Method and device for measuring fluidic or calorimetric parameters

A method and a device serve for measuring fluidic or calorimetric parameters, for example the velocity of flow, and comprise the steps of heating up a sensor element arranged in a measuring environment, to a temperature higher than the surrounding temperature of the measuring environment, and deriving the parameter from the heat transmission between the measuring environment and the sensor element. In order to permit measurements the result of which is systematically independent of the absolute value of the heating power in the sensor element, two measurements are carried out successively at different temperatures, in the stationary condition. One determines the heating power at both these operating conditions and derives therefrom the parameter to be measured (FIG. 7).

The present invention relates to a method and a device for measuring 
fluidic or calorimetric parameters comprising the steps of heating up a 
heatable, temperature-sensitive sensor element, which is in thermal 
contact with a measuring environment, successively to at least two 
different temperatures higher than the surrounding temperature of the 
measuring environment, and deriving the parameter from the heat 
transmission between the measuring environment and the sensor element, by 
means of the heat transmission function for the sensor element, defined as 
the ratio between the thermal flow at the higher temperature and the 
difference between the higher temperature and the surrounding temperature, 
as a function of the parameter. 
The method and the device according to the invention serve preferably for 
measuring the speed of a flowing medium, the volume flow or the mass flow 
of a fluid, the filling level of fluids, or for measuring the thermal 
conductivity, the heat capacity or the heat transport. 
A method and a device for determining air mass flows have been known from 
German Disclosure Document No. 37 10 224. In these known arrangements, a 
heatable, temperature-sensitive sensor element, which is in thermal 
contact with the measuring environment, is heated up and cooled down in 
periodic succession. To this end, one applies initially a heating current 
to a heatable element, whereby the temperature of the element, and the 
voltage drop across the element, are caused to rise according to an 
exponential function. Once a predetermined upper voltage threshold has 
been reached, the current is switched over from a relatively high value of 
the heating current to a considerably lower value of a measuring current, 
with the result that the temperature drops again according to an 
exponential function, and the voltage, too, decreases in the same manner, 
except for a voltage surge occurring when the current is switched over. 
One then measures the time interval between the moment when the current is 
switched over and the moment at which a second predetermined lower voltage 
value is reached, i.e. the length of the cooling-down phase to a 
predetermined lower temperature. The length of this cooling-down phase 
provides a measure for the air mass flow to be measured, the cooling 
efficiency being the higher the greater the air mass flow is. 
U.S. Pat. No. 4,501,145 describes a method and a device for measuring a 
fluidic parameter by means of a sensor immersed in a fluid. According to a 
first variant of this known method the sensor is heated up, by means of a 
short-term heating-current pulse from a static balanced condition, in 
which it finds itself at the temperature of the surrounding fluid. After 
switching-off the heating-current pulse, the sensor is then only supplied 
with a much lower measuring current which, while permitting resistance 
measurements to be carried out, does not notably heat up the measuring 
resistor of the sensor. Simultaneously with switching over the heating 
current to the much lower measuring current, a first pulse is generated 
for starting a time-measuring arrangement. When the temperature of the 
sensor, which has risen as a result of the heating-current pulse, drops 
again a discriminator circuit, which is capable of detecting the moment 
when two threshold values of the temperature or the associated resistance, 
respectively, are reached, will trigger again measuring pulses for the 
time-measuring arrangement at the moment the predetermined threshold 
values are reached. At the end of each measurement, a total of three 
measuring pulses have been generated, and the two time intervals between 
the three measuring pulses have been recorded. It is then possible, with 
the aid of known formulas, to derive from these time intervals the heat 
transmission and, from the latter, the desired fluidic parameters. 
According to another variant of this known method, a Peltier element is 
used instead of a sensor with a heating resistor, the Peltier element 
being initially also set to the surrounding temperature of the fluid. The 
Peltier element is then supplied with current from a current source until 
the "hot" measuring point on the one hand and the "cold" measuring point 
on the other hand have assumed a predetermined temperature difference or 
voltage difference, respectively. One then switches off the Peltier 
current and observes, in the manner described before, the equalization of 
temperatures or voltages of the two measuring points of the Peltier 
element for the purpose of deriving time intervals, as a function of 
predetermined threshold values, corresponding to the voltage difference. 
A very similar method has been known from German Disclosure Document No. 
3639666. According to this known method, a heatable measuring sensor is 
also initially supplied with a heating-current pulse of high intensity and 
then supplied with a measuring current of low intensity, in order to 
determine, at the end of the heating interval, the exponential drop of the 
internal resistance of the measuring sensor, by measurements of the time 
intervals between the moments when predetermined threshold values are 
reached. 
According to another known method described by European Disclosure Document 
No. 210509, a heating-current pulse of a predetermined amplitude and 
length is applied to a suitable measuring element. At the same time, one 
determines alternatively, during the heating-up period or following the 
latter, the heating-up curve of the measuring element, which rises 
exponentially, and its cooling-down curve, which drops exponentially. The 
desired value to be measured can then be derived from the steepness of the 
respective curve, the speed of the temperature rise or the temperature 
drop providing a measure for this value. 
Another known method described by French Disclosure Document No. 2487973 
uses an arrangement where a first sensor, a heating element and a second 
sensor are arranged in the direction of flow in a pipe passed by a flowing 
fluid. This arrangement enables the flow rate of the fluid to be measured 
by determining either the temperature difference of the two sensors, at 
constant heating power, or alternatively the heating power to be applied 
for keeping the temperature difference of the two sensors constant. This 
is effected, according to the known method, by applying the heating power 
also in the form of heating-current pulses and recording the exponential 
curve of the measuring voltages obtained. 
These known methods are generally described as "dynamic" methods, because 
the exponential functions of the temperature rise or drop are obtained 
only by sections and because no stationary final value of the temperature 
or voltage (at constant current) is ever reached. 
German Disclosure Document No. 3706622 describes another method and a 
device for determining the air mass flow where a temperature-sensitive 
sensor element is supplied with a constant electric heating power. The 
current and the voltage are measured at the heatable element, and the 
heating power is derived, and then adjusted to a constant value, by 
multiplying the measured values. Further, a momentary resistance value of 
the heatable element is determined by dividing the voltage and the current 
values, and the resistance value so obtained is translated into a 
temperature value by means of a corresponding curve. Another curve then 
serves for deriving an air mass value from the temperature value, taking 
into account the surrounding temperature. This other known method is 
generally described as a "static" method because the sensor element 
remains constantly in a stationary state of equilibrium. 
However, these known methods and devices are connected with a number of 
disadvantages. 
As mentioned before, in the case of the dynamic method, there always exists 
a thermal imbalance between the sensor element and the measuring 
environment because the interval between the voltage dropping across the 
element (or alternatively the time interval) are intentionally fixed in 
such a manner that no stationary conditions are obtained between the 
heating-up or the cooling-down process, in order to obtain the shortest 
possible measuring cycle time, compared with the thermal time constant of 
the sensor element. This operating mode necessarily leads to the result 
that the temperature distribution in the sensor element, the development 
in time of the cooling-down curve and, accordingly, the measuring result 
are made dependent explicitly on the heating infeed, in particular the 
heating current or the heating voltage so that precise constant-feed 
sources are required. 
Dynamic methods and devices of the known type are further connected with 
the drawback that the measuring result depends on the output temperature 
of the measuring environment, i.e. on the surrounding temperature. In 
order to achieve results which are independent of this interfering value, 
complex and expensive compensation measures would be required in the case 
of dynamic methods and devices. 
On the other hand, the known static methods and devices are connected with 
the disadvantage that the usual drift problems of static methods have to 
be overcome. In particular, it is absolutely necessary also with the 
static methods to correct the measuring result with regard to the 
surrounding temperature because one cannot tell from the measuring result 
whether the measured value, for example the air mass flow, or only the 
surrounding temperature has changed. In order to compensate this 
interfering influence, one therefore has to measure the surrounding 
temperature. And this requires the use of an additional sensor element 
causing additional expenses. 
Now, it is the object of the present invention to improve a method and a 
device of the type described above in such a manner that the measuring 
results obtained are free from such interfering values, in particular free 
from any influence of the heating infeed and the surrounding temperature, 
without the need to provide expensive compensation measures, and that the 
method and device can be implemented at low cost. 
Starting out from the method described above, this object is achieved 
according to the invention by the steps of: 
adjusting a first operating condition at the sensor element in a manner 
such that a stationary temperature equilibrium is obtained between the 
sensor element and the measuring environment at a first predetermined 
higher temperature; 
determining a first value of the electric heating power at the first 
operating condition; 
adjusting a second operating condition at the sensor element in a manner 
such that a stationary temperature equilibrium is obtained between the 
sensor element and the measuring environment at a second predetermined 
higher temperature; 
determining a second value of the electric heating power at the second 
operating condition; 
determining the difference between the first and the second values of the 
heating power; 
dividing the difference between the values of the heating power by the 
difference of the first and the second predetermined higher temperature 
values, and comparing the quotient with the heat transmission function to 
derive therefrom the parameter as a numerical value. 
Starting out from the device described before, the object underlying the 
present invention is achieved by the following features: 
The sensor element is formed preferably with the aid of a 
temperature-dependent heating resister; 
the sensor element is connected to an electric supply source; 
measurement pick-ups are connected to the sensor element for picking up the 
current flowing through the heating resistor and the voltage dropping 
across the heating resistor; 
the measurement pick-ups are connected to a divider; 
the divider is connected to the input of a comparator; 
another input of the comparator can be connected alternatively to a first 
constant-value storage or a second constant-value storage, via a 
change-over switch; 
the output of the comparator is connected to the control input of the 
electric supply source; 
the measurement pick-ups are connected to a multiplier; 
the multiplier can be connected alternatively to a first intermediate 
storage or a second intermediate storage, in response to the position of 
the change-over switch; 
the intermediate storages are connected to a subtractor; 
the subtractor is connected to a display unit, via a weighing stage. 
This solves the object underlying the invention fully and perfectly because 
by combining the measured values obtained at the two operating conditions, 
the influence of the surrounding temperature is finally eliminated. 
Consequently, the measuring result is systematically free from any 
influences of this interfering value, so that no additional temperature 
compensation is required. Given the fact that the measuring values are 
picked up at a state of temperature equilibrium, the measuring result is 
also independent of the development in time of the heating-up and 
cooling-down curves. 
The measuring result is also independent of the resistance value of the 
particular heating resistor used and, accordingly, also independent of any 
aging phenomena of the heating resistor, and any current and voltage 
variations. 
Further, the measuring values obtained are independent of the shape of the 
temperature curve of the sensor element and also of its dynamic 
characteristics. 
Due to the fact that the measured values are picked up at the two operating 
conditions in succession, a multiplex measuring system is realized which 
can do with a single sensor element. One arrives in this manner at a 
compact and also a low-cost solution which is free from influences 
resulting from unit variations and from positional correlations between 
the measuring element and the reference element, as occurring in 
arrangements using a plurality of sensor elements. 
A preferred embodiment of the method according to the invention is 
characterized by the fact that 
the first and the second operating conditions are adjusted by means of an 
automatic control circuit which compares the quotient of the actual 
voltage and current values occurring at a temperature-dependent resistor 
of the sensor element with a predetermined resistance value of the 
temperature-dependent resistor corresponding to the predetermined higher 
temperature, and makes use of the difference for adjusting the operating 
condition. 
According to other, alternative embodiments of the invention, the 
temperature-dependent resistor may take the form of a separate measuring 
resistor which may, preferably, be arranged on the same chip as the 
heating resistor of the sensor element. According to a preferred 
embodiment, however, the heating resistor is used itself as 
temperature-dependent resistor. One obtains in this manner a 
single-element sensor with incorporated heating where all relevant 
measuring processes occur at one and the same point within the sensor 
element. 
Although, preferably, for adjusting the operating condition, the current is 
adjusted via the heating resistor, it is also possible to adjust the 
voltage at the heating resistor. 
This type of regulation results in advantageously short measuring cycle 
times. The adjusting time constant for the heating-up and cooling-down 
phases is smaller in this case than the thermal time constant of the 
sensor element, by the amplification factor of the regulating loop. For, 
thanks to the use of such a regulation, it is now possible to heat the 
heating resistor up rapidly by applying initially a very high heating 
power, in order to "brake" the heating process later in a controlled 
manner, until the desired stationary final value has been reached. 
Consequently, it is not necessary in the case of the present invention to 
wait until the exponential temperature curve has approximated 
automatically to the final value with sufficient accuracy, with the 
respective time constant. It is, thus, possible to achieve extremely short 
measuring times which is of critical importance in particular in the case 
of measuring processes involving temperature measurements. The regulator 
used in this connection is also described as "constant-value regulator" 
according to the "BCTR method" ("Bistable Constant Temperature 
Regulation"). 
Another particularly preferred embodiment of the method according to the 
invention is characterized by the fact that the environmental temperature 
is derived from the values of the heating power and the predetermined 
higher temperatures. 
This feature provides the advantage that the method according to the 
invention and/or the devices used for carrying out this method may be used 
simultaneously for determining the environmental temperature, which is 
often also of interest, without the need to provide substantial additional 
measures. 
Other advantages of the invention will appear from the specification and 
the attached drawing. 
It is understood that the features that have been described before and will 
be explained hereafter may be used not only in the described combinations, 
but also in any other combination, or individually, without leaving the 
scope and intent of the present invention.

In FIG. 1, a measuring arrangement of the type which is of interest in 
connection with the present invention is designated generally by reference 
numeral 10. 
A fluid flow 12, for example a gas or a liquid, is passed through a pipe 
11. The fluid flow 12 acts upon a heatable, temperature-sensitive sensor 
element 13 comprising a heating resistor 14. The sensor element 13 is 
connected to a measuring and regulating circuit 16 via a line 15. The 
circuit 16 in turn is connected to an indicator unit 17. 
With the aid of the measuring arrangement 10 it is possible to determine 
the speed of the fluid flow 12, its volume flow or mass flow. It is 
expressly noted, however, that the described measurements are to be 
understood only as examples and that the present invention may be used 
also to solve other measuring problems. As the present invention makes use 
of the heat transmission between the heatable sensor element 13 and its 
environment, the invention may be used with advantage also for measuring 
the filling level of liquids and other media which either surround or do 
not surround the sensor element 13, depending on the filling level, so 
that the heat transmission varies according to the latter. In addition, 
the present invention may be used with advantage for measuring the thermal 
conductivity, the heat capacity or the heat transport when the sensor 
element 13 consists, for example, of a first material to be examined and 
the environment consists of a second material to be examined, and the 
interaction between these materials is to be determined. 
In the case of the measuring arrangement 10 according to FIG. 1, the sensor 
element 13 is heated up to a temperature .theta. higher than the 
surrounding temperature .theta..sub.o of the fluid flow 12. The heat flow 
Q at the higher temperature .theta. is then determined by the formula: 
EQU Q(.theta.)=G(w)(.theta.-.theta.0), 
wherein G (w) is the heat transmission function defining the dependence on 
the parameter w to be measured, with respect to the particular 
configuration of the measuring arrangement 10. 
If, for example, the measuring parameter w defines the velocity of the 
fluid flow 12, then the heat transmission function G (w) is defined by the 
following rule: 
EQU G(w)=A.alpha..sub.0 (l+.gamma.w.sup.1/2), 
wherein A is the area of thermal contact, .alpha..degree. is the heat 
transmission constant between the sensor element 13 and the fluid flow 12, 
in the stationary condition of the fluid flow 12, and .gamma. is the 
so-called kinematic convection factor, i.e. a constant determined by the 
geometry of the measuring arrangement 10, the density of the fluid flow 
12, its viscosity and the thermal conductivity and specific heat capacity 
during the measurement. 
Now, if a special parameter w is to be determined, the respective heat 
transmission function G (w) of the measuring arrangement used must first 
be solved with respect to the parameter w, whereafter the numerical value 
of the parameter w can be derived from the before-described relation 
between the heat flow Q, the heat transmission function G (w) and the 
temperatures .theta., .theta..sub.o. 
In the case of known measuring arrangements, one proceeds in the manner 
illustrated in FIG. 2 by the first curve 20 for the temperature .theta. of 
the sensor element 13, plotted as a function of the time t. 
According to a first variant of the prior art, one presets a predetermined 
temperature interval .DELTA..theta., i.e. a given difference between a 
higher temperature .theta..sub.1 and a lower temperature .theta..sub.2, 
both temperatures being substantially higher than the surrounding 
temperature .theta..sub.o of the fluid flow 12. One then connects and 
disconnects alternately an electric energy source to and from the heating 
resistor 14 so that one obtains the phases 21 for the heating-up process 
and 22 for the cooling-down process of the sensor element 13, which can be 
seen clearly in FIG. 2. The temperatures .theta..sub.1 and .theta..sub.2 
may be preset in this case for example in the form of predetermined 
thermoelectric voltages of a thermocouple element 13 comprised in the 
sensor element 13. 
If the electric energy is disconnected from the heating resistor 14, for 
example at the point in time t.sub.1, the first curve 20 follows the 
cooling phase 22 to the moment t.sub.2 when the lower temperature 
.theta..sub.2 is reached. After the electric energy has been connected 
again, the curve then follows a heating phase 21 until the higher 
temperature .theta..sub.1 is reached at the moment t.sub.3. The respective 
time intervals elapsed are defined as .DELTA..sub.1 t for the cooling 
phase 22 and .DELTA..sub.2 t for the heating phase 21. 
Now, the numerical value of the parameter w can be determined in the manner 
described above, for a particular measuring arrangement 10, from the time 
intervals .theta..sub.1 t and .theta..sub.2, for a given temperature 
interval .DELTA..theta.. 
From FIG. 2 it follows directly that it is just as well possible, for 
another variant according to the prior art, to proceed in the opposite 
manner, by presetting the time intervals .DELTA..sub.1 t and .DELTA..sub.2 
t and deriving therefrom, as parameters to be measured, the temperatures 
.theta..sub.1 and .theta..sub.2 occurring in the sensor element 13 at the 
end of the heating phase 21 and the cooling phase 22, respectively. 
Further, it follows directly from FIG. 2 that the measuring result is 
directly dependent on the amount of heating power applied and also on the 
surrounding temperature .theta..sub.0. 
For the purposes of the present invention one now makes use of the 
following considerations: 
If one presets for the sensor element 13 two temperatures .theta..sub.1 and 
.theta..sub.2 as constants, at which a stationary condition is obtained, 
then the heat flow Q (.theta.) occurring at these two stationary 
conditions at the temperatures .theta..sub.1 and .theta..sub.2 will be 
equal to 
EQU Q(.theta..sub.1)=G(w)(.theta..sub.1 -.theta..sub.0) 
EQU Q(.theta..sub.2)=G(w)(.theta..sub.2 -.theta..sub.0) 
according to the formula described further above. As a stationary state of 
equilibrium is reached at the temperatures .theta..sub.1 and 
.theta..sub.2, the heat flow Q from the sensor element 13 to the fluid 
flow 12 is just equal, when this equilibrium is reached, to the steady 
infeed of heating power P: 
EQU Q(.theta..sub.1)=P.sub.1 
EQU Q(.theta..sub.2)=P.sub.2 
When forming the difference between these heating power values, one obtains 
the formula 
EQU .DELTA.P=G(w)(.theta..sub.1 -.theta..sub.2), 
which shows clearly that the difference .DELTA.P is independent of the 
surrounding temperature .theta..sub.0 and, when constant values are preset 
for the temperatures .theta..sub.1 and .theta..sub.2, is a function only 
of the parameter w. 
If one then determines the heating power P.sub.1 and P.sub.2, respectively, 
at the two operating conditions with a stationary state of equilibrium, at 
the temperatures .theta..sub.1 and .theta..sub.2, respectively, one 
obtains the following measuring formula for the difference .DELTA.P: 
EQU P=(U.multidot.I).sub.1 -(U.multidot.I).sub.2 
from which the parameter w to be measured can be derived independently of 
the surrounding temperature .theta..sub.0, by application of the relation 
described before. 
FIG. 3 shows a second, comparable curve 25 which is similar to that of FIG. 
2 but which--contrary to the prior art as illustrated in FIG. 2, where no 
stationary conditions are encountered at the reversal points of the curve 
20--exhibit upper areas 28 and lower areas 29 reflecting stationary states 
for both the heating phases 26 and the cooling phases 27, respectively. 
In the case of the second curve 25 illustrated in FIG. 3, the heating power 
P.sub.1 and P.sub.2 encountered is measured, according to the invention, 
at the moments t.sub.1 and t.sub.2, respectively, for the purpose of 
determining the numerical value of the parameter w in the manner described 
above. 
For this purpose, one needs to know the dependence of the difference 
.DELTA.P on the parameter w to be measured, which is illustrated for a 
given example by the curve 35 of FIG. 4. As mentioned before, this third 
curve 35 is a function of the heat transmission function G (w) and, 
accordingly, of the respective configuration of the measuring arrangement 
10 as regards its geometry, the materials used and their physical 
characteristics. 
From the two equations of state defining P.sub.1 and P.sub.2 the 
surrounding temperature .theta..sub.0 can be determined in addition to the 
parameter w. By transforming the equations in a convenient manner, the 
following formula is obtained for the surrounding temperature 
.theta..sub.0 : 
EQU .theta..sub.0 =.theta..sub.2 (P.sub.1 /.DELTA.P)-.theta..sub.1 (P.sub.2 
/.DELTA.P) 
The above relation is independent, explicitly, of the parameter w and 
constitutes, therefore, the conditional equation for the surrounding 
temperature .theta..sub.0, the two higher temperatures .theta..sub.1, 
.theta..sub.2 being firmly predetermined. 
For determining the heating power P in the heating resistor 14, one may 
make use alternatively of two arrangements of the type illustrated by 
FIGS. 5 and 6 by way of example. 
In the case of the embodiment according to FIG. 5, a signal processor or 
microcontroller 40 is provided which is equipped with digital regulating 
means 41 with discrete values in time. The regulating means 41 generates 
an output current I flowing through the heating resistor 14. The voltage U 
dropping consequently across the heating resistor 14 is supplied to the 
processor 40 as an input value. The processor 40 is connected, via a bus 
interface 42, to a measuring data line 43 and a control line 44 in order 
to transmit measured parameters for w and .theta..sub.0 and to control, 
for example, peripheral regulating units. The indicator unit 17 may be 
connected directly to the processor 40. 
The operation of the arrangement illustrated in FIG. 5 will be explained in 
more detail below, with reference to the block diagram of FIG. 7. 
Alternatively, FIG. 6 shows a similar arrangement which differs from that 
illustrated by FIG. 5 essentially insofar as the output value generated by 
the digital control means 41' is a voltage U which is applied to a voltage 
divider consisting of the heating resistor 14 and a fixed resistor 45. The 
measuring signal consists of the current I flowing through the voltage 
divider 14, 45, which is picked up at the fixed resistor 45 and supplied 
to the processor 40'. The other elements are identical to those 
illustrated in FIG. 5 and are, therefore, identified only by an 
apostrophe. 
FIG. 7 shows a block diagram of one embodiment of a measuring and 
regulating circuit 16 according to the invention, which may be used, for 
example, in the measuring arrangement 10 illustrated in FIG. 1. 
A weighing stage 50, in which the third curve 35 according to FIG. 4 is 
stored as a characteristic curve or field, has its first output 51 
connected to the indicator unit 17. 
A second output 52 is connected to one input of a first control element 53 
which is preferably designed as an AND gate. The first control element 53 
controls a change-over switch 54 which enables a first constant-value 
storage 55 or a second constant-value storage 56 to be connected 
alternatively to an inverting input of a comparator and/or subtracter 57. 
The latter's non-inverting input is connected to a first computing stage 
58 whose input end consists of two measurement pick-ups 59, 60, while its 
output end consists of a divider 61. 
The output of the comparator 57 controls, via the control stage 62, a 
variable current source 63 comprising three outputs 64a, 64b and 64c. 
The first output 64a is connected to the temperature-responsive heating 
resistor 14 via the line 15 and, via other lines, to the first measurement 
pick-up 59 of the first computing stage 58 and to a fourth measurement 
pick-up 67 of a second computing stage 65. The second output 64b is 
connected to the second measurement pick-up 60 of the first computing 
stage 58, and the third output 64c is connected to a third measurement 
pick-up 66 of the second computing stage 65. 
The output of the second computing stage 65 takes the form of a multiplier 
68. The latter can be connected selectively to a first intermediate 
storage 70 or a second intermediate storage 71, depending on the position 
of the change-over switch 54. The outputs of the storages 70, 71 are 
connected to a subtracter which in turn is connected to one input of the 
weighing stage 50. 
Another output of the divider 61 of the first computing stage 58 controls a 
threshold-value detector 75 one output of which is connected to another 
input of the first control element 53, for actuation of the change-over 
switch 54. Another output of the threshold-value detector 75 is connected 
to inputs of a second control element 76 and a third control element 77, 
whose other inputs are connected to the control outputs of the first 
constant-value storage 55 and the second constant-value storage 56, 
respectively. The outputs of the control elements 76, 77 control the 
intermediate storages 70, 71 in such a manner that the measured values 
received from the output of the multiplier 78 are stored in the 
intermediate storage 70, 71 assigned to that constant-value storage 55 or 
56 which is connected to the subtracter 57 via the change-over switch 54. 
In FIG. 7, one can further see another weighing stage 80 whose input is 
connected to the constant-value storages 55, 56, the intermediate storages 
70, 71 and the subtractor 72. One output of the other weighing stage 80 is 
likewise connected to the indicator unit 17 which is equipped with a 
second numerical indication for displaying the output signal of the other 
weighing stage 80 in numerical values. The elements described above serve 
for determining and indicating the surrounding temperature .theta..sub.0 
in the manner described in more detail further above. 
The operation of the arrangement illustrated in FIG. 7 is as follows: 
The temperatures .theta..sub.1 and .theta..sub.2 according to FIG. 3 have 
been entered as constant values into the constant-value storages 55, 56. 
Given the fact that the relation between the resistance value R of the 
heating resistor 14 and the temperature .theta. is known, the temperature 
values .theta..sub.1 and .theta..sub.2 may also be expressed as resistance 
values or, by application of Ohm's Law, as quotients (U/I).sub.1 or 
(U/I).sub.2 of the voltage U and the current I. If the higher temperature 
value .theta..sub.1 is to be selected first, the change-over switch 54 
must assume the position indicated in FIG. 7. In this position, the 
constant value (U/I).sub.1 stored in the first constant-value storage 55 
is fed to the inverting input of the subtractor 57 whose non-inverting 
input is supplied with a quotient U/I from the output of the divider 61. 
This quotient is the quotient of the actual values of the voltage U and 
the current I encountered at the heating resistor 14 which have been 
supplied, as measured values, to the measurement pick-ups 59 and 60, i.e. 
to a voltmeter and an ammeter. 
As long as the desired temperature .theta..sub.1 has not been reached, the 
output signal of the divider 61 will remain smaller than the signal 
received from the first constant-value storage 55, with the result that 
the resistance/current converter 63 feeds a higher current I into the 
heating resistor 14 via its first output 64a and the line 15. 
The control loop formed by the elements 57, 58, 63 and 14 continues to 
adjust the current I via the heating resistor 14 until the desired final 
value .theta..sub.1 has been reached. The current I may initially be set 
to a very high value so that the regulating cycle in the regulating loop 
will be run through within a minimum of time. 
The measured values of the voltage U and the current I are picked up in 
parallel in the second computing stage 65 by an ammeter and a voltmeter, 
i.e. the measurement pick-ups 66 and 67, and are multiplied in the 
multiplier 68 whereby one obtains (UI).sub.1, i.e. the electric heating 
power P.sub.1. 
However, this value (UI).sub.1 must not be further processed as long as the 
stationary state, as reflected by the upper area 28 in FIG. 3, has not 
been reached. 
In order to detect the moment when a stationary state of equilibrium is 
obtained, or when a condition approximating this state with sufficient 
exactness prevails, the individual increments of the quotient U/I are 
picked up from another output of the divider 61 and processed in a 
threshold-value detector 75. 
The approximation of the increment to zero may be detected, for example, by 
comparing the increment in a comparator with a predetermined lower 
threshold value. 
If a sufficiently exact approximation to the stationary threshold value is 
reached, an output signal will be generated by the threshold-value 
detector 75 in both these cases. The output signal causes, on the one 
hand, via the control elements 76 and 77, the value for the momentary 
heating power formed in the multiplier 68 to be inscribed into the second 
intermediate storage 71, and has on the other hand the effect that the 
change-over switch 54 is switched over and the heating resistor 14 is 
adjusted to the lower temperature value .theta..sub.2. 
The regulating cycle of the elements illustrated in FIG. 7 is then repeated 
analogously until the threshold-value detector 75 signals that the lower 
threshold value, or a sufficiently exact approximation thereto, has been 
reached. 
After both a heating phase 26 and a cooling phase 27 (FIG. 3) have been run 
through in this manner, the respective stationary values for the heating 
power P.sub.1 and P.sub.2 are stored in the intermediate storages 71 and 
70. The substractor 72 then forms the difference of these values and feeds 
the difference to the weighing stage 50 so that, by application of the 
characteristic curve .DELTA.P (w) of the respective heat transmission 
function G (w), the numerical value of the parameter w is made available 
at the first output 51. 
The above explanations relating to the regulating unit 57, 61, 63 refer to 
a regulation system with current infeed, i.e. to the case illustrated in 
FIG. 5, where the current I is adjusted and the voltage U obtained is 
picked up as measured value. However, it goes without saying that the 
block diagram of FIG. 7 may be modified also to replace the current infeed 
by a voltage infeed for the heating resistor 14, as illustrated in FIG. 6. 
It is further understood that the components described above may be 
implemented also using analog technology, in which case multiplier and 
divider elements, differential amplifiers, analogue nominal-value 
selectors, storage elements and a regulator, for example with PI or PID 
regulating characteristics, will be required. 
However, in order to minimize the circuitry input, the measuring and 
regulating circuit 16 is implemented preferably using digital technology, 
as indicated before in connection with FIGS. 5 and 6. One then needs a 
microcontroller or a signal processor provided with an adaptive regulating 
algorithm.