of common mode signals.

It is an object of the present invention to overcome the above disadvantages of the prior art.

According to an aspect of the present invention, there is provided a method of determining electrical impedance of an object, the method comprising: connecting the object in series with a first limb of a current mirror circuit; connecting a reference impedance in series with a second limb of the current mirror circuit, wherein the current in said first limb is substantially proportional to the current in said second limb; and determining a potential difference in the object and the potential difference across the reference impedance.

By providing a current mirror circuit in which the current in one limb of the circuit has a known relationship to the current in another limb of the circuit, the impedance of the object can be determined by comparing a potential difference in the object to the potential difference across a known reference impedance. Since variations in the current in the first limb of a current mirror circuit with frequency will be matched by similar variations in the current in the second limb, and the impedance is determined from a comparison of potential differences, the accuracy of the method extends over a wider frequency range than is the case with existing methods.

Preferably, the potential differences in the object and across the reference impedance are determined by means of substantially identical voltage determining means.

In this way, variations in the behaviour of each voltage determining means will be substantially the same, and will therefore cancel each other when the potential differences are compared.

Preferably, each said voltage determining means comprises a single ended amplifier or a differential amplifier.

Said first and second limbs may form respective first and second sides of the current mirror circuit, wherein the currents flowing in said first and second sides are substantially equal to each other.

Preferably, the object is connected with said first limb via the output of an operational amplifier.

This provides the advantage of ensuring that there is always sufficient power to drive current through the object.

Preferably, the object is connected to an output of' a transistor output stage connected in series with said first limb of the current mirror circuit.

This ensures that the current in the first limb of the current mirror circuit is substantially proportional to the current in the second limb of the current mirror circuit, even in the case of non-negligible operational amplifier current.

The method may be a method of determining the electrical impedance of an electro-chemical cell having a first electrode thereof connected to said first limb of a current mirror circuit, and the potential difference between second electrode and a reference electrode of the electro-chemical cell is determined.

According to another aspect of the invention there is provided an apparatus for determining electrical impedance of an object, the apparatus comprising: a current mirror circuit having a first limb connected in use in series with the object, and a second limb connected in use in series with a reference impedance, wherein the current in said second limb is substantially proportional to the current in said first limb; first voltage determining means for determining a potential difference in the object; and second voltage determining means for determining a potential difference across the reference impedance.

Preferably, said first and second voltage determining means are substantially identical.

In a preferred embodiment, the first and second voltage determining means each comprises an operational amplifier or a differential amplifier.

The first and second limbs may comprise respective first and second sides of the current mirror circuit, wherein the currents flowing in said first and second sides are substantially equal to each other.

The apparatus may further comprise an operational amplifier having an output connected in series with the object.

In this way, the operational amplifier provides sufficient power to ensure that current is driven through the object.

Preferably, the apparatus further comprises a push-pull output transistor stage connected in series with said first limb and having an output connected in use to the object.

This ensures that the current in the first limb of the current mirror circuit is substantially proportional to the current in the second limb of the current mirror circuit.

The output transistor stage may comprise a pair of transistors connected in series with said first limb, wherein the object is connected in use to the junction of said pair of transistors.

The current mirror circuit may comprise at least two substantially identical first transistors having respective bases connected together, wherein the base and collector of one of the transistors are connected together.

The current mirror circuit may comprise at least two substantially identical second transistors, the bases of said second transistors being connected together, wherein the base and collector of one of the second transistors are connected together.

This provides the advantage of improving the stability of the current mirror circuit.

The current mirror circuit may comprise at least two substantially identical resistors in series with respective limbs of the current mirror circuit.

This further enhances the stability of the current mirror circuit.

In a preferred embodiment, the current mirror circuit comprises first and second current mirror circuit means of opposite polarity, wherein the object and the reference impedance are connected in series with respective sides of each said first and second current mirror circuit means, The current mirror circuit may comprise at least two substantially identical transistors manufactured on a single substrate.

In this way, the characteristics of each of the transistors are always matched to each other.

The current mirror circuit may comprise an integrated circuit having multiple transistors manufactured on a single substrate.

Preferably, the apparatus further comprises one or more peltier effect cooling devices for controlling the temperature of the transistors.

In this way, matched performance of the transistors of the circuit is optimised.

The apparatus may be an apparatus for determining the electrical impedance of an electro chemical cell having a first electrode (secondary) connected in use in series with said first limb, wherein the potential difference determined in the electro chemical cell is determined between second (working electrode) and reference electrodes of the electro chemical cell.

According to a further aspect of the invention, there is provided an electro chemical impedance measuring apparatus comprising an apparatus as defined above, a first electrode (secondary) connected in series with said first limb, a working electrode and reference electrode, wherein the potential difference between said working and reference electrodes is determined using said second voltage determining means.

For a better understanding of the invention, preferred embodiments will now be described, by way of example only, and not in any limitative sense, with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of an apparatus of a first embodiment of the invention for measuring the electrical impedance of an electro chemical cell; Figure 2 shows a modification of the apparatus of Figure 1; Figure 3 shows a modification of the apparatus of Figure 2; Figure 4 shows a modification of the apparatus of Figure 3; Figure 5 shows a practical modification of the circuit of Figure 4, in which specific component values are indicated; and Figure 6 is a graph showing the variation with frequency of the current through the limbs of the circuit of Figure 5.

Referring in detail to Figure 1, an apparatus 1 for measuring electrical impedance in an electro chemical cell 2 comprises a current mirror circuit 3 into a first limb 4 of which a secondary electrode 5 of the electro chemical cell 2 is connected, such that the electro chemical cell 2 is connected in series with limb 4 of the current mirror circuit 3. A load 6 having known electrical impedance (such as an ohmic resistor) is connected in series in a second limb 7 of the current mirror circuit. A first voltage measuring circuit 8, is connected between a reference electrode 9 and a working electrode 10 of the cell 2, the working electrode 10 being connected to ground. A second voltage measuring circuit 11, generally identical in construction with the first measuring circuit 8, has its inputs connected across the load 6.

The current mirror circuit 3 comprises a pair of matched PNP transistors 12, 13 of which the emitters are connected to the positive power supply terminal, and the bases are connected to each other, the collector and base of transistor 12 being connected to each other. The positive supply terminal (pin 7) of an operational amplifier 14 is connected to the collector of transistor 12, the output terminal (pin 6) of the operational amplifier 14 being connected to secondary electrode 5 of the electro chemical cell 2. The load is connected in series with the collector of transistor 13. Similarly, the emitters of a pair of matched NPN transistors 15, 16 are connected to the negative power supply terminal, and the bases of transistors 15, 16 are connected together, the base and collector of transistor 15 being connected together.The collector of transistor 15 is connected to the negative power supply terminal (pin 4) of the operational amplifier 14, and the collector of transistor 16 is connected to the reference impedance 6.

The first voltage measuring circuit 11 comprises a first buffer amplifier 17 having its inverting input connected to the junction between the collector of transistor 13 and load impedance 6, and a second buffer amplifier 18 having its inverting input connected to the junction of the collector of transistor 16 and the load impedance 6. The outputs of first and second buffer amplifier 17, 18 are connected to noninverting and inverting inputs respectively of a differential amplifier 19.

In a similar manner, the second voltage measuring circuit 8 comprises a third buffer amplifier 20 having its inverting input connected to reference electrode 9 of the electro chemical cell 2 and a fourth buffer amplifier 21 having its inverting input connected to the working electrode 10 of the electro chemical cell. The outputs of the third and fourth buffer amplifier 20, 21 are connected respectively to the noninverting and inverting inputs of a differential amplifier 22.

The operation of the apparatus 1 of Figure 1 will now be described.

When a positive voltage is output from operational amplifier 14, it will drive a current through cell 2, the current being supplied by the positive supply via the positive supply terminal (pin 7) of the amplifier 14 and passing through transistor 12. The current passing through transistor 12 causes a specific voltage to occur at the base-emitter junction of transistor 12 which, because transistors 12, 13 are matched to each other, is directly connected to the base-emitter junction of transistor 13 to cause a substantially identical current to flow through transistor 13.Accordingly, transistor 13 mirrors exactly the current passing through transistor 12, and a potential difference is developed across load impedance 6 which is directly proportional to the current flowing through load 6 and is therefore also proportional to the current flowing through secondary electrode 5 of electro-chemical cell 2.

Similarly, when a negative voltage is output from operational amplifier 14, the current passing through secondary electrode 5 of electro-chemical cell 2 is derived from the negative supply via negative supply terminal (pin 4) of amplifier 14. This current flows through transistor 15, which causes a specific voltage Vbe across the base-emitter junction of transistor 15, which will be mirrored onto the base-emitter junction of transistor 16 is a manner similar to that of transistors 12, 13. In this way, transistor 16 passes a current substantially identical to that passing through transistor 15 and therefore the current passing through load impedance 6 is substantially equal to the current entering secondary electrode 5 of cell 2.The potential difference across load impedance 6 is therefore directly proportional to the current passing through secondary electrode 5 of electrochemical cell 2. In each of the above cases, the small base currents of the transistors have been ignored.

The current flowing through electrode 5 of cell 2 can therefore be easily calculated from the output of diffetential amplifier 19, and the voltage between the reference electrode 9 and working electrode 10 of the electro-chemical cell 2 can therefore be calculated from the output of differential amplifier 22. The resultant impedance can then be calculated from the ratio of the outputs of amplifiers 22 and 19.

Because the current in first limb 4 is always approximately equal to the current in second limb 7 of the current mirror circuit 3, and the first and second voltage measuring devices 8, 11 are identical in construction, any variations of the behaviour of the circuits 3, 8, 11 with temperature or current values will be approximately the same for both limbs 4, 7 of the circuit and will therefore be eliminated when the ratio of the outputs of differential amplifiers 18, 21 is taken.

Figure 2 shows a modification of the apparatus of Figure 1, in which components common to the apparatus 1 of Figure 1 are denoted by like reference numerals, but increased by 200 The stability of current mirror circuit 203 is enhanced by the inclusion of a pair of identical resistive loads 225 between the emitters of transistors 212, 213 and the positive power supply terminal, and by connecting a further pair of PNP transistors 226, 227. The emitter of transistor 226 is in series with the collector of transistor 212 and the collector of transistor 226 is connected to the positive power supply terminal (pin 7) of operational amplifier 214. The emitter of transistor 227 is connected to the collector of transistor 213, the collector thereof being connected to load impedance 206.

The bases of transistors 226, 227 are connected together, as are the base and collector of transistors 212 and 226.

Similarly, a pair of identical resistive loads 228, 229 are connected between NPN transistors 215, 216 and the negative power supply terminal, respectively, and transistors 230, 231 are connected in series between transistors 215 and operational amplifier 214 and transistor 216 and load impedance 206, respectively. The connections of resistive loads 228, 229 and transistors 230, 231 are anaiogous to those of resistive loads 225 and transistors 226, 227, the bases are collectors of transistors 215, 230 being connected together and will therefore not be described in further detail.

The operation of the circuit of Figure 2 will now be described. When a current, the level of which is set by operational amplifier 214, flows through transistors 212, 226 a voltage drop occurs across resistive loads 225. This reduces the effect of any variation in Vbe with collector voltage of transistors 212, 213.

Because the bases of transistors 226 and 227 are connected together and transistors 226, 227 are in series with transistors 212, 213 respectively, the collector of transistor 227 is held at 2Vbe below the emitter voltage of transistor 213. This cascoding of transistors 226, 227 thus reduces variations in the collector-emitter voltage of transistor 213.

A similar situation applies to transistors 230, 231.

Figure 3 shows a current mirror circuit 303 which is a variation of the current mirror circuit 203 shown in Figure 2 and components common to the circuit 3 of Figure 1 have like reference numerals but increased by 300.

Transistors 312, 313, 315, 316 and load impedance 306 are connected in a manner similar to that shown in Figure 2 and will not be described in further detail. The output terminal (pin 6) of operational amplifier 314 is connected to input terminal 332 of a push-pull output stage 333 comprising a pair of transistors 334, 335. Output terminal 336 of the output stage 333 is connected to electrode 5 of the electro chemical cell 2 (not shown). The collector of transistor 334 is connected to the emitter of transistor 312, and the collector of transistor 335 is connected to the collector of transistor 315, the emitters of transistors 334, 335 being connected together via output terminal 336.

As a result, if base currents of transistors 334, 335 are ignored (or if transistors 334, 335 are field effect transistors, in which case there will be no gate current) the current flowing through transistors 334, 335 will always be equal to the current flowing through transistors 312, 315 respectively. Consequently, the current flowing thoughloutput terminal 336 (and hence through the electro chemical cell 2) will always be equal to the current flowing through load impedance 306. Figure 4 shows a modification of the apparatus shown in Figure 3, in which parts of current mirror circuit 403 corresponding to the circuit 303 of Figure 3 have like reference numerals, but increased by 100, and will not be described in further detail.

In the arrangement of Figure 4, the bases and collectors of transistors 427 and 431 are connected together, the collectors being connected to opposite terminals of voltage divider 406 which replaces load impedance 306. Transistor 426 is provided with the necessary bias via impedances 436 and 437, and in a similar manner, transistor 430 is provided with bias via impedances 438 and 439. It should be noted that in this arrangement the transistors in the circuit 3, i.e. 326 and 330 have changed in Figure 4 (426 and 430) to PNP and NPN transistors. They now form cascoded loads for trawsistors 434 and 435 and enhance the frequency performance of the circuit.

When a current is output from pin 6 of amplifier 414, the current flowing through push-pull transistors 434, 435 is fed to secondary electrode 5 of electro-chemical cell 2. The current flowing through push-pull transistors 434, 435 is mirrored by transistor pair 412, 413 or transistor pair 415, 416 and passes through transistors 413, 427, 431, 416 in series with voltage divider 406, the potential difference across which can be measured by voltage measuring means 411.

The circuits 3, 203, 303, 403 preferably are provided by an integrated circuit in which the transistors are manufactured on the same substrate. These transistors may have matched values of Vbe at a certain temperature, and then held at this temperature by the use of Peltier effect cooling devices. A suitable integrated circuit is the TPQ 6507, which has the following specification: Table A Dissipation 500m W per transistor derated 1.79m W/ C above 550C Ic 150mA Vcso 30 V C0 60 V hfe 40 Operating Temp 0 to 850C Finally, Figure 5 shows a practical arrangement of the circuit 403 of Figure 4, in which push-pull transistor pair 414, 435 is provided with the necessary bias via a diodecapacitor network 550 and a potential divider 551.

The behaviour of the circuit of Figure 5 with frequency (i.e. in an arrangement in which a DC bias is imposed on electro-chemical cell 2 and a relatively smaller AC signal is then super imposed on the bias) is shown in Figure 6, from which it can be seen that output voltage A across electrochemical cell 2 is substantially identical with output voltage B across load impedance 406 over a very wide frequency range.

It will be appreciated by persons skilled in the art that the above embodiments have been described by way of example only, and not in any limitative sense, and that various alterations and modifications of the invention are possible without departure from the scope of the invention as defined by the appended claims.

Claims

CLAIMS:

1. A method of determining electrical impedance of an object, the method comprising: connecting the object in series with a first limb of a current mirror circuit; connecting a reference impedance in series with a second limb of the current mirror circuit, wherein the current in said first limb is substantially proportional to the current in said second limb; and determining a potential difference in the object and the potential difference across the reference impedance.

2. A method according to claim 1, wherein the potential differences in the object and across the reference impedance are determined by means of substantially identical voltage determining means.

3. A method according to claim 2, wherein each said voltage determining means comprises a single ended amplifier or a differential amplifier.

4. A method according to any one of the preceding claims, wherein said first and second limbs form respective first and second sides of the current mirror circuit, and the currents flowing in said first and second sides are substantially equal to each other.

5. A method according to any one of the preceding claims, wherein the object is connected with said first limb via the output of an operational amplifier.

6. A method according to any one of the preceding claims, wherein the object is connected to an output of a transistor output stage connected in series with said first limb of the current mirror circuit.

7. A method according to any one of the preceding claims, wherein the method is a method of determining the electrical impedance of an electro chemical cell having a first electrode thereof connected to said first limb of a current mirror circuit, and the potential difference between a second electrode and a reference electrode of the electro chemical cell is determined.

8. An apparatus for determining electrical impedance of an object, the apparatus comprising: a current mirror circuit having a first limb connected in use in series with the object, and a second limb connected in use in series with a reference impedance, wherein the current in said second limb is substantially proportional to the current in said first limb; first voltage determining means for determining a potential difference in the object; and second voltage determining means for determining a potential difference across the reference impedance.

9. An apparatus according to claim 8, wherein said first and second voltage determining means are substantially identical.

10. An apparatus according to claim 8 or 9, wherein the first and second voltage determining means each comprises an operational amplifier or a differential amplifier.

11. An apparatus according to any one of claims 8 to 10, wherein the first and second limbs comprise respective first and second sides of the current mirror circuit, wherein the currents flowing in said first and second sides are substantially equal to each other.

12. An apparatus according to any one of claims 8 to 11, further comprising an operational amplifier having an output connected in series with the object.

13. An apparatus according to any one of claims 8 to 12, further comprising a push-pull output transistor stage connected in series with said first limb and having an output connected in use to the object.

14. An apparatus according to claim 13, wherein said output transistor stage comprises a pair of transistors connected in series with said first limb and the object is connected in use to the junction of said pair of transistors.

15. An apparatus according to any one of claims 8 to 14, wherein the current mirror circuit comprises at least two substantially identical first transistors having respective bases connected together, wherein the base and collector of one of the transistors are connected together.

16. An apparatus according to claim 15, wherein the current mirror circuit comprises at least two substantially identical second transistors, each of which is connected in series with a respective said first transistor, the bases of said second transistors being connected together, wherein the base and collector of one of the second transistors are connected together.

17. An apparatus according to any one of claims 8 to 16, wherein the current mirror circuit comprises at least two substantially identical resistors in series with respective limbs of the current mirror circuit.

18. An apparatus according to any one of claims 8 to 17, wherein the current mirror circuit comprises first and second current mirror circuit means of opposite polarity, wherein the object and the reference impedance are connected in series with respective sides of each said first and second current mirror circuit means.

19. An apparatus according to any one of claims 8 to 18, wherein the current mirror circuit comprises at least two substantially identical transistors manufactured on a single substrate.

20. An apparatus according to claim 19, wherein the current mirror circuit comprises an integrated circuit having multiple transistors manufactured on the single substrate.

21. An apparatus according to claim 19 or 20, further comprising one or more peltier effect cooling devices for controlling the temperature of the transistors.

22. An apparatus according td any one of claims 8 to 21, wherein the apparatus is an apparatus for determining the electrical impedance of an electro chemical cell having a first electrode (secondary) connected in use in series with said first limb, wherein the potential difference determined in the electro chemical cell is determined between second (working element) and reference electrodes of the electro chemical cell.

23. An electro chemical impedance measuring apparatus comprising an apparatus according to claim 22, a first electrode (secondary) connected in series with said first limb, a working electrode and reference electrode, wherein the potential difference between said working and reference electrodes is determined using said second voltage determining means.

24. A method of determining electrical impedance of an object, the method substantially is hereinbefore described with reference to the accompanying drawings.

25. An apparatus for determining electrical impedance substantially as hereinbefore described with reference to the accompanying drawings.

26. An electro chemical impedance measuring apparatus substantially as hereinbefore described with reference to the accompanying drawings.