Question 1
An active transducer has an auxiliary source of power which supplies a major part
of the output power while the input signal supplies only an insigni cant portion.
A passive transducer is a component whose output energy is supplied entirely by its
input signal.
Question 2
Null type is more accurate but tedious to use. De ection type is less accurate but
easier to use. Explain the difference by means of an example, e.g., null and
de ection types of pressure gauge (See Section 2.2 in the book for full details). Null
type normally reserved for calibration duties where best accuracy is needed.
Question 3
Static characteristics: These are the steady-state attributes of transducers (when
the output measurement value has settled to a constant reading after any initial
varying output) such as accuracy, measurement sensitivity, and resistance to errors
caused by variations in their operating environment.
Instrumentation Page 1 of 7 HW1
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Question 4
Both accuracy and precision re ect how close a measurement is to an actual value,
but they are not the same. Accuracy re ects how close a measurement is to a
known or accepted value, while precision re ects how reproducible measurements
are, even if they are far from the accepted value. Measurements that are both
precise and accurate are repeatable and very close to true values.
Question 5
Sensitivity
4.37 mV
= 0.0175 ∘
250 C
Instrumentation Page 2 of 7 HW1
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Question 6
Zero drift is sometimes known by the alternative term, bias. Zero drift or bias
describes the effect where the zero reading of an instrument is modi ed by a
change in ambient conditions. This causes a constant error that exists over the full
range of measurement of the instrument.
Sensitivity drift (also known as scale factor drift) de nes the amount by which an
instrument's sensitivity of measurement varies as ambient conditions change. It is
quanti ed by sensitivity drift coef cients that de ne how much drift there is for a
unit change in each environmental parameter that the instrument characteristics are
sensitive too. Many components within an instrument are affected by environmental
uctuations, such as temperature changes.
Instrumentation Page 3 of 7 HW1
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Question 7
a.
13.1
= 2.62
5
b. Sensitivity
Sensitivity drift
14.7
= 2.94
5
2.94 − 2.62 = 0.32
Instrumentation Page 4 of 7 HW1
Question 8
a. Sensitivity at 21 degree
1 mm
= 0.02
50 kg
Sensitivity at 35 degree
1.1 mm
= 0.022
50 kg
b. Sensitivity drift
mm
0.022 − 0.02 = 0.002
kg
Zero drift
0.2 − 0 = 0.2 mm
b. Sensitivity drift coe cient
0.002 μm
× 103 = 0.143
35 − 21 kg ∘C
Zero drift coe cient
0.2 μm
× 103 = 14.286 ∘
35 − 21 C
Instrumentation Page 5 of 7 HW1
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Question 9
a.
Tx T − 0.01x 20 − 0.005t
Tr = = 0 =
1 + τD 1 + 50D 1 + 50D
−t −t
Trcf = Ce 50 , Trpi = 20 − 0.005(t − 50) ⟹ Tr = Trcf + Trpi ⟹ Tr = 20 + Ce 50 − 0.005(t − 50)
Time Depth Temp Reading Temp Error
0 0 20 0
100 50 19.716 0.216
200 100 19.245 0.245
300 150 18.749 0.249
400 200 18.250 0.250
500 250 17.750 0.250
b.
d = 0.5 × t ⟹ 1000 = 0.5 × t ⟹ t = 10.25 ∘C
Instrumentation Page 6 of 7 HW1
Question 10
a2 x·· + a1x· + a0 x = y
ℒ
S 2 a2 x + Sa1x + a0 x = y
y ω02
= 2
x S + 2ξω0 S + 1
In which we have:
a0 a1
ω0 = , ξ=
a2 2 a0 a2
Having 0.6 < ξ < 0.8 is usually preferable.
Instrumentation Page 7 of 7 HW1
