Resistive Stepped Transducer Used for Water Level Measurement

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1 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) esistive tepped Transducer Used for Water Level Measurement GABIEL NICOLAE POPA IOIF POPA COINA MAIA DINIŞ ANGELA IAGĂ Department of Electrotechnical Engineering and Industrial Informatics Politechnica University Timişoara tr. evoluţiei, no.5, Hunedoara OMANIA Abstract: - In this work is analyzed a resistive stepped transducer used for water level measurement. For sending remote the information regarding the level, is used a level-frequency converter with an astable circuit. Are established the frequency limits of the astable circuit and are dimensioned the transducer s resistances. Experimentally it was determined the frequency modification from output depending on the water level in two situations: when the transducer s steps above the water are wet and when these steps are dry. In both situations is found a non-linear frequency modification, depending on the level. Were calculated the transducer s resistances in such way that the frequency will modify linearly with the level. Key-Words: - level, resistive transducers, level-frequency converters Introduction Electric measurement of the non-electric measures is applied on large scale in almost all domains. The advantages of the measuring electric methods against the non-electric methods are: high precision, high sensitivity, possibility for sending remote information, great adaptability, possibility and safety of recording, possibility to process the values obtained by measurement [,2]. In practice, there are many conversion methods of the level of a liquid into an electric signal. When measuring the liquids level, there can be more measuring methods: with floating mechanism and electric transmission, impulse system for level s remote measurement, capacitive measuring methods, methods based on radioactive radiations, methods based on pressure measurement, methods based on mass measurement, resistive methods [3,4,5,6]. Level s measurement can be continuous or discontinuous [2]. 2 esistive level transducer with level-frequency converter The resistive transducers are safe in operation and should achieve a conversion as good as possible of the level into another measure. An astable circuit alternates between two different output voltages. The output remains at each voltage level for a defined period of time. The astable circuit has two outputs, but no input [7]. The resistive level transducer with level-frequency converter is presented in fig.. Fig.. esistive level transducer with levelfrequency converter The level-frequency conversion takes place in two steps: a level-resistance conversion achieved with the stepped level transducer itself (resistive transducer), followed by a resistance-frequency conversion made by a symmetric astable trigger circuit. The astable trigger circuit has the resistances 2 and 3 from the transistors bases T and T 2 connected to the source s positive polarity through the resistive transducer. The resistive transducer is formed by putting in serial the resistances 0 (the steps of the transducer s resistances). By increasing the level, are short-circuited, in order, the resistances, 2,, 0. The modification of the equivalent resistance from the transistors bases leads to the frequency modification of the voltage IN: IBN:

2 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) U out. For the symmetric astable circuit (C =C 2 =C, 2 = 3 = b ), the output signal s frequency is [7]: f = ( 2 C 3 C2 ) ln 2 () The circuit being symmetric, () becomes: f =.38 b (2) C For designing the electronic circuit, is imposed to modify the frequency between the limits 5 khz and 30 khz regarding the signal s transmission on the line. Are calculated the values of the resistances from the transistors collectors: U s c (3) 0.5 Ic max where U s is the value of the supply voltage (U s =0 V), and I cmax is the maximum value of the collector current (I cmax =0.A). With these values and with (3) is obtained c 200Ω. To obtain a low energy consumption, is chosen c =3 kω. Are calculated the resistances from the transistors bases T and T 2 : b β min c (4) where β min is the transistor s minimum amplification factor. If β min =200, can be determined b 600 kω. Is chosen b =300 kω. For the maximum values of the resistances bmax from the transistors bases, the oscillating frequency is minimum f min. The minimum imposed frequency being of 5 khz, can be determined the values of the capacities: C =.38 b max f (5) min Using the relation (5), is obtained C= 60 pf. Are chosen C=C =C 2 =80pF. For the maximum frequency f max =30 khz is obtained the minimum value of the resistances bmin from the transistors bases: bmin =.38 C f (6) max With (6) it results bmin =34 kω. Is chosen bmin = 2 = 3 =20 kω. The transducer s resistance t is calculated with: t = b max b min (7) It results t =60kΩ. If the resistive transducer is formed by 0 steps, are obtained the values of the resistances, 2,, 0 : t i =,,,0 (8) 0 With (8) it results = 2 = = 0 =6 kω. Is taken the standardized value immediately superior: = 2 = = 0 =8 kω. Is recalculated the value of the minimum frequency depending on the transducer s total resistance and the resistance from base: Fig.2. esistive level transducer with levelfrequency converter and separation circuit fmin =.38 b C (9) With (9) f min =3.42 khz. The resistive transducer was provided with a separation circuit, repeater on emitter, achieved with the transistor T 3 (fig.2). The transducer s resistances were introduced in plastic boxes with Φ 22 mm diameter and 30 mm length, and the boxes were filled with electrical insulating paste. The boxes where mounted on a stainless steel support. The transducer has the active length of m, and the distance between two successive resistances is 0 cm. The resistances are serial, with tinned copper plates with the surface of 2.5 cm 2 and the distance against the metallic support of cm (distance between plates). The resistive level transducer with level-frequency converter was practically tested into a tank of which principle diagram is presented in fig.3. In fig.3: tank, 2 filler funnel, 3 filler tap, 4 tube scaled in level units, 5 drain tap, 6 vent valve, 7 support. In fig. 4. is presented the resistive transducer used in experiments. Fig.3. The tank used for checking the resistive transducer IN: IBN:

3 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) Fig.4. The resistive transducer used in experiments To determine the frequency s real values depending on resistivity, should be determined the resistivity of the water used in experiments. In order to determine the resistivity of the potable water, it was used the volt-ammeter measuring method of the resistance. This method was used in alternate current to avoid the water s electric polarization phenomena. It was used an experimental device formed by two plane-parallel plates of surface =20.8 cm 2 and distance between them of l =.8 cm in upstream (fig.5) and downstream (fig.6) montage. The potable water resistances and resistivities for the upstream montage are determined with the relations: U = ma (0) I U ρ = ma () I l and for the downstream montage with: U = v I U (2) v U ρ = v (3) I v U l For the measuring instruments, v =000Ω and ma =275Ω. The measurement results and the calculation of resistances and resistivities are given in table. From table it results the average value for the potable water resistivity used in experiments: ρ avg =52.35 Ω m. Table Electric Determination of water s resistivity Montage type Average Measures upstream downstream value U [V] I [ma] [Ω] ρ [Ω m] Electric Montage type Average Measures upstream downstream value U [V] I [ma] [Ω] ρ [Ω m] By measuring the resistances, the transducer has the following values for the resistance steps (fig.2): =7.66 kω; 2 =7.5 kω; 3 =7.3 kω; 4 =6.96 kω; 5 =7.2 kω; 6 =6.98 kω; 7 =7.26 kω; 8 =7.5 kω; 9 =7.08 kω; 0 =7.32 kω and B =2.4 kω and C=80 pf. To verify the operation of the transducer from fig.2, was measured the output frequency, by short-circuiting the resistance steps. The measurements of the signal s frequencies from the circuit s output were made with the TM Protek 506 multimeter. If the tank is empty (h=0), the transducer has all the resistances: t = -0 = 2 0 (4) If the tank has h=0cm of water, then the transducer s resistance is: t = 2-0 = (5) For h=90 cm, the transducer s resistance is: t = 0-0 = 0 (6) For h=00 cm, the transducer s resistance is t =0. In the calculation relation of the output signal s frequency (2): b = B t (7) Fig.5. The volt-ammeter method upstream montage Fig.6. The volt-ammeter method downstream montage Fig.7. The output signal s measured frequency (f) depending on level (h) and supply voltage (U s ), when the resistance steps are short-circuited IN: IBN:

Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) For U s =0V it was made a comparative analysis in table 2, between the frequency s calculated values (f c ) and the

It was determined the relative error with: fc fm ε r = 00 [%] fm (8) Table 2 The calculated and measured frequency depending on the level (by short-circuiting the steps) U s =0V h [cm] 0 0 20 30 40

4 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) For U s =0V it was made a comparative analysis in table 2, between the frequency s calculated values (f c ) and the measured ones (f m ). It was determined the relative error with: fc fm ε r = 00 [%] fm (8) Table 2 The calculated and measured frequency depending on the level (by short-circuiting the steps) U s =0V h [cm] f c [khz] f m [khz] ε r [%] h [cm] f c [khz] f m [khz] ε r [%] From table 2, one can notice that when b = B (h=00 cm) ε r is small, (2) being useful when determining the frequency. In return, by the level decrease, ε r is higher and higher, reaching the value of 32.04% for h=0. For the other output frequency values, (2) can not be used anymore. The relation (2) is valid for the symmetrical astable circuit in which the resistances from the two transistors bases (T and T 2 ) are equal and are connected to the source s positive potential ( t =0). In the circuit from fig.2 the resistance from base is not directly connected to the source s positive potential, but through the transducer s resistance t, which has higher and higher values by level decrease, and (2) can not be used for the precise determination of the output signal s frequency. The signals from fig.8 and 9 were measured with the color digital oscilloscope Matrix MTX The signals from fig.8 correspond for a classic symmetrical multi-vibrator circuit in which t =0 (fig.2), and the signals from fig. 9 correspond for the multi-vibrator circuit in which t 0. Fig.9. Voltage collector-emitter (up) and voltage base-emitter (down) at short-circuiting the transducer s resistances for U s =0V, f=0.36 khz, 25μs/div, 5V/div, V ppce =.7 V, V ppbe =9. V The wave shapes from fig.8, 9 indicate other operation mechanisms of the electronic circuit from fig.2 against the classic symmetrical astable circuit. In fig.0 and were measured the circuit s output signal frequencies depending on h and U s, in two situations: - at a rapid water level modification, the superior resistance steps remain wet (fig.0); - at a slow water level modification, the superior resistance steps having time to dry-up (fig.). The first situation is rarely met in practice than the second situation. Fig.0. The output signal s measured frequency (f) depending on level (h) and supply voltage (U s ), when the transducer is introduced in water, the resistance steps above the water being wet Fig.8. Voltage collector-emitter (up) and voltage base-emitter (down) at short-circuiting the transducer s resistances for U s =0V, f=32.76 khz, 0μs/div, 5V/div, V ppce =.2 V, V ppbe =8.85 V Fig.. The output signal s measured frequency (f) depending on height (h) and supply voltage (U s ), when the transducer is introduced in water, the resistance steps above the water being dry IN: IBN:

5 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) For determining the signal s frequency depending on the transducer s resistance, it should be used the transducer s electric model in real operation conditions (is taken into account the water resistance between the transducer s plates). Further, the resistance steps above the water are assumed to be dry. The resistance between the plates, when the water is at their mid-height, is s : l s = ρ (9) 2 where ρ is the water resistivity, l is the distance between the transducer s plates, and is the common surface between the plates, when the water is at their mid-height. With the calculated data (ρ) and measured data (l, ) is obtained s =.68 kω. For h=0 (fig.2), the transducer s resistance is given by (4). 0 = (20) CB0 B i With the resistances measured values is obtained t = CB0 = kω. For h=0 cm, in situation when the water is at the mid-height of the plate for the first step, the electric model of the transducer s resistance is t = CB is presented in fig.3. 0 s CB = B i (2) 2 s Is obtained CB = kω. For h=20 cm, in situation when the water is at the mid-height of the plate for the first step, the electric model of the transducer s resistance is t = CB2 is presented in fig.4. tep is completely under water, the metallic plates being completely covered. Their equivalent resistance is s /2. Fig.2. Electric model for h=0 Fig.3. Electric model for h=0cm Fig.4. Electric model for h=20cm CB2 = B s s i 3 s 2 2 s (22) Is obtained CB2 = kω. Calculating little by little, are determined also the other values of the resistances for the other values of the water height (table 3). In table 3, f m is the output signal s frequency when U s =0V, and the resistance steps above the water are dry. Was determined the power function f=f( CB ) using the experimental data from table 3 (f m and CBi ). Were obtained:.2002 f = (23) In (23) f [khz] and [kω]. With (23) was calculated f c, then the relative error with (8). Table 3 The measured and calculated frequency depending on CBi h [cm] CBi [kω] f m [khz] f c [khz] ε r [%] h [cm] CBi [kω] f m [khz] f c [khz] ε r [%] From table 3, one can notice that the relative errors are small between the measured values and the calculated ones with the power function (23). 3 Linearization of the characteristic of the resistive level transducer with level-frequency converter The characteristics from fig.0 and are nonlinear. The issue is to determine the values of the transducer s resistances in such way that the frequency indication depending on level to be linear. Is imposed the modification of the output signal s frequency between 0.36 khz and 30 khz (fig., U s =0V), with.964 khz step. From (23) is calculated the resistance depending on frequency: f = (24) Table 4 The imposed frequency and resistances CBi f m [khz] CBi [kω] ,0 f m [khz] CBi [kω] ,0 s s IN: IBN:

Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) This frequency interval is divided to the number of resistance steps of the transducer, and then, by (24) are determined

6 Proceedings of the st WEA International Conference on ENO and IGNAL (ENIG '08) This frequency interval is divided to the number of resistance steps of the transducer, and then, by (24) are determined the resistances CBi from the transducer s electric model (table 4). For f=30 khz, is chosen CB0 = B =2.4 kω (the fix resistance from the transistor s base, fig.2). Further, is considered that when the water is at a certain level, the water covers half of the surface common between the two plates, and the water s equivalent resistance is. If the plates are completely covered, then the water s equivalent resistance is /2. For h=0 (fig.2): 0 = (25) CB0 B i From (25), it results = kω. For h=0 cm (fig.3): 0 CB = B 2 i (26) By making the difference between CB (26) with CB0 (25), is obtained: CB CB0 = (27) From (27), 2 = kω. Proceeding similarly by achieving the transducer s electric model for each case in part, are obtained also the other resistance values which will determine a linear modification of the frequency depending on level. Table 5 The resistances calculated and used in experiments for the circuit from fig.2 linearized characteristic esistance calculated [kω] measured [kω] esistance calculated [kω] measured [kω] Fig.5. The measured frequency of the output signal (f) depending on level (h) and supply voltage (U s ) (the water level modifies overhand) fig.2, were determined experimentally the frequency s variation curves depending on level and the supply voltage. 4 Conclusion It was analyzed a 0-step resistive transducer connected to an astable trigger circuit in such way to achieve the level-frequency conversion. The condition (wet or dry) of the resistances above the water influences the transducer s operation. For equal values of the transducer s resistance steps, the frequency depends non-linear on the water level. Were analytically determined the transducer s resistance steps in such way that the frequency to depend linearly on the level. The transducer can be used in applications where the level does not fluctuate (does not modify up and down with high speed) in order that the insulating support of the resistances above the water to have time to dry-up. Can be also used other electronic circuits attached to this type of transducer, that should achieve the levelfrequency conversion. eferences: [] H.F. Grave, Electrical Measurement of Non-electric Measures, Akademische Verlagsgesellshaft, Leipzig, Germany, 965. [2] A. Ignea, Electrical Measurement of Non-electric Measures, West Publishing House, Timişoara, omania, 995. [3] W.D. Wallace, L.G. pielvogel, Field Performance of team and Hot Water Electric Boilers, IEEE Transactions on Industry Applications, Vol.IA-0, No.6, november/december, 974, pp [4] B.D. Keeland, J.F. Dowd, W.. Hardegree, Use of Inexpensive Pressure Transducers for Water Level Measurement in Wells, Wetlands Ecology and Management, No.5, 997, Kluwer Academic Publishers, Netherlands, pp [5]. Khan and other, Capacitive Transducer Circuits for Liquid Level Measurement, International Journal of Computer ciences and Engineering ystems, Vol.2, No.3, july, 2008, pp [6]. Cai, C. Lu, H. Wang, Measurement Technology of the Physical Model Test in the Hydraulic Engineering, International Conference on Hydro-cience and Engineering, 988. [7] W. Pfeiffer, Impulse Technique, Darmstadt, Germany, 976. IN: IBN:

A STUDY ABOUT A RESISTIVE STEPPED TRANSDUCER USED FOR WATER LEVEL MEASUREMENT

A STUDY ABOUT A RESISTIVE STEPPED TRANSDUCER USED FOR WATER LEVEL MEASUREMENT Gabriel Nicolae POPA, Iosif POPA, Sorin Ioan DEACONU, Corina Daniela CUNŢAN Politehnica University Timişoara, Faculty of Engineering