EEM 323/3 - Assignment
1. A platinum resistance sensor has a resistance of 100 Ω at 0 °C and a temperature
o
coefficient of resistance of 4 10 C . Given that a 15 V supply is available, design
a deflection bridge giving an output range of 0 to 100 mV for an input range of 0 to 100
°C:
(a) using the procedure discussed in lectures.
(b) using the linear approximation discussed in lectures.
(c) how should the circuit be altered if the input range is changed to 50 to 150 °C?
Give values for all circuit components and assume a high impedance load.
2. The resistance
kΩ of a thermistor at o K is given by:
1 1
1.68 3050
298
The thermistor is incorporated into the deflection bridge circuit shown in Fig. 2
(a) Assuming that !" is measured with a detector of infinite impedance, calculate:
(i) the range of !" corresponding to an input temperature range of 0 to 50
°C.
(ii) the non-linearity at 12 °C as a percentage of full-scale deflection.
(b) Calculate the effect on the range of !" of reducing the detector impedance to 1
kΩ.
Fig. 2
1
3. Fig. 3 shows a four-lead bridge circuit; # is the resistance of the leads connecting the
*
sensor to the bridge circuit. Show that $%& ' ( ) + , -., i.e. the bridge output voltage
is unaffected by changes in # . State all assumptions.
Fig. 3
4. A low-voltage Schering bridge shown in Fig. 4 is used to measure the unknown
permittivity of a specimen using 2-plate capacitor, / with area A and distance d.
R1 R3
C1 C3
Vl
C2 C4
R4
Vc
Fig. 4
Referring to Fig. 4, is a stray resistor, and 0 are pure non-reactive resistors, and
/1 , / and /0 are pure non-reactive capacitors. Without the specimen the following
balanced condition are attained: / /0 120 pF, /1 140 pF and 0 5000 Ω.
With the specimen the values changed to / 200 pF, /0 1000 pF, /1 900 pF, and
0 500 Ω. If # 10 V RMS and 8 5000 rad/s, calculate the relative
permittivity of the specimen.
2
5. (a) List common source of errors in AC bridge circuits. Hence, state several
precautions that should be taken to reduce the errors.
(b) In designing a sensing circuit for measuring the level of oil (ε oil ) inside a tank,
the capacitive level sensor has been proposed. Meanwhile, the simplified four-
arm De-Sauty bridge has been suggested for signal detection. Figure 1 shows
the instrumentation and measurement system. In this figure R4 and C 2 are pure
resistance and capacitance respectively, C h is the sensor capacitance at a
height h of the oil and R4 is the variable resistance.
Ch R3
Vout
C2 R4
Vs
Fig. 5
The relationship between C h and h of the capacitive sensor is as follows:
2πε 0
Ch = [1 + (ε oil − 1)h]
b
log e
a
(i) Derive the balanced conditions of Fig. 5,
3
(ii) Calculate h when at balance C 2 = 1000 µF , R4 = 10 Ω , R3 = 1250 Ω , ε 0 = 1 ,
ε oil = 3 , b = 2 cm and a = 0.5 cm ,
(iii) State the main source of error in 1(b) (ii).
6. (a) Explain the important of the quality factor Q and the damping factor ξ in filter
design.
(b) The Sallen-Key second order low pass filter is shown in Fig. 6.
R1 Rf
-
R2 R3
+
Vout
Vin C2 C3
Fig. 6
Prove the transfer function of the above filter is given by
G
R2 R3C 2 C3
H (s ) =
R C + R2 C3 + R2 C 2 − GR2 C 2 1
s 2 + 3 3 s +
R2 R3C 2 C3 R2 R3C 2 C3
Rf
and G = 1 + .
R1
Assuming R2 = R, R3 = 2 R, C 2 = C , C3 = 2C /and R f = R1,
4
(i) Design filter in Figure 2 such that the resonance frequency ω o = 1000 rad/sec ,
(ii) From 2(b)(ii), calculate the Q and damping ξ factors of the filter,
(iii) Hence, modify Figure 2 so that the above filter has the Butterworth response such
that H ( jω 0 ) = 1 or 0 dB.
7. (a) Explain the terms (i) resolution, (ii) quantum error, (iii) acquisition time t aq , (iv)
aperture time t ap and (v) settling time t s with respect to the analogue-to-digital
converter.
(b) The 4-bit R − 2 R type digital-to-analogue converter is shown in Fig. 7.
Vref
B3
B2
B1
Rf
B0
2R 2R 2R 2R
-
2R R R R 2R
+
Vout
Fig. 3
5
(i) Derive the output Vout when the most significant bit (MSB) is turned on only,
(ii) Repeat 3(b)(i) for the least significant bit (LSB),
(iii) Repeat 3(b)(i) for an input B3 B2 B1 B0 = 1001 ,
(iv) From 3(b)(i-iii) derive the general expression for Vout .
