Download Question 3 [instrument specifications]

Exercises for "Instrumentation for Embedded Systems"
Question 1 [signal values]
The figure shows exactly 1 period of a periodic signal. Calculate the rms value of this
periodic signal.
V (mV)
2
t (ms)
0
1
-1
2
3
4
5
6
-3
a. 1.1 mV
b. 1.26 mV
c. 1.9 mV
d. 3.6 mV
Question 2 [signal values]
The figure shows exactly 1 period of a periodic signal. Calculate the mean (or average) value
of this periodic signal.
V (mV)
2
0
1
2
3
4
5
t (ms)
-3
a. -1.5 mV
b. -1.0 mV
c. -0.3 mV
d. 0 mV
Question 3 [instrument specifications]
In the specification sheet of a digital voltmeter the next data are listed:
uncertainty:
±2.10-5 full scale; ±5.10-4 of the indication; ±0.5 digits, at 25 C.
The full scale value is 2 V; 1 digit is equivalent to 0.01 mV.
This meter is connected to an ideal voltage source, at 25 C. The indication is 6 mV. Calculate
the maximal error in this measurement result.
a. 48 V
b. 55 V
c. 70 V
d. 75 V
Question 4 [non-linearity]
The static transfer characteristic of a non-linear system is described by:
v0 = vi - ßvi3, with  = 8 en ß = 0.04 V-2.
Determine the relative non-linearity (in %) over the interval vi[-3V;+3V]. As criterion, use the
deviation from the tangent through the point (0,0).
a. 0.5
b. 4.5
c. 13.5 d. 36
Question 5 [instrument loading]
A resistor with unknown resistance R is measured by connecting it to an ideal voltage source
with value Vi = 8.0 V (see figure). To measure the current through the resistor, a current meter
is inserted in the circuit, in series with the resistor. The current meter indicates 2.0 mA.
The current meter introduces an error, which should be less 0.1%. Determine the requirement
with respect to the internal resistance of the current meter.
+
Vi
R
a. > 4 
b. >4 k
c. > 4 M
d. < 4
Question 6 [dB notation]
The power transfer of a passive two-port network is –40 dB.
The ouput power appears to be 20 mW. Determine the input power.
a. 2 W
b. 200 W
c. 2 W
d. 200 W
Question 7 [common mode rejection]
The voltage gain of a voltage amplifier is 20. Both inputs of this amplifier are connected to a
voltage of 15 V. At the output a voltage of 3 mV is observed. Calculate the common mode
rejection ratio, assuming this is the only deviation from an ideal behaviour.
a. 10-5
b. 4.10-3
d. 105
c. 250
Question 8 [models]
Determine the short circuit current of the next circuit.
1 k
+
2V
-
a. 0.5 mA
1 k
b. 0.66 mA
1 k
c. 1 mA
d. 2 mA
Question 9[models]
Determine the source resistance of the circuit below.
1 k
2 mA
1 k
a. 0.5 k
b. 0.66 k
1 k
c. 1.0 k
d. 1.5 k
Question 10 [models]
Calculate the open voltage of the same circuit (Question 9).
a. 0.67 V
b. 1.0 V
c. 1.33 V
d. 2.0 V
Question 11 [temperature measurement; thermocouple]
The temperature of a hot fluid is measured using a thermocouple. The temperature value falls
in the range 200-600 C. The sensor sensitivity is 30 V/K. The required accuracy is +/-0.1
C.
The sensor voltage is small, so it is amplified with a voltage amplifier, which temperature can
vary between 15 en 25 C. At 21 C the offset of the amplifier is adjusted to 0.
What should be the maximum temperature coefficient of this amplifier?
a. <0.3 V/K
b. <0.5 V/K
c. <0.75 V/K d. <3 V/K
Question 12 [bridge circuit; sensors]
The figure shows a strain gauge bridge with 4 strain gauges. In the initial state (unloaded) the
resistance of all four strain gauges is 500 . A voltage of Vi = 12 V is connected to the
bridge.
In a particular application, only R4 acts on an applied force. This force results in a relative
resistance change of 3.10-4 (relative to the initial value).
Calculate the output voltage Vo of the bridge.
R3
R1
Vi
+ Vo -
R4
R2
a. 0.75 mV
b. 0.9 mV
c. 1.8 mV
d. 3.6 mV
Question 13 [complex variables; impedance]
Determine the impedance of the next given network.
a.
1  jR1C
1  j R1  R2 C
R1
R2
C
b.
1  jR2C
1  j R1  R2 C
c. R2
1  jR1C
1  j R1  R2 C
d. R1
1  jR2 C
1  j R1  R2 C
Question 14 [complex variables; impedance]
Determine the impedance of the next given network.
a.
1  jRC
1  jRC   2 RL
L
C
1   2 LC
b.
1  jRC   2 LC
1   2 LC
c. R
1  jRC   2 LC
R
1   LC
1  jRC   2 LC
2
d. R
Question 15 [complex variables; amplitude transfer]
The components in the network below have values:
R = 10 k
C = 15 nF
The input is a sinewave voltage, with amplitude 3.5 V and radial frequency 104 rad/s.
Calculate the output amplitude.
R
+
+
Vi
Vo
-
C
-
a. 0.55 V
b. 1.94 V
c. 2.33 V
d. 2.91 V
Question 17 [Bode plot]
The figure shows a two-port network and four frequency characteristics. Component values
are all different. All slopes are + or – 6dB/octave. Which of these four characteristics belongs
to the network?
C1
+
+
R2
Vi
R1
Vo
C2
-
a.
c.
b.
d.
Question 18 [Bode plot; filters]
A first-order lowpass filter has a cutoff frequency of 100 Hz. Determine the amplitude
transfer at 10 kHz (approximated).
a. 1/100
b. 1/10
c. 1
d. 100
Question 19 [filters]
A first-order lowpass filter consisting of a resistance R and capacitance C should have a
cutoff frequency of 15 Hz. A capacitor is available of which the capacitance amounts 6.8 F.
Determine the value for the resistance R.
a. 250 
b. 1560 
c. 9.8 k
d. 351 k
Question 20 [filters]
A first-order lowpass filter consisting of a resistance R and capacitance C should have a
cutoff frequency of 6 kHz. A resistor is available of which the resistance value is 1.8 k.
Determine the value for the capitance C.
a. 14.7 nF
b. 93.6 nF
c. 582 nF
d. 20.9 F
Question 21 [filters]
Proper measurement of a particular measurement signal requires its signal-to-noise ratio
(SNR) to be better than a factor of 100. It appears that the signal consists of two sinewave
components: a measurement signal with frequency 2 Hz and amplitude 50 mV, and an
interference signal with frequency 100 Hz and amplitude 150 mV. What should be the
minimum order of the filter to obtain the required SNR?
a. 1
b. 2
c. 3
d. 4
Question 22 [filters]
A sinusoidal measurement signal with frequency 2 kHz is disturbed by an additional sinewave
signal with frequency 50 Hz. The sinewaves have equal amplitudes. Using a highpass filter,
the amplitude ratio should be reduced down to 1% or less. Determine the minimum order of
this filter.
a. 1
b. 2
c. 3
d. 4
Question 23 [load effect of filters]
The figure shows an RC-lowpass filter and the asymptotic approximation of its frequency
characteristic. The output of the filter is connected to an instrument with input resistance Rb.
How will this affect the asymptotes of the filter?
R
+
+
Vi
c
C
Vo
Rb
a
b
d
a. a
b. b
c. c
d. d
Question 24 [AD-DA converters]
The input range of a particular 12-bit AD converter is -5 to +5 V. Calculate the value of its
LSB, expressed in mV.
a. 2.4
b. 4.9
c. 9.8
d. 833
Question 25 [AD-DA converters]
The input range of an 8-bit AD omzetter is 0 - 10 V. Determine the output code for an input
voltage 4.5 V (MSB first).
a. 0011 1001
b. 0111 0011
c. 1000 1100
d. 1100 1110
Question 26 [AD-DA converters]
The input range of an 8-bit AD omzetter is 0 - 10 V. Determine the output voltage for an input
code 0101 0101 (MSB first)
a. 3.320 V
b. 6.570 V
c. 6.641 V
d. 6.680 V
Question 27 [AD-DA converters]
The input range of a 8-bit AD converter is -10 to +10V. Determine the output voltage for an
input code 1000 1000 (MSB first).
a. -4.688 V
b. -0.375 V
c. 0.625 V
d. 5.313 V
Question 28 [sampling]
The frequency band of a particular measurement signal runs from 1 kHz to 3 kHz. Determine
the (theoretically) minimum sample frequency for a correct digitization of this signal.
a. 2 kHz
b. 3 kHz
c. 4 kHz
d. 6 kHz
Question 29 [sampling]
A sinewave measurement signal with frequency 15 Hz is sampled using an ideal sampler. The
sampling frequency is 200 Hz. What are the first five frequency components in the frequency
spectrum of the sampled signal?
a.
b.
c.
d.
15, 185, 215, 385 en 415 Hz
15, 200, 400, 600 en 800 Hz
15, 215, 415, 615 en 815 Hz
185, 215, 385, 415 en 585 Hz
Question 30 [amplification]
The figure shows an amplifier circuit built up with an ideal operational amplifier. Resistance
values are R1 = 10 k and R2 = 100 k. Calculate the output voltage, for an input voltage of
16 mV.
R2
R1
vo
vi
a. 176 mV
b. 160 mV
c. +160 mV
d. +176 mV
Question 31 [amplification]
Using the circuit in the next figure with ideal operational amplifier, a voltage gain of 150
should be realized. Which combination of resistance values makes this possible?
R2
R1
vo
vi
a. 1 k and 149 k
b. 1.2 k and 180 k
c. 14.9 k and 100 
d. 150 k and 1 k
Question 32 [amplification]
Next figure shows a circuit composed of an ideal operational amplifier. What combination of
properties is valid for this circuit?
vo
vi
a
transfer
1
input resistance
0
output resistance

b
c
d
1
1
1

0

0
0
0
Quastion 33 [sensors]
Which of the next statements about a piezoelectric transducer is NOT correct?
a.
a piezoelectric transducer applied as force sensor is not suitable for the measurement of
static forces.
b.
a piezo-electric transducer used as an accelerometer works only properly at the
resonance frequency of the sensor.
c.
a piezoelectric transducer can be used both as a sensor and as an actuator.
d.
the primary output signal of a piezoelectric transducer is charge.
Question 34 [sensors]
Which of the next statements about a strain gauge is NOT correct?
a.
the resistance change is directly proportional to the applied strain
b.
a strain gauge is based on the piezoelectric effect
c.
a strain gauge is a sensor for the measurement of forces in a mechanical construction.
d.
a strain gauge has directional sensitivity (i.e. it is sensitive mainly in 1 direction of the
applied strain).
Question 35 [modulation]
The figure shows the (complete) frequency spectrum of a signal.
Vk (V)
1
f (Hz)
0
0
100
200
This signal is modulated on a sineshaped carriere with frequency 8 kHz, using an ideal
product modulator. Which frequency components build up the modulated signal?
a) 100, 200 and 8000 Hz
b) 100, 200, 7800, 7900, 8100 and 8200 Hz
c) 7800, 7900, 8100 and 8200 Hz
d) 8000 n.100 n. 200 Hz, n real, odd