UNIVERSITY OF OSLO
Faculty of Mathematics and Natural Sciences
Exam in: INF1411 – Introduction to electronic systems
Day of exam: May 28th 2014
Exam hours: 4 hours
This examination paper consists of 6 pages.
Appendices: None
Permitted materials: All printed and written, and pocket calculator
Make sure that your copy of this examination paper is complete before answering.
Unless explicitly stated, all questions within the same problem have the same weight
If you do not have a pocket calculator, explain how you would calculate the answers where
applicable
Problem 1 (Weight 20%) – Resistors and capacitors
R2=10kΩ
R3=15ΩkOhm
Vin=1+2sin(t)
Vout
R1=5kΩ
Figure 1
1-a) (Weight 4%)
If R1, R2 and R3 in figure 1 are replaced by a single resistor RX, what size will it have to be?
1-b) (Weight 4%)
Find the current i1 through resistor R1 in Figure 1.
1-c) (Weight 4%)
Determine the largest and the smallest instantaneous value of Vout.
1-d) (Weight 4%)
R1 is now replaced by a capacitor C=50uF. Find the ratio A between Vout and Vin as a function of
R1, R2 and XC.
1-e) (Weight 4%)
Between which values will A=Vout/Vin be when the frequency of Vin varies from 0Hz (direct
voltage) to a very high frequency ac?
1
Problem 2 (Weight 17,5 %) – Diodes
Figure 2: Diode characteristics
2-a) (Weight 5%)
Given the diode characteristics of figure 2: Find approximate values for the diode resistance when
VR =-60volt, VF = 0,5volt and VF = 0,8volt, respectively.
2-b) (Weight 5%)
V=1 volt
R
V=sin(t) volt
Figure 3: Diode circuit
The circuit of figure 3 consists of an ac source, a battery, a diode and a resistor. Assume that the
diode has ideal characteristics with a barrier voltage of 0,7volts. Furthermore assume that R=10kΩ.
Find the value of the current through R when V=sin(t) has a) the most positive value and b) the
most negative value.
2-c) (Weight 7,5%) Function of a diode circuit
Figure 4 shows a digital circuit with two diodes and a bipolar transistor. Va, Vb and Vout are digital
signals which either take the value of 0 volt or +5 volt, i.e. logic “0” or “1”. You can assume that
the threshold voltage of the transistor is larger than the barrier voltage of the diode. Explain which
Boolean function the circuit performs. (Hint: Identify which function the transistor has first).
2
+Vcc=5volt
R2
R1
Vout
Va
Vb
Figure 4: Digital logic circuit with transistor and diodes
Problem (Weight 22,5 %) – Operational amplifiers
3-a) (Weight 5%) Opamp circuit
V1
R1=4,7kΩ
Rf=14,1kΩ
R2=4,7kΩ
+
V2
V3
Vout
R3=4,7kΩ
Figure 5
3a-1) What is the circuit in Figure 5 called?
3a-2) Determine the amplification of the circuit
3a-3) Find V3 in the case of V1=1volt, V2=-2volt and Vout = -8volt
3-b) (Weight 7,5%) Active filtres
Vout
+
Vin
R
C
Figur 6: Active filter
3b-1) What is the difference between and active and a passive filter?
3b-2) If the input Vin is a dc voltage or an ac voltage with a low frequency, what function does the
circuit in figure 6 perform (in addition to being a filter)?
3b-3) What is the value of A in the pass band of the filter in Figur 6, assuming all components are
ideal? Justify briefly.
3
3-c) (Weight5%) Integrator
C
-
Vin
R
Vout
+
Figure 7: Integrator
The circuit in figure 7 is called an integrator. Draw the output signal Vout of the integrator when
Vin is a square wave signal with a duty cycle of 50% and centered around 0 volt (i.e. a balanced
signal)
3-d) (Weight 5%)
What happens to the output signal in problem 3-c) if the opamp no longer is ideal, but suffers from
a constant offset such that Vout >0V when Vin=0V? Justify your answer!
Problem 4 (Weight 20 %) – Transistors
4-a) (Weight 5%)
Given the transistor in figure 8: Internally in the transistor there is a fault either in the base, the
collector or the emitter, and measurements on the terminals reveal that VB=3 volt and VC=9 volt
(see the drawing). Assume a threshold voltage of VTH= 0.7 volt. Is the internal fault either in the
base, the collector or in the emitter? Justify your answer!
Vcc
+9 v
RC=560 Ohm
9v
3v
VBB=3v
RB=56 kOhm
Figure 8: BJT with an internal fault
4-b) (Weight 2,5%)
Vcc=25volt
R1=44kΩ
RC=2kΩ
R2=10kΩ
RE=2kΩ
Figure 9
4
What are the functions of the resistors RE and RC in Figure 9? What will happen if both resistors
are removed and the emitter is connected directly to ground and the collector directly to Vcc?
4c) (Weight 2,5%)
If IE=4mA and IB=10µA, what will be the values of IC and β?
4e) (Weight 5%)
Assume now that the resistor R2 in Figure 9 has an unknown value. What is the smallest value R2
must have in order to prevent the transistor from being in cutoff? Assume VTH=0.7 volt
4d) (Weight 5%)
Vcc
R1
Vcc
RC
R1
Vout1
Vin2
Vin1
Vout2
R2
R2
RE
RE
Figure 10: BJT amplifier circuits
What is the phase shift between Vin1 and Vout1, and between Vin2 and Vout2 in the amplifier
circuits in Figure 10? Explain and justify your answer!
Problem 5 (Weight 20 %) – Multiple choice
5-a) Current, voltage and impedance
Which statement is correct?
1) The sum of the voltages around a closed loop equals the sum of the impedances around
the same loop
2) The sum of the impedances around a closed loop is independent of frequency
3) The sum of the currents entering a node has the same sign as the voltage of that node
with respect to ground
4) Whether the voltages are algebraically added clockwise or counter-clockwise does not
matter when applying KVL
5) KVL does not apply to circuits containing reactive elements
5-b) Capacitors
Which statement is correct?
1) A capacitor stores electrical current
2) A capacitor stores electrcal charge
3) The impedance of a capacitor is independent of frequency
4) Another name for the impedance of a capacitor is inductive reactance
5) The inverse of capacitive reactance is reactive impedance
5
5-c) DA converters
Which statement is correct?
1) The resolution of a DA converter can’t improve the resolution of the input signal
2) DA converters always require a clock signal to function
3) DA converters use an internal AD converter as a voltage reference
4) Digital signals can have infinite resolution as opposed to analog signals
5) Operational amplifiers cannot be used in DA converters
5-d) AD converters
Which statement is correct?
1) An AD converter converts an analog current to a digital voltage
2) If a DA converter is connected to the output of an AD converter, the resolution of the
analog signal is not altered end-to-end
3) AD converters cannot be used in net pads
4) AD converters can convert both currents and voltages
5) High-frequency non-periodic noise in the analog signal being converted will always
propagate to the digital signal
5-e) Transistors
Which statement is correct?
1) Bipolar transistors are independent current sources
2) Bipolar transistors are independent voltage sources
3) Bipolar transistors are current controlled current sources
4) Bipolar transistors are voltage controlled voltage sources
5) All bipolar transistors have the same current amplification
6