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Electronic compensation of an absolute differential radiometer
Solar Energy, Vol. 20, pp. 175-178. Pergamon Press 1978. Printed in Great Britain
TECHNICAL NOTE Electronic compensation of an absolute differential radiometer G. BRAUTTI, B. MARANGELLI and A. RAINO Istituto di Fisica, University of Bari, Italy
(Received 12 January 1977; in revised fornz 16 June 1977) trical power (a power transistor). When there is a difference between the radiant energy falling on the two collectors, from the thermistors we obtain an electrical signal whose magnitude is a monotonic function of the temperature difference existing bebetween the same collectors. The signal is fed to a high gain amplifier, whose output current warms up the collector which is colder, until the temperature is equalized. In this condition of balance, the electrical power fed to one collector is equal to the difference between the radiation power falling on the two collectors. It is irrelevant, then, whether the balance is dynamic or static, because the condition of "equal temperatures" means that the temperature rate of change, dTIdt, and the power losses by radiation, conduction and convection are the same for both collectors. To assure oneself that these conditions are satisfied, care must be taken to build both collectors as far as possible of equal shape, thermal insulation and shielding, exposure to wind and to diffuse radiation sources, when the latter are not to be measured.
l. I N T R O D U C T I O N
The problem of measurement of radiant energy has been widely studied[l]. Among others, the technique.of absolute radiometry based on the principle proposed by Angstrom seems to us particularly interesting, also because such an instrument turns out to be useful for the precise evaluation of the transmission and reflection coefficients of system components. However, we think that the compensating method commonly used in such an instrument, including an human operator in the feedback loop, is not certainly the best to get the maximum performance inherent to the principle. Therefore, we have built an electronically compensated absolute, differential radiometer following the abovementioned principle, but exploiting some modern electronic circuitry. The exclusion of the human operator from the compensating loop allows a more precise analysis of the time response and of the compensation errors. In this technical note, we turn our attention chiefly to the electronic circuit implementing the feedback loop. For the purpose of testing the circuit, we have also built two simple collectors, described below. 2. P R I N C I P L E
OF OPERATION
A schematic diagram of the instrument is in Fig. l, It consists of two "blackbody" collectors of radiant energy, both provided with a temperature sensor (a thermistor) and a source of elec-
3. ELECTRONIC CIRCUIT Figure 2 shows the electronic circuit. The electrical power is dissipated directly on one of the power transistors, both having constant collector-to-emitter voltage Vo (i.e. without resistor load at the transistor collector). Thus, the current I flowing in the
//b
C
/o . . . . . . . .
_......
a
/' jO
, \
J
Fig. 1. Schematic diagram of the radiometer: a, mask; b, diaphragm; c, thermistor; d, power transistor; e, PVC box; f, aluminium heat sink; g, heating current; h, electronic circuitry. 175
Technical Note transistor is linearly related with the power W to be measured, i . e . / = WI V o. Actually, as shown in the Fig. 2, we measure the emitter current, obtaining directly the difference in radiation power fed to the collectors. A small correction, which takes into account the base current, has been applied directly on the scale of the reading instrument. To close the loop with negative feedback, the thermistor (NTC) labelled with one asterisk (see Fig. 2) must be mounted on the same collector plate as the PNP transistor (one asterisk); elements labelled with two asterisks are mounted on the other collector. 4. CIRCUIT ANALYSIS The circuit must be stable against oscillations, which may start up if at some frequency the loop gain in /> 1. A linearized equivalent circuit is given in Fig. 3. A complete mathematical analysis, not reported here, allows to find the conditions to achieve the desired degree of stability, also taking into account the change of the thermistor sensitivity, which happens in the usable temperature range. The "input" to the system is given by the output voltage v~ of the thermistor bridge. The integrated amplifier, the driver transistors, and the power transistors are represented by the sources Kv~, hfeiI, h~,htei~,respectively (K = 5o). In the thermal section of the equivalent circuit, the power dissipated at the collector of the transistor which conducts current, is represented by a current generator W~, and from now on the signals at the following nodes of the equivalent circuit are the temperatures, in °K; the thermal capacitances are in J/°K. the thermal resistances in °K/W. The ground is the ambient temperature. The complete list of the symbols used is given in Table 1. Table 1. List of symbols used in Fig. 2 K ht, R~ WE h~, Ojc Oc~
0,o Os,,. 0~o
0,_.~ T
voltage gain of operational amplifier ,ttA 74I current gain of driver transistor BC 119 input impedance of conducting power transistor (in this case, the 2N 3055) generator simulating the electrical power dissipated on the power transistor 2N 3055 current gain of 2N 3055 thermal resistance between junction and case of the power transistor thermal resistance between case and sink (radiation collector) on which the power transistor is mounted thermal resistance between sink and ambient thermal resistance between the sink and the case of the thermistor thermal resistance between the case of the power transistor and ambienl thermal resistance between the case of the thermistor and the ambient absolute temperature
Since both the collectors can be used to collect the radiant energy, but only the one receiving less radiant energy is fed with electrical power, the equivalent circuit is shown for the particular case where only the PNP transistor (and the collector on which it is mounted) is illuminated by the sun, where heat is accepted by the thermal capacitor labelled by the "sun face". Of course, in that case only the NPN (single asterisk) transistor is conducting. Data for thermal capacity and resistance were obtained from the manifacturer data sheets, whenever possible, or by a direct measurement. However, it should be noted that these values are only relevant for the time response and the stability of the instrument, while not influencing the equilibrium readout. 5. MECHANICALCONSTRUCTION Both radiation collectors were built using black fumed aluminium plates normally used as heat sink for power transistor cooling. On each plate a power transistor and a thermistor were
177
mounted. Silicon grease was used to reduce the thermal resistance between the contact surfaces, The sensing thermistors are screwed as near as possible to the transistors. The collectors are then mounted in two PVC boxes (internal dimensions 13 x 13 x 10 cm3). The front of the box is a polished aluminium diaphragm, whose double function is to define precisely the sensitive area, and to reflect back on the collector most of the radiation which is diffused by the same collector because of imperfect "black". A schematic cross-section drawing of both collectors is in Fig. 1. 6. OPERATION AND RESULTS The instrument response to a step function was tested with an artificial radiation source, and may be seen, in normalized form, in Fig. 4. The open loop gain was adjusted to obtain the fastest rise-time with less than 5 per cent overshoot. If the loop gain is not carefully controlled, larger overshoot, or even instability, can occur. For the present instrument the open loop gain is now 62dB at 0 Hz, the dominant time constant 16rain. When normally operated (i.e. with closed loop) the rise-time is 20 sec. The operational parameters are collected in Table 2. The angle of sensitivity of the instrument is defined by the object we use to mask one of the collectors of radiant energy, rather than by diaphragms, as done in all other instruments. The test measurements were taken with a simple mask of circular shape, which subtended a solid angle of approximate half-opening of 20° (full sensitivity), to 50° (penumbra limit). The results of these test measurements, taken in Bari, are summarized in Fig. 5. All the measurements were taken with fine weather and no visible clouds. The read-out reliability is actually limited by the mechanical construction of the collectors. Their physical dimensions, as well as the absence of those refinements that may be found in commercial collectors, make the instrument not particularly insensitive to the air turbulence and to other external disturbances, that are not seen as "common-mode" signals. Reading the output current by means of a digital meter, it turns out that the short term stability of the read-out is about 5 per cent, due to the low common-mode rejection of the collectors. Coupling the circuit with collectors particularly insensitive to turbulence and wind, would reduce considerably this drawback, perhaps well below the stated precision of commercial instruments (0.5 per cent). Another cause of error could be the power supply regulation: however, this is certainly a second order effect, because it will contribute very little (0.01 per cent) using well designed modern power supplies.
,
f-.._
O5
0
5o
i00
150
20o
sec
Fig. 4. Normalized transient response of the radiometer. Table 2. Parameters of the instrument 1. 2. 3. 4. 5. 6.
Sensitive area of the collector Absolute sensitivity Max. measurable power (full scale) R.m.s. noise in quiet air (input equivalent) Thermal drift of output base-line Rise-time of the response
50 cm 2 67 mA/W 30 W 10-2W 20 mW/°K hr 20 sec
178
Technical Note
9
O75
0.,~
0.25
1
I
I
8
12
16
hr
Fig. 5. Test measurements, taken at Bari (lat. 41°08'N, height ~ m over m.w.I.). O, 10 June, 1976; +, I1 June, 1976; 0 , 12 June, 1976; &, 14 June, 1976.
Finally, also the response time is certainly far above the performance of commercial instruments (1 sec for thermopile instruments): however, it actually depends essentially on the thermal capacitance of the collectors and may be easily reduced by reducing the collector area and, at the same time, the sensitive area of the diaphragms, because of the maximum power ratings of the transistors.
7. CONCLUSIONSAND IMPROVEMENTS The elementary automation of an old-type instrument has led to a direct-reading, absolute, cheap and sensitive device that, with improvements in collector mechanics, could overcome the drawbacks of the instruments calibrated by direct comparison. Our work will continue, to obtain the following features: (a) Full portability (now the power supply is operated with line power). (b) Reduction of the collector size, to reduce both the open loop time constant and the electrical resistance from the heat source to the thermal sensor. These improvements will allow us to increase the overall speed of response of the instrument, and to obtain a better balance by increasing the open-loop gain. (c) Improvement of the mechanical construction, to reduce the sensitivity to turbulence, which is now the main limitation to the instrument stability. (d) Improvement of the geometry of shielding and masking, for better definition of the acceptance angle, when the instrument is used as a normal incidence pyrheliometer. (e) Alternatively, we will evaluate the capability of the instrument as an absolute pyranometer (i.e. 2~r acceptance in solid angle with cosine type sensitivity law, full spectral sensitivity from a = 103/zm to vacuum UV).
Acknowledgements--The authors wish to thank Messrs. B. Bia, N. Ceci and R. Liuzzi for their valuable technical assistance. REFERENCE
1. Kinsell L. Coulson, Solar and terrestrial radiation. Academic Press, New York (1975).
TECHNICAL NOTE Electronic compensation of an absolute differential radiometer G. BRAUTTI, B. MARANGELLI and A. RAINO Istituto di Fisica, University of Bari, Italy
(Received 12 January 1977; in revised fornz 16 June 1977) trical power (a power transistor). When there is a difference between the radiant energy falling on the two collectors, from the thermistors we obtain an electrical signal whose magnitude is a monotonic function of the temperature difference existing bebetween the same collectors. The signal is fed to a high gain amplifier, whose output current warms up the collector which is colder, until the temperature is equalized. In this condition of balance, the electrical power fed to one collector is equal to the difference between the radiation power falling on the two collectors. It is irrelevant, then, whether the balance is dynamic or static, because the condition of "equal temperatures" means that the temperature rate of change, dTIdt, and the power losses by radiation, conduction and convection are the same for both collectors. To assure oneself that these conditions are satisfied, care must be taken to build both collectors as far as possible of equal shape, thermal insulation and shielding, exposure to wind and to diffuse radiation sources, when the latter are not to be measured.
l. I N T R O D U C T I O N
The problem of measurement of radiant energy has been widely studied[l]. Among others, the technique.of absolute radiometry based on the principle proposed by Angstrom seems to us particularly interesting, also because such an instrument turns out to be useful for the precise evaluation of the transmission and reflection coefficients of system components. However, we think that the compensating method commonly used in such an instrument, including an human operator in the feedback loop, is not certainly the best to get the maximum performance inherent to the principle. Therefore, we have built an electronically compensated absolute, differential radiometer following the abovementioned principle, but exploiting some modern electronic circuitry. The exclusion of the human operator from the compensating loop allows a more precise analysis of the time response and of the compensation errors. In this technical note, we turn our attention chiefly to the electronic circuit implementing the feedback loop. For the purpose of testing the circuit, we have also built two simple collectors, described below. 2. P R I N C I P L E
OF OPERATION
A schematic diagram of the instrument is in Fig. l, It consists of two "blackbody" collectors of radiant energy, both provided with a temperature sensor (a thermistor) and a source of elec-
3. ELECTRONIC CIRCUIT Figure 2 shows the electronic circuit. The electrical power is dissipated directly on one of the power transistors, both having constant collector-to-emitter voltage Vo (i.e. without resistor load at the transistor collector). Thus, the current I flowing in the
//b
C
/o . . . . . . . .
_......
a
/' jO
, \
J
Fig. 1. Schematic diagram of the radiometer: a, mask; b, diaphragm; c, thermistor; d, power transistor; e, PVC box; f, aluminium heat sink; g, heating current; h, electronic circuitry. 175
Technical Note transistor is linearly related with the power W to be measured, i . e . / = WI V o. Actually, as shown in the Fig. 2, we measure the emitter current, obtaining directly the difference in radiation power fed to the collectors. A small correction, which takes into account the base current, has been applied directly on the scale of the reading instrument. To close the loop with negative feedback, the thermistor (NTC) labelled with one asterisk (see Fig. 2) must be mounted on the same collector plate as the PNP transistor (one asterisk); elements labelled with two asterisks are mounted on the other collector. 4. CIRCUIT ANALYSIS The circuit must be stable against oscillations, which may start up if at some frequency the loop gain in /> 1. A linearized equivalent circuit is given in Fig. 3. A complete mathematical analysis, not reported here, allows to find the conditions to achieve the desired degree of stability, also taking into account the change of the thermistor sensitivity, which happens in the usable temperature range. The "input" to the system is given by the output voltage v~ of the thermistor bridge. The integrated amplifier, the driver transistors, and the power transistors are represented by the sources Kv~, hfeiI, h~,htei~,respectively (K = 5o). In the thermal section of the equivalent circuit, the power dissipated at the collector of the transistor which conducts current, is represented by a current generator W~, and from now on the signals at the following nodes of the equivalent circuit are the temperatures, in °K; the thermal capacitances are in J/°K. the thermal resistances in °K/W. The ground is the ambient temperature. The complete list of the symbols used is given in Table 1. Table 1. List of symbols used in Fig. 2 K ht, R~ WE h~, Ojc Oc~
0,o Os,,. 0~o
0,_.~ T
voltage gain of operational amplifier ,ttA 74I current gain of driver transistor BC 119 input impedance of conducting power transistor (in this case, the 2N 3055) generator simulating the electrical power dissipated on the power transistor 2N 3055 current gain of 2N 3055 thermal resistance between junction and case of the power transistor thermal resistance between case and sink (radiation collector) on which the power transistor is mounted thermal resistance between sink and ambient thermal resistance between the sink and the case of the thermistor thermal resistance between the case of the power transistor and ambienl thermal resistance between the case of the thermistor and the ambient absolute temperature
Since both the collectors can be used to collect the radiant energy, but only the one receiving less radiant energy is fed with electrical power, the equivalent circuit is shown for the particular case where only the PNP transistor (and the collector on which it is mounted) is illuminated by the sun, where heat is accepted by the thermal capacitor labelled by the "sun face". Of course, in that case only the NPN (single asterisk) transistor is conducting. Data for thermal capacity and resistance were obtained from the manifacturer data sheets, whenever possible, or by a direct measurement. However, it should be noted that these values are only relevant for the time response and the stability of the instrument, while not influencing the equilibrium readout. 5. MECHANICALCONSTRUCTION Both radiation collectors were built using black fumed aluminium plates normally used as heat sink for power transistor cooling. On each plate a power transistor and a thermistor were
177
mounted. Silicon grease was used to reduce the thermal resistance between the contact surfaces, The sensing thermistors are screwed as near as possible to the transistors. The collectors are then mounted in two PVC boxes (internal dimensions 13 x 13 x 10 cm3). The front of the box is a polished aluminium diaphragm, whose double function is to define precisely the sensitive area, and to reflect back on the collector most of the radiation which is diffused by the same collector because of imperfect "black". A schematic cross-section drawing of both collectors is in Fig. 1. 6. OPERATION AND RESULTS The instrument response to a step function was tested with an artificial radiation source, and may be seen, in normalized form, in Fig. 4. The open loop gain was adjusted to obtain the fastest rise-time with less than 5 per cent overshoot. If the loop gain is not carefully controlled, larger overshoot, or even instability, can occur. For the present instrument the open loop gain is now 62dB at 0 Hz, the dominant time constant 16rain. When normally operated (i.e. with closed loop) the rise-time is 20 sec. The operational parameters are collected in Table 2. The angle of sensitivity of the instrument is defined by the object we use to mask one of the collectors of radiant energy, rather than by diaphragms, as done in all other instruments. The test measurements were taken with a simple mask of circular shape, which subtended a solid angle of approximate half-opening of 20° (full sensitivity), to 50° (penumbra limit). The results of these test measurements, taken in Bari, are summarized in Fig. 5. All the measurements were taken with fine weather and no visible clouds. The read-out reliability is actually limited by the mechanical construction of the collectors. Their physical dimensions, as well as the absence of those refinements that may be found in commercial collectors, make the instrument not particularly insensitive to the air turbulence and to other external disturbances, that are not seen as "common-mode" signals. Reading the output current by means of a digital meter, it turns out that the short term stability of the read-out is about 5 per cent, due to the low common-mode rejection of the collectors. Coupling the circuit with collectors particularly insensitive to turbulence and wind, would reduce considerably this drawback, perhaps well below the stated precision of commercial instruments (0.5 per cent). Another cause of error could be the power supply regulation: however, this is certainly a second order effect, because it will contribute very little (0.01 per cent) using well designed modern power supplies.
,
f-.._
O5
0
5o
i00
150
20o
sec
Fig. 4. Normalized transient response of the radiometer. Table 2. Parameters of the instrument 1. 2. 3. 4. 5. 6.
Sensitive area of the collector Absolute sensitivity Max. measurable power (full scale) R.m.s. noise in quiet air (input equivalent) Thermal drift of output base-line Rise-time of the response
50 cm 2 67 mA/W 30 W 10-2W 20 mW/°K hr 20 sec
178
Technical Note
9
O75
0.,~
0.25
1
I
I
8
12
16
hr
Fig. 5. Test measurements, taken at Bari (lat. 41°08'N, height ~ m over m.w.I.). O, 10 June, 1976; +, I1 June, 1976; 0 , 12 June, 1976; &, 14 June, 1976.
Finally, also the response time is certainly far above the performance of commercial instruments (1 sec for thermopile instruments): however, it actually depends essentially on the thermal capacitance of the collectors and may be easily reduced by reducing the collector area and, at the same time, the sensitive area of the diaphragms, because of the maximum power ratings of the transistors.
7. CONCLUSIONSAND IMPROVEMENTS The elementary automation of an old-type instrument has led to a direct-reading, absolute, cheap and sensitive device that, with improvements in collector mechanics, could overcome the drawbacks of the instruments calibrated by direct comparison. Our work will continue, to obtain the following features: (a) Full portability (now the power supply is operated with line power). (b) Reduction of the collector size, to reduce both the open loop time constant and the electrical resistance from the heat source to the thermal sensor. These improvements will allow us to increase the overall speed of response of the instrument, and to obtain a better balance by increasing the open-loop gain. (c) Improvement of the mechanical construction, to reduce the sensitivity to turbulence, which is now the main limitation to the instrument stability. (d) Improvement of the geometry of shielding and masking, for better definition of the acceptance angle, when the instrument is used as a normal incidence pyrheliometer. (e) Alternatively, we will evaluate the capability of the instrument as an absolute pyranometer (i.e. 2~r acceptance in solid angle with cosine type sensitivity law, full spectral sensitivity from a = 103/zm to vacuum UV).
Acknowledgements--The authors wish to thank Messrs. B. Bia, N. Ceci and R. Liuzzi for their valuable technical assistance. REFERENCE
1. Kinsell L. Coulson, Solar and terrestrial radiation. Academic Press, New York (1975).