Followings are the excerpts from the specifications of a laser displacement sensor:
 Measurement range: 30mm-60mm
 Resolution: 6μm
 Linearity: ±3% Full Scale
 Response time: 0.18ms
 Linear output: 4-20mA
Answer:
 O  Omin 
O  Omin =  max
  I  I min 

I
I
 m ax min 
O = KI + a
O  Omin
K = max
I m ax  I min
a = Omin  K I min
Given, I min  30mm
I max
Omin  4mA
 60mm Omax  20mA
1. Suppose the distance between the sensor and the object is 45mm. Then what
would be nominal output in mA?
a) 12mA
b) 18.24mA
c) 6.55mA
d) 7mA
Answer: (a)
16mA
K=
 0.533 mA mm
30mm
16mA
a = 4mA =
 30mm
30mm
 12mA
O at I  45mm
O   0.533  45   12  mA
 12mA
2. What can the maximum error due to nonlinearity under the above condition?
a) ±0.35mm
b) ±1.33mm
c) ±0.48mm
d) ±0.91mm
Answer: None of the answers are correct
Given, Linearity = ± 3% full scale
Maximum error= (60x0.03)=1.8 mm
3. Find out the change in output current per unit change in distance between the
sensor and the object.
a) 1.869 mA/mm
b) 0.533 mA/mm
c) 0.1 33mA/mm
d) 2.2 66mA/mm
Answer: (b)
K  0.533 mA mm 2. Find the resolution of an 8-bit ADC, if it has an analog voltage reference of 10V.
a) 39.21mv
b) 21.07mv
c) 30.76mv
d) 55.77mv
Answer: (a)
8bitADC, voltRef.10V
Resolution,
10V
 39.21mV
28  1
3. The accuracy specified for a pressure gauge of range 0-25kPa is 5%of full scale.
Find the maximum error in measurement in Pa if it gives a reading of 4.0 kPa.
a) ±8.2kPa
b) ±15.2kPa
c) ±1.25kPa
d) ±0.9kPa.
Answer: (c)
Range: O  25kPa
Accuracy:5%ofF.S.D
Maximumerror,(25kPa*0.05)
 1.25kPa. 4. Figure below shows a block diagram of a force transducer using negative
feedback. The elastic force sensor gives a displacement output for a force input; the
displacement sensor gives a voltage output for a displacement input. VS is the
supply voltage for the displacement sensor.
Calculate the output voltage V0 when
A.VS =1.0 V, F=50 N
B. VS =1.5 V, F=50 N.
Input
force
Output
voltage
+
10-5
F
Balancing
force
Elastic force
sensor
10 × Vs
Displacement
sensor
103
V0
Amplifier
10
Coil and
magnet
a) A.Vo=4.93 V , B.Vo= 4.90
b) A.Vo=4.93 V , B.Vo= 4.93
c) A.Vo=4.93 V , B.Vo= 4.96
d) A.Vo=4.90 V , B.Vo= 4.93
Answer: None of the answers are correct
Vo
105 10  Vs 103

F 1  105 10  Vs 103 10
A. Vs  1.0V ,
F  50
Vo  2.6V
B. Vs  1.5V ,
F  50
Vo  3V
The data provided is not very appropriate for typical feedback instruments. The loop
gainisveryhigh.
5. A level transducer has an output range of 0 to 10 V. For a 3 metre level, the output
voltage for a falling level is 3.05 V and for a rising level 2.95 V. Find the hysteresis as
a percentage of span. (John P. Bentley)
a) 1%
b) 2%
c) 4%
d) 7%
Answer: (a)
Hysteresis 
H
100
Omax  Omin
O P
Omax H Omin
H  3.05  2.95V  0.1V
Omax  Omin  10  0  10V
%Hysteresis=1%
Imax I min i P 6. What is the total sensitivity of the system? Ki is the sensitivity of the ith block.
Amplifier
TC
Thermocouple
Indicator
K1 = 30µV/oC
K3 = 20oC/V
K2 = 500V/V
Fig. Simple Temperature measurement System.
a) 0.8
b) 0.5
c) 0.3
d) 1.3
Answer: (c)
I = I1
K1 1 O1  K1 I1 O2  K 2 I 2  K 2 K1 I1
O3  K3 I 3  K3 K 2 K1I
K  K3 K 2 K1   20  500  30 
 0.3 O1 = I 2 K2
2
O2 = I 3 K3
3
O3 TC
7. What is the overall relative error of the system? Ei is the relative error of the ith
block as a percentage of the reading.
Amplifier
Thermocouple
Indicator
TC
TC
E1 = 1%
E3 = 4%
E2 = 3%
Fig. Simple Temperature measurement System.
a) 12%
b) 8%
c) 6%
d) 10%
Answer: (b) Z  xy
z
x
y
dz  xdy  ydx
dz dy dx
 
z
y
x
Or,
Z  z   x  x  y  y 
 xy  xy  yx  xy
z x y xy



z
x
y
xy
Therelativeerrorisinterpretedhaveastheworstcaserelativeerror.
8. If the analog signal is
100 sin 2 ∗ ∗ 100 ∗ . Choose the proper sampling
frequency based on practical considerations from the options given below?
a)
b)
c)
d)
10 Hz
100 Hz
200 Hz
1000 Hz
Answer: (d)
If
Fs  200 Hz.
0.01 sec Fs  1000 Hz.
0.01 sec 9. A signal contains components with frequencies up to 10 kHz, although no useful
information is contained at frequencies above 6 kHz. What is the minimum
frequency at which the signal should be sampled?
a)
b)
c)
d)
6 KHz
16 KHz
12 KHz
20 KHz
Answer: (b)
16 KHz
Fs
16KHz
6KHz 10KHz
10. Match the types of Analog input subsystem given in the left column with their
corresponding advantage/disadvantage given in the right column.
1
AA Filter
2
Input Signals
Mux
3
n
S/H
A/D
Signal
Conditioning
Digital Output Code
Fig. A
1
Analog Input
Signals
2
n
S/H
S/H
Mux
A/D
Digital N-bit
output
S/H
Fig. B
Type A Analog input subsystem
Type B Analog input subsystem
I. Cost is lower,
II. Cost is Higher,
III. Will create less time delay
IV. Will create more time delay
a) A: Cost is lower, Will create more time delay, B: Cost is Higher, Will create less
time delay
a) Type A Analog input subsystem: I, II , Type B Analog input subsystem: III,IV
b) Type A Analog input subsystem: II, III , Type B Analog input subsystem: I, IV
c) Type A Analog input subsystem: I, IV , Type B Analog input subsystem: II, III
Answer: (C)
Type A Analog input subsystem: I, IV, Type B Analog input subsystem: II, III
11. The minimum sampling frequency for xa(t) is real with Xa(f) non-zero only for 9
KHz < |f| < 12 KHz is
a) 6 KHz
b) 9 KHz
c) 12 KHz
d) 3 KHz
Answer: (a)
Fs   BW  2  9KHz
12KHz 3KHz