GB2278200A - Linearising circuit for use with semi-logarithmic sensing devices - Google Patents

Description

2278200 1 - LINEARISING CIRCUIT FOR USE WITH SEMI-LOGARITHMIC SENSING

DEVICES Some classes of sensing devices used to measure important physical quantities or properties of materials have characteristics which show an approximately logarithmic relationship between the quantity to be measured, expressed in the normal units of measurement, and the electrical or other property of the sensor which changes in response to the quantity sensed.

In modern instrumentation it is desirable to translate the measured property of the type of sensing device which it is most convenient to use into a linear output, i.e. an electrical or other signal wflich is a direct analogue of the quantity under test. This is especially desirable in the case of digital instrumentation, where the output is to be displayed In the normal units of measurement and the digital display devices are preferably driven by standard anal ogue-t o-digit al converter circuits which require as input a voltage, or more strictly a ratio of two voltages, which has a linear relationship with the measured quantity. However it has proved difficult hitherto to achieve a good linear output when using semi-logarithmic sensing devices, except over restricted ranges of measurement.

The invention to be described provides a means whereby the semilogarithmic properties of certain common types of sensor can be translated into voltages W suitable for t lie inputs of standard inexpensive analogue-to-digital converter circuits, scaled in such a way as to display the quantity under test in the normal units of measurement, with good accuracy over a wide range of sensing inputs.

This linearising circuit has been devised to work in the same way as a type of mathematical relationship developed by the inventor to describe the characteristics of semi-logarithmic sensing devices. The use of this mathematical formula, with specific constants derived from the actual properties of the sensing device to be used, is an important aid to calculating the values of certain components to be used in the circuit. A further feature of the invention caters for types of sensor which have properties which bear a semi-logarithmic relationship to two independent physical quantities, and compensates for one of the quantities while providing an electrical signal proportional to the othe r.

The invention comprises a first pair of bipolar transistors, circuit arrangements for controlling the collector currents of these transistors, a potential divider, a second pair of bipolar transistors with circuit arrangements to control the voltages applied between their emitters and bases, and an output resistor network.

The collectors of the first pair of transistors are arranged to receive currents from the sensing device and from a reference component in such a way that the ratio of the collector currents Is equal to the ratio of the currents from the sensing device respectively. If the sensing device component will also be resistive and that the sensor and the reference applied across them.

and from the reference component is resistive in nature the reference the input circuit will be arranged so have substantially the same voltage The bases or the emitters of the first pair of transistors are held at a controlled potential relative to one another. If the input currents are unequal there will be a difference between the base-emitters voltages of the first pair of transistors. A precise fraction of this voltage difference, determined by the potential divider, is applied to the emitters or bases of the second pair of transistors, which need to be at substantially the same temperature as the first pair.

The voltage difference established between the emitter-base voltages of the second pair of transistors determines the ratio of their collector currents. The collectors of these transistors are connected to an output network of resistors with precisely determined values relative to one another, connected in such a way that two pairs of output lines provide the correct voltage signals to drive a standard type of analogue-todigital converter.

The invention will now be described with reference to the accompanying tables and diagrams, which show examples of the sensor characteristics referred to and of the existing art in using such devices, and examples of the use of the linearising circuits which are the subject of the invention.

The first exeraple of a semi-logarithmic sensing device is the negative temperature coefficient thermistor, used for measuring temperature. The characteristics of one device of this type (Philips Type No. 2322 640 63104) are shown in the first three columns of Table 1 and in Figure 1.

Figure 3 shows a conventional way of connecting a thermistor to measure temperature, when the result of the measurement is to be displayed using a standard type of analogue-to-digital converter. ReferrinS to Fig. 3, a negative temperature coefficient thermistor 61 is connected in series with fixed resistors 62 and 63 between lines 66 and 67. A suitable voltage is applied between lines 66 and 67. Two further fixed resistors 64 and 65 are connected in series across the same lines.

Line 68, from the junction of resistors 62 and 63, and 'Line 69, from the junction of resistors 64 and 65, carry the measurement signal inputs to an anal ogue-t o-digit al converter 71, and lines 66 and 67 provide the reference voltage inputs to the same convert.er. The resistor values calculated to give the best measurement results with the thermistor example already mentioned over a span from 5 deg.C to 30 deg.C are:

R62 = 11.0162 k.0, R63 = 88.9838 kQ, R65/R64 = 0.24211.

Column 4 of Table I shows the ratio of the voltage at point 70, the Junction of the thermistor 61 and resistor 62, to the voltage on line 66. Figure 2 is a graph of the variation of this voltage ratio with the temperature of the sensor. As can readily be seen, this is an S-shaped curve which can only be considered linear over a small part of the range of measurement over which the thermistor is designed to be used.

Column 5 of Table 1 shows the numbers which would be displayed by a standard digital instrument, driven by the outputs of the circuit of Fig. 3, scaled for 1000 counts with weasurement and reference inputs equal and with the decimal point placed before the last digit. Column 6 of Table 1 shows the amounts by which these Indications would be in error.

As the table shows, this form of measuring circuit can only be considered reasonably accurate over a span of about 30 deg.C, between 5 and 35 degrees in the case Illustrated, and the errors start to become unacceptably large if the temperature is more than 20 deg.C above or below the centre point of the linear range.

It is of course possible nowadays to use an analogue-to-digital converter in conjunction with a computer circuit, to digitise a curve like that of Fig. 2, to calculate the measured quantity using a look-up table or interpolation program, and to drive a digital display. This approach will give better results over the central part of the measuring range, but it introduces a considerable complexity into a measuring instrument and it will give poor xesults towards the ends of the curve where the progressive reduction in the slope means that an ordinary anal ogue-t o- digi t al converter will have insufficient resolving power to provide the computer with the fine changes in input data which it requires.

The mathematical relationship between the resistance of a negative temperature coefficient thermistor and its temperature is commonly approximated by the formula R(Tl> = exp. (--2- - 13 R (T2 > T1 T2 [Equation 1] where R(T1) and R(T2) are the resistance values at temperatures T1 and T2 and B is a constant; TI, T2 and B all being expressed in degrees Kelvin. This formula is not very accurate, and is in a form which does not lend itself readily to implementation by means of any simple electronic circuit.

The inventor has discovered that a better representation of the characteristic of certain semi-logarithmic sensing devices, including the negative temperature coefficient thermistor, can be given by a relationship of the form:

R(xl) xl + X0 R (x2) (x2 + xO [Equation 2] where R(xl) and R(x2) are the resistances of the sensor corresponding to values x1 and x2 of the measured quantity, XO is a constant expressed in the units of measurement and m is a dimensionless constant greater than unity.

Table 2 compares the maker's figures for the same thermistor with resistances calculated by the Inventor's formula. In the case of temperature measurement this formula can be written:

R(81) el + 80 R(e2) (92 + 0-0) [Equation 3] - 5 where R(el) is the resistance at the measured temperature el deg.C, R(e2) is the resistance at a reference temperature 82, usually 25 deg.C, and eO and m are constants. The values of these constants calculated to give the correct resistances for the thermistor illustrated at zero, 25 and 85 deg. C are: eO = 153. 4556 deg, G, iii = 8. 121938.

The calculated results are in good agreement with the maker's figures over a wide temperature range. The calculated errors are less than 0.3 deg.C over a temperature span exceeding 110 degrees and are less than 1.0 des. C over a span exceeding 155 degrees. These errors are better than the manufacturing tolerances for precision thermistors.

One possible implementation of the electronic circuit which is the subject of this invention is shown in simplified form in Figure 4.

Referring to Fig. 4, a positive supply line 55 is connected through a resistor 23 to a sensing device 20 and to a comparison component 21. The currents which flow through components 20 and 21 are made to pass through the collector junctions of a first pair of bipolar transistors 29 and 30. If this is a circuit for measuring temperature then the sensor 20 will be a negatipe temperature coefficient thermistor and the comparison component 21 will be a fixed resistor with a value equal to that of the thermistor at the reference temperature E32.

The bases of transistors 29 and 30 are connected in common to a suitable bias potential applied to line 41. A current feedback amplifier 37 is connected so as to cause a current very nearly equal to that through sensor 20 to flow through the collector junction of transistor 29.

An operational amplifier 33 is connected to draw a current from the emitter of transistor 30 such that the voltages across components 20 and 21 are very nearly equal and the collector current of transistor 30 is the current through the component 21.

There will be established a difference in voltage between the emitters of transistors 29 and 30 which is a function of the ratio of their collector currents, and hence of the ratio of the resistances of the sensor 20 and the comparison component 21. Tbis way be calculated as follows:

6 - The base-emitter voltage of a bipolar transistor is given by the equation:

Vbel = Vbe0M + () lri.(!-') q 10 [Equation 4] where Vbel and VbeO are the base-emitter voltages at collector currents II and 10 respectively; k is Boltzmann's constant, T is the Junction temperature in degrees Kelvin and q is the charge on an electron. VbeO is also temperature dependent, but this dependence is the same for all transistors of the same type.

The circuit sets the voltages across components 20 and 21 equal, so if we call the collector current of transistor 29 Ic(Q29) and the resistance of component 20 R20, and so on for the other components:

Ic(Q29) R21 IC(Q30) R20 Ybe(Q29)-Vbe(Q30) = (kT)1n.(R21) q - -R20 [Equation 51 Referring again to Fig. 4, The emitters of transistors 29 and 30 are connected through a potential divider made up from two fixed resistors 38 and 40. A second pair of bipolar transistors 31 and 32, at substantially the same temperature as the first pair 29 and 30, have their bases joined and their emitters connected as shown. The emitter of transistor 31 is connected to the emitter of transistor 30. The junction between resistors 38 and 40 is connected to the non-inverting input of a second operational amplifier 34, connected as a unity gain buffer, the output of which is connected to the emitter of transistor 32.

Ihe collector of transistor 31 is connected through resistors 45 and 46 to a suitable bias potential on line 42. The collector of transistor 32 is connected through resistor 49 to the same line 42.

The difference between the base-emitter voltages of transistors 31 and 32 is thus set by the circuit at a fixed fraction of the difference between the base-emitter voltages of transistors 29 and 30, the fraction being equal to R40/(R38+R40>. This defines the ratio of the collector currents of transistors 31 and 32, as follows:

From Equation 4t VIbe(Q32)-Vbe(Q31> = (kT).1{ Ic(Q32)} [Equation 6] q lc (Q31) and by Lhe desigis of the. circuit:

Vbe(Q32)-Vbe(Q31) = ( R40) IVbe(Q29>-Vbe(Q30)} R38+R40 from Equation 5. Therefore:

R40) (1 R38+R40 q R20 n. { I c (Q32)} = ( R40) 1n. ( R21 [Equation 7] IC\Q31> R38+R40 R20 The values of the resistors 38 and 40 are chosen such that the ratio RS,L'5+R40)iR40 = m, the constant in the inventor's Equation 2 above.

Equation 7 then gives:

I c (Q32) = (1) 1 '1 n, IC (Q31) R20 The input circuit is set up so that:

R21 R(xl) 1 =(xl + X0 R20 - {R(x2)}- x2 + xO)111 whence Ic(Q32> = (xl + xO IC(Q31> x2 + xO [Equation 8] from Equation 2 [Equation 9] Thus the circuit establishes a ratio of the currents at the collectors of the second pair of transistors which is a linear function of the measured quantity. The temperature dependencies in the characteristics of the four transistors 29, 30, 31 and 32 all balance out. Equation 9 is independent of the temperatures of these transistors and it. is also unaffected by variations in the supply and bias voltages in the circuit.

One further step is needed to produce a pair of output. voltages suitable for the inputs to an anal ogue-t o-vol t age converter. This is provided by a network of resistors which receive the collector currents of transistors 31 and 32 and combine them in a precisely determined fashion, to provide the coirect potential differences on two pairs of output 1iries.

Referring again to Fig. 4, the voltages developed across resistors 45, 46 and 49 are taken to the inputs of an analogue-to-digital converter 54 via lines 53, E32, 50 and 51. Lines 52 and 53 provide the reference voltage and lines 50 and 51 provide the measurement voltage for the converter unit.

Figure 5 shows an alternative circuit for converting the collector currents of transistors 31 and 32 to the voltages required for the inputs of an analogue-to-digital converter. This arrangement needs to be used instead of the circuit of Fig. 4 in certain cases. In the circuii of Fig. 5 there is an extra resistor 47 between the bias point 42 and the junction of resistors 45 and 49. The output connection 50 is the same as the bias juriction 42 in this version of the circuit.

In order to give the correct Inputs to the analogue-to-digital converter, the ratios of the resistors 45, 46, 49 and 47 must be as follows:

Lel. the number ol counts displayed by the analogueto-digltal converter when its Inputs are equal be Ee, let the number to be displayed when the measured quantity x in Equation 2 has the value x2 be N2, and let the number to be displayed when the measured quantity has one other defined value x3 be N3.

Calculate:

R46 N3(x2+xO) - N2<x3+xW R45 Ne(x3-x2) [Equation 10] If the result is positive, the circuit of Fig. 4 is used and the ratio R46/R45 is defined. If the result is negative, the circuit of Fig. 5 should be used and the ratio calculated, with its sign reversed, becomes the value for R471R45.

Now the ratio R49/R45 can be calculated. In the circuit of Fig. 4.

R49 l,3-N2)(x2+xO) R45 Ne (x3-x.2) and in the circuit of Fig. 5:

R49 A---+N3%',x2+Y05 R45 fie+ (x3x-- [Equation 11] [Equation 112] 9 As a first example of these calculation--,, let the circuit and the thermistor already cited be used to measure temperature in degrees Celsius with a resolution of I count 0. 1 deg. C, using a standard type 7106 or 7107 analogue-to-digital converter- to drive the display. This converter gives a count of 1,000 when its measurement and reference input voltages are equal, so the number Ne in the above equations is 1,000.

Let x2 and x') be 25. 0. and 100. 0 deg. C and let N2 and M3 be 250 and 1, 000 respectively. In this case, Equation 10 gives R46/R45 = +1.534556. This is p1 Equation 11 gives 0S.Ltive so the circui L of Fig. 4 applies, and R49/R45 = 1. 7(G4556.

As a second example of these calculations, let the same thermistor, circuit and converter be used to display temperature in degrees Fahrenheit, with a resolution of i count = I degree. The Fahrenheit equivalents to 25 deg. C and 100 deg. C are 77 and 212 degrees respectively, so the numbers N2 and N3 in the above equations become 77 and 212.

Then Equation 10 gives R46/R45 = +0. 24422. This is positive so the circuit of Fig. 4 applies, and Equation 11 gives R49/R45 = 0.32122.

As a third example of these calculations, let the same thermistor, circuit and converter be used to display temperature in degrees Kelvin, with a resolution of 1 count = 1 degree. The Kelvin equivalents of 25 and 100 deg,C are 298 and 373 deg.K (to the nearest whole numbers), so the numbers N2 and N3 in the equations become 298 and 373.

Then Equation 10 gives R46/R45 = -0. 1195444. This is negative, so the circuit of Fig. 5 applies, with R47/R45 = 0. 1195444, and Equation 12 gives R49i-R45 = 0.0589112.

Different values of the resistors 46,49 and 47 in the output network can be corubined in a single instrument if this is required to have more than one measuring range, and Figure 6 shows one way of doing this. Referring to this diagram, resistor 49 is now made up from a series combinatIon of three resistors 48a, 48b and 49. Resistor 46 is made up from two resistors 46a and 46b in series, and Lhere is a resistor 47 in the same circuit.

Two switch poles 27, 26 select one of three pairs of connections for the output. lines 50 and 51,and another Pole on the same switch, not shown, would connect, the drive to the decimal poiijt. on the display where appropriate.

The network of Fig. 6 could be used in an ii-isi-r-urfiejif. lo measure temperature and Lo dJsplay this in degic-es Celsius, Fahrenheit or Kelvin, as ill the examples calculaled above.

Another example of a semi -logari thmi c sensIng device is the measurement of the moistuie content of certain solid and particulate materials by measuring the electrical resistance of a sample of the material. A number of natuf-ally occurt-ing and mari-made substances, including wood, grain, pulses, straw, Paper, cotton, brick and concrete, are hygroscopic and exhibit electrical conductivities which vary with their percentage moisture content.

One type of moisture meter used with certain of these materials comprises a set of electrodes, placed in contact with a sample of the material to be tested, connected to a circuit which measures the electrical conductivity or resistance of the sample and interprets this in terms of the percentage moisture content of' the material. The relationship between moisture content and resistance for the given electrode system can be found for each material by a series of experiments using samples of known moisture content, deteriftined by other means, and the measuring instrument can then be calibiaLed Ixom the iesults obtained.

A number of inoisture meters based on the 'resistance method' have been developed and manufactured, but they are limited in accuracy and ease of use by the facts that for most of' the substances of' interest the resistivity turns out to be approximately a logarithmic function of the moisture content, and is also s-ignJficaritly dependent upon the temperature of the s amp 1 e.

Table 3 and Figure 7 show an example of a set of' content calibration data, in this case for samples of straw tested at 20 deg.C using a penetration probe of known dimensions.

The chaiacteristic curve tor this material ecii be approYimated using a version of 1-he inventor-'s l- -Love, 1 jIne pei c en 1. age rijrj i s t ur e - 11 content is called h, the variation of the resistance of a sample with moisture content. can be represented by:

RO-il> ( 111 + 1-10 R (t12) ht 2 + h 0 where R(M) and moisture contents moisture content material.

[Equation 13] R(h2) are the electrical resistances of the sample at. Jil and h2, hO is a 'zero offset' expressed in percentage and m is a dimensionless constant calculated for this The values of hO and m which give the correct results using the data for this straw tester at moisture contents of 13.9, 21.9 and 34.3% are hO = -5.15508 %H:nO, 5.402763 Column 4 of Table 3 shows the resistances calculated using these figures in Equation 13. The last two columns of the same table show moisture contents calculated back from the original calibration data using this formula, and the differences between these figures and the data figures. The calculated figures are in good agreement with the calibration data except at the highest and lowest points, so the inventor's linearising method can give good results with this material over the moisture content range 10% to 40% H:20.

These calibration data refer to the resistance of samples of the material at 20 deg.C. But the resistivity of this material is a function of its temperature as well as of its moisture content, and for a moisture meter of this type to be accurate it is necessary to compensate for the temperature eflect.

In the linearising circuit described this is achieved by the use of a temperature sensor in the input connections, Referring to Fig. 4; for rftoisturE measurement the sensing device 20 would be the electrode system which Js placed in contact with the sample and the comparison component 21 would be a temperature sensor. This temperature sensor 21 would be of a type which has substantially the same variation of resistance with temperature as the sample, and il. would be mounted within the measurement probe so as to attain appy-oximat.c--ly lhe temperature. of the sample.

rhe inventor has found from tests that the resistances of samples of a number of settiicoiidtici.ii-i8 oi-gariic materIals at constant moisture contents vary with temperature in approximately the same way as negative temperature coefficient thermistors. So for moisture meters constructed In accordance with this invention lor testing materials of this type it is convenient to use a negative temperature coefficient thermistor of suitable resistance value as Lhe compailson component 21 in the circuit of Fig. 4.

Figure 8 shows an example of a measuring circuit according to the present invention, designed to measure both the temperature of a material and its moisture content. For the sake of' clarity a number of preset adjustment, decoupling and biassing components have been omitted from this diagram.

Referring to Fig. 8, the sensing device 20 is a sample of the material under test, held in contact with suitable electrodes. The comparison component 21 is a negative tempex-ature coefficient thermistor. A second comparison component 22 is a fixed resistor with a value equal to that of the thermistor at a reference temperature.

Five poles 24, 25, 26, 27 and 28 of a two-way switch connect the circuit to measure temperature or moisture content. When testing for moisture content the circuit measures the ratio of the currents through the sample 20 and the thermisLor 21. When testing for temperature the circuit measures the ratio of the currents through the thermistor 21 and the comparison resistor 22.

The ratio of' the potential divider is changed between the two values of the constant m by switch pole 26. The output resistor network 45, 46, 47, 48 and 49 combines the values required for the two measuring ranges and the voltages required by the anal ogue-t o-digit al converter 54 are selected by switch poles 27 and 28 in the manner previously described.

1 S TABLE 1

Thermistor 100 kO Display Temperature Resistance Q+100k) Output R (Offins) lo (R) Fi. 3 Error a --- -a--- ---- -40 3 665 000 6.5641 0.0266 -30 1 914 000 6.2819 0.0497 -20 1 040 000 6.0170 0.0877 -10 585 500 5.7675 0.1459 -6.5 -3.5 0 340 700 5.5324 0.2269 0.7 -0.7 204 400 5.3105 0.3285 9.7 +0.3 126 100 5.1007 0.4423 19.9 +0.1 100 000 5.0 0.5 25.0 0.0 79 820 4.9021 0.5561 30.0 0.0 51 760 4.7140 0.6589 39.1 +0.9 34 320 4.5355 0.7445 46.8 +3.2 23 230 4.3660 0.8115 16 030 4.2049 0.8618 11 260 4.0515 0.8988 8 043 3.9054 0.9256 5 836 3.7661 0.9449 4 297 3.6332 0.9588 3 207 3.5061 0.9689 TABLE 2

Thermistor Calculated R' Temperature Resistance 0+eo Res. R' from R ---or, 0 d2S. 9 R (Ohms) e de.-C ---------- _e -40 3 665 000 113.46 3 959 300 1.080 +1.2 -30 1 914 000 123.46 1 993 700 1.042 +0.7 -20 1 04-0 000 133.46 1 059 100 1.018 +0.3 585 500 143.46 588 930 1.006 +0.1 0 340 700 153.46 340 700 1.000 0.0 204 400 163.46 204 030 0.998 -0.0 126 100 173.46 125 960 0.999 -0.0 100 000 178.46 100 000 1.000 0.0 79 820 183.46 79 897 1.001 0.0 51 760 193.46 51 918 1.003 0.1 34 320 203.46 34 478 1.005 0.1 23 230 213.46 23 351 1.005 0.1 16 030 223.46 16 099 1.004 0.1 11 260 233.46 11 282 1.002 0.1 9 498 238.46 9 498 1.000 0.0 8 043 243.46 8 024.8 0.998 -0.1 5 836 253.46 5 786.9 0.992 -0.3 4 297 263.46 4 226.2 0.984 -0.5 3 207 273.46 3 122.8 0.974 0.9 i ib TABLE 3

Moisture Sample Resistance % H,0 Content resistance calc. from calc. from error % H,0 SR, Q log(SR) Equation 13 Col. 2 % H,0 9.5 835 000 000 8.9217 1 763 000 000 10.2 -0.6 11.4 200 000 000 8.3010 258 000000 11.7 -0.3 13.9 41 800 000 7.6212 41 800 000 13.9 0.0 16.3 11 900 000 7.0755 11 280 000 16.2 0.1 18.8 4 000 000 6.6021 3 780 000 18.7 0.1 21.9 1 250 000 6.0969 1 250 000 21.9 0.0 25.2 456 000 5.6590 473 000 25.3 -0.1 29.4 167 000 5.2227 169 000 29.5 -0.1 34.3 62 600 4.7966 62 600 34.3 0.0 40.9 23 300 4.3674 20 800 40.2 0.7

Claims (13)

1. I. A linearising circuit for use with semi-logarithmic sensing devices comprising a first pair of bipolar transistors, a potential divider, a second pair of bipolar transistors af substantially the same temperature as the first pair, circuit arrangements to control the collector currents in the first pair of transistors in such a way that the ratio of these currents is equal to the ratio of the current from a sensing device to the current from a reference component, and circuit arrangements to control the relative base-emitter voltages in the second pair of transistors so that the difference between these voltages is a fixed fraction of the difference between the base-emitter voltages of the first pair of transistors; whereby the ratio of the collector currents of the second pair of transistors is made a known linear function of the physical quantity or property of a material measured by the sensing device.
2. 2. A linearising circuit as claimed in Claim 1, in which the sensing device is resistive in nature, the reference component is also resistive and the circuit is arranged so that the sensor and the reference component each have substantially the same voltage applied to them.
3. 3. A linearising circuit as claimed in Claim I or Claim 2, in which the collector current of the first transistor of the first pair is made very nearly equal to the current from the sensing device by means which include an inverting current amplifying circuit, and the collector current of the second transistor is made very nearly equal to the current from the reference component while at the same time the collector voltages of the this pair of transistors are made very nearly equal to each other, by means which include an operational amplifier.
4. 4. A linearising circuit as claimed in any preceding claims, in which the potential divider takes the form of a pair of resistances connected in series.
5. 5. A linearising circuit as claimed in Claim 4, in which the potential divider is connected between the emitters of the first pair of transistors.

   - IG -
6. 6. A linearising circuit as claimed in any preceding claims, in which the required fraction of the difference betweei) the base-emitter voltages of the first pair of transistors is applied to the base-emitter circuits of the second pair of transistors by rijeans which include an operational amplifier.
7. 7. A linearising circuit as claimed in Claim 5, in which the voltage dropped across one of the resistances which make up the potential divider is applied to the emitters of the second pair of transistors by means which include an operational amplifier.
8. S. A linearising circuit as claimed in any preceding claims, in which the currents frow the collectors of the second pair of bipolar transistors are passed to a network of resistances which have values calculated or adjusted to correspond to the characteristics of the sensing device.
9. 9. A linearising circuit as claimed in Claim 8, in which a pair of voltages, tapped from points in the network of resistances connected to the collectors of the second pair of transistors, provide measurement and reference inputs to an analogue-to-digital converter circuit.
10. 10. A linearising circuit as claimed in Claim 9, in which the analoguetodigital converter is a type which drives a digital display and the values of the resistances in the network connected to the collectors of the second pair of transistors are chosen or adjusted such that the display will give a readout of the quantity or property measured by the sensing device.
11. 1 1.

    A A 1Inearising circuit. as clairned in any of claims 2 to 10, in which the sensing device is a negative temperature coefficient thermistor and the reference component is a fixed resistance.
12. 12. A linearising circuit as claimed in any of Claims 2 to 10, in which the sensing device is a sample of hygroscopic material held in contact with elecLrodes and the reference component is a negative temperature coefficient thermistor.
13. 13. A llil-leari. g s; n circuit substantially in one of the forms described herein with reference to Figures 4, 5, 6 and 8 of the accompanying drawings.