1. A 1V signal ( V s) with a 600 Ω source resistance is connected to an oscilloscope which has an input impedance of Ri = 1 MΩ in parallel with capacitance C i = 30pF. The coaxial cable connecting the source to the oscilloscope has a 100 pF capacitance. Calculate the oscilloscope terminal voltage (V i) when the signal frequency is 100 Hz. 2. An integrated circuit chip contains 10 5 transistors. The transistors have a mean current gain of 20 and a standard deviation of 2. Calculate the following: (a) the number of transistors with a current gain between 19.8 and 20.2. 7960 (b) the number of transistors with a current gain greater than 17. 93.32% 3. Design a signal conditioning for a grounded load that converts a 0-10V input to a 420mA output current. The circuit is to be powered from ±15-V regulated supplies. 4. Explain the functioning and hence obtain the transfer functions for the op-amp based all pass filters working in all pass phase phase lead and all pass phase lag modes. Use one of the relevant transfer function from the above designs to design an all pass phase lag circuit to produce a phase shift of -135º at 1kHz. 5. Design a signal conditioning for a grounded load that converts a 4-20mA input current to a 0-10V output voltage. The circuit is to be powered from
±15-V
regulated supplies.
6. A strain guage based experimental setup makes use of full bridge configuration. Obtain an expression for the off null bridge voltage. Also describe techniques for strain gauge calibrations, thermal compensation and obtaining maximum sensitivity. 7. Describe the Aggregation of errors (one numerical example each) from separate measurement system components. A. Error in a sum B. Error in a difference C. Error in a product D. Error in a quotient 8. In the arrangement shown A, B, C and D are resistance strain gauges bonded to a steel ring. These form the four arms of a Wheatstone bridge, so as to give temperature compensation and to offer maximum possible sensitivity. When a force is applied, the compression of rubber block is 1mm and the output of bridge is 4units. For calibration of the bridge circuit, a shunt resistance of 0.2 MΩ is connected parallel to A and an output of 1.2units is observed. Find the compression modulus of rubber used. [5] Gauge factor=2.2, Resistance of gauge element =120 Ω, Young’s modulus E= 2x10 5 N/mm2, r=40mm, b=15mm, t=1.5mm where r is the mean radius of the ring, b its width and t its thickness. (For the ring, strain at the gauge location is given by 1.1Pr/(Ebt2), P being the force applied on the ring.)
9. A force measuring device, using resistance strain guage, is shown in Fig., R 1 is an active guage and R 2 a dummy guage for thermal compensation. R 1=R 2=R 3=R 4= 120Ω. Guage factor = 2.5, maximum guage current is limited to 30mA. Find the required battery voltage. If a calibrating resistance R c = 1.2MΩ is used and connected parallel to R 1, trace shift on oscilloscope reads 5units. Find the corresponding trace shift due to the applied force. If thermal compensation were not used what would have been the output voltage if temperature is increased by 10ºC? Temperature coefficient of guage material = 10-5/ºC. Take oscilloscope I/P impedance as infinity. Due to force P, strain
in the guage is = 10 -5.
10. A load cell is formed of a hollow steel cylinder loaded axially as shown in adjoining Figure. The four strain gauges are so connected to enhance the signal and provide the thermal compensation. The load cell has a cross sectional area of 2cm 2. Young’s modulus of steel is 2.07x10 11 N/m2 and Poisson’s ratio of 0.3. Given the strain gauge resistance of 1000Ω, and Gauge factor is 2.1. The current in each gauge has the upper limit of 20mA. Calculate, i. Supply voltage, ii, current in the detector arm if it consists of a micro ammeter of 500 Ω, when the load cell is subjected to a force of 105 N. [8]
11. Draw an equivalent circuit of PZT, connecting cable and the voltage measuring device. Derive a mathematical expression for frequency response of PZT using this combination. Sketch the typical response plot. Use the frequency response to find the suitability of PZT for measurement of a constant force .
12. The capacitance level transducer making use of two concentric cylinders is to be used to measure the height (level) h of liquid in a tank between 0 and 7 m. The total height l of the transducer is 8 m and the ratio b/a of the diameters of the concentric cylinders is 2.0. The dielectric constant ε of the liquid is 2.4 and the permittivity of free space ε0 is 8.85pFm−1. The transducer is incorporated into the deflection bridge of Figure below with R2 = 100 Ω, R3 = 10 kΩ and Äs = 15V. (a) Calculate the value of C 0 so that the amplitude ÊTh is zero when the tank is empty. (b) Using this value of C 0 calculate ÊTh at maximum level.
13. In a POT transducer, the POT has a a resistance of 24kΩ. During a measurement POT moves between 20mm and 60mm positions. a) If the voltmeter of 15kΩ is used to read the output voltage find out the er ror due to loading at the above mentioned two positions. b) If the error is to be kept within 3% what should be the resistance of the voltmeter
14. A thermistor is to monitor room temperature. It has a resistance of 3.5kΩ at 20ºC with a slope of -10%/ºC. The dissipation constant of this device is 5mW/ ºC. It is proposed to use this thermistor in the divider circuit of Fig. 3 to provide 5.0V at 20 ºC. Evaluate the effects of self heating.
15. Figure 4 shows a circuit with variable air gap parallel plate capacitor as sensing element. Show that the circuit acts as a velocity sensor for small displacements, find the proportionality constant between the voltage V out(t) and the input velocity. Assume nominal, (zero displacement) capacitance (Cs) as 50pF and the nominal, (zero displacement) distance between the capacitor plates x 0 as 5mm. Use the other circuit parameters as R F=100kΩ and supply voltage Vs(t) = 100V.
16. The resistance R ө kΩ of a thermistor at өK is given by R ө = 1.68 exp
This thermistor is incorporated into the deflection bridge as shown in figure. Assume that the Vout is measured with the help of a detector of infinite input impedance.
i) ii)
Calculate the range of Vout for input temperature of 0 – 50°C. [4] the non-linearity at 12 °C as a percentage of full-scale deflection.
iii)
Calculate the effect on the range of Vout of reducing the detector impedance to 1kΩ
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18. A temperature sensor is exposed to a sudden change of 20 oC to 80oC as shown in Fig. 2. The sensor outputs 0.02 volts for every oC of temperature and has a time constant of 2.3s. (a) What is the sensor output voltage at 1.5s? (b) At what time, t , does the sensor output become 1.0 volts? [5]
T( oC ) 80 Sensor
o
0.02 V/ C
V(t)
20
t
19. Fig. below shows an arrangement for calibration of an accelerometer. The mass m is constrained to move vertically with harmonic motion. Resistance R 1 and R 3 are bonded along the length of the strip and R 2 and R 4 are bonded along the width of the strip. Strip width = 20mm. Thickness of the strip = 1mm. The gages, each of 120Ω and gauge factors of 2, form the four arms of a Wheatstone bridge. The output of the bridge is connected to one channel of an oscilloscope, while that from the accelerometer is connected to second channel. Calibration is done by connecting a 1MΩ resistance, parallel to R 1, giving a shift of 2cm on the oscilloscope. During accelerometer calibration, output of the acceleration corresponds to a shift of 5cm while that of the strain gauge bridge gives a shift of 3.2cm, on the respective channels. Oscilloscope sensitivity on accelerometer channel is = 20mV/cm. [6] Find the sensitivity of the accelerometer in mV/g. Given, Youngs’s modulus of strip material = 7x1010 N/m2, Poisson’s ratio = 0.3.
20. It is proposed to use three 4-bits identical DACs for implementing a 12-bit DAC. Assume that b0 represents LSB, b11 MSB of the 12 bits proposed DAC. Design an opamp based summer which will sum the outputs of the three DACs so as to generate an effective 12 bits DAC. Assume input bits are assigned as b 3 b2 b1 b0 to 1st DAC, b7 b6 b5 b4 to 2nd DAC and b11 b10 b9 b8 to 3rd DAC. 21. A balloon is equipped with temperature and altitude measuring instruments and has radio equipment that can transmit the output readings of these instruments back to ground. The balloon is initially anchored to the ground with the instrument output readings in steady state. The altitude-measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 15 seconds. The temperature on the ground, T0, is 10°C and the temperature Tx at an altitude of x metres is given by the relation: Tx =T0 - 0.01x. (a) If the balloon is released at time zero, and thereafter rises upwards at a velocity of 5 metres/second, draw a table showing the temperature and altitude measurements reported at intervals of 10 seconds over the first 50 seconds of travel. Show also in the table the error in each temperature reading. (b) What temperature does the balloon report at an altitude of 5000 metres? 22. A pressure transducer consists of a Bourdon tube elastic element connected to a potentiometer displacement sensor. The input range of the Bourdon tube is 0 to 104 Pa and the output range is 0 to 1 cm. The potentiometer has a length of 1 cm, a resistance of 10 kΩ and a supply voltage of 10 V. If the input pressure is 5 × 10 3 Pa, calculate: (a) the displacement of the potentiometer wiper (assume a linear Bourdon tube) (b) the open circuit transducer output voltage (c) the voltage indicated by a voltmeter of resistance 10 kΩ connected across the potentiometer.
23. Figure below shows a bridge for temperature measurement using two RTDS R A and R B. Ra is maintained at t1 while Rb senses the unknown temperature T2. At T1 both have same resistances R o. and R2 = R3.
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