Written exam for
IE1206 Enbedded electronics
thursday 5 june 2014 09.00-13.00
At the same time there is a similar exam for IF1330 – choose the right
exam!
General Information
Examiner: William Sandqvist.
Teacher: William Sandqvist, phone 08-790 4487 (Campus Kista),
Exam text does not have to be returned when you hand in your writing.
Aids: Calculator/Graphical calculator. Formula sheet for the course is included in the exam.
Information about the marking of the exam
You must motivate all answers.
Calculations that are used must be readable and presented in the solution. If the answer to a
question is "42" you must also state why.
Incomplete reasoned answers do not give full points!
The written exam has a maximum of 28 p, the pass limit is 12 p. At the first ordinary exam, to an
already passed exam up to four points could be added from the programming task, to get a higher
rating, ( at that time the maximum point will be 32p )
0–
F
10 –
Fx
12 –
E
17 –
D
20 –
C
The result is expected to be announced before Thursday june 26.
1
22 –
B
25–
A
1. 2p
R1 = 330Ω, R2 = 54Ω, R3 = 330Ω, R4 = 220Ω,
R5 = 132Ω.
Give an expression for RERS .
Calculate the equivalent resistance RERS.
RERS = ? [Ω]
2. 4p
Use Kirchhoffs laws to to set up and calculate
the three currents and their directions (signs).
(The task can give partial credit even if the
system of equations is not resolved).
E1 = 50V E2 = 80V E3 = 60V E4 = 120V
R1 = 20Ω R2 = 10Ω R3 = 30Ω
I1 = ? I2 = ? I3 = ?
3. 4p
a) Derive the Thévenin equivalent two-terminal circuit, with E (also the sign) and R, for the circuit
with the voltage source (10V) and current source (6,25 mA).
E = ? [V] R = ? [kΩ]
b) Derive the equivalent Norton two-terminal circuit, with I (also the direction) and R.
I = ? [mA] R = ? [kΩ]
2
4. 4p
E is a DC voltage source 24V. The Capacitor C =
10 µF. The switch has been closed a long time
before t = 0 when it will be opened.
a) What time constant will the charging of the
capacitor have after t = 0. τ = ?
b) Which value will thr voltage over the capacitor
uC have after a long time, t = ∞. uC = ?
c) Calculate what time (after t = 0) it will take for
the voltage over the capacitor to reach value 3V.
t = ?, uC = 3.
5. 4p
An AC voltage U with the frequency f = 50 Hz
supplies a circuit with an inductor L = 250 mH in
paralell with a resistor RB = 40 Ω in series with a
resistor R = 20 Ω.
One measures the voltage UL = 150 V.
a)
b)
c)
d)
Calculate
Calculate
Calculate
Calculate
IB
IL
I
UR
6. 4p
RFID-key-tags are used instead of door phone for access to apartment buildings. The communication is with
radio frequency. The key tag containes a printed coil L r and a capacitor C, that forms a resonance circuit for the
communication frequency. The resonance circuit is also loaded with a processor RPIC.
L = 0,43 mH r = ? Ω C = 3,77 nF RPIC = 30 kΩ
a) What is the resonance frequency of the key tag? f = ? [kHz]
b) What resulting Q-value (with the processor included) must the resonance circuit have for the bandwidth
BW= 2,5 kHz at resonance frequency? Qres = ? [times]
c) Both the parallel load resistance RPIC and the coil series resistance r will contribute to the circuit Qres. What
value should the coil series resistance r have? r = ? [Ω]
3
7. 4p
The figure shows a simple filter with (L+R)||R and a R.
a) Derive the filter complex transfer function U 2 /U 1 .
a + jb
Answer on the form
c + jd
b) What will the transfer function absolute value be at low frequencies, ω ≈ 0 , what will the
transfer function phase be at low frequencies?
c) What value will the transfer function absolute value have at high freguencies, ω ≈ ∞ , what value
will the transfer function phase have at high frequencies?
d) What value will the phase have when ωL = R ?
a)
U2
= ? b) ω ≈ 0 ⇒
U1
U
d ) ωL = R ⇒ arg 2
U1
U 
U2
= ? arg 2  = ? c) ω ≈ ∞ ⇒
U1
U1 
U 
U2
= ? arg 2  = ?
U1
U1 

 = ? [°]

8. 2p
Internet consists of millions of interconnected electrical equipments – and it all works perfectly,
despite the obvious risk of electrical interference! The reason is that there are a lot put on
interference immunity.
a) The equipment is connected by twisted wires. How can this counteract electrical disturbances?
b) What is the use for the transformers at both ends of the data transfer?
Good luck!
4
Formula sheet for exam in Embedded Electronics, IE1206
Resistance
l
R=ρ
a
Resistance R , resistivity ρ (note! [Ωmm2/m])
R2 = R1 + R1 ⋅ α( t 2 − t1 )
Resistance temperature dependence.
R2 = hot resistance, R1 = cold resistance
α = temperature coefficient
Circuit analysis
U = I⋅R I = G⋅U
RERS = R1 + R2 + R3 + …
1
1
1
1
=
+
+
+ ...
RERS R1 R2 R3
R1 || R2 =
R1 ⋅ R2
R1 + R2
Two resistors in paralell.
Kirchhoffs current law. A node is a connection point.
Currents in to the node are taken positive and currents
out of the node negative.
Kirchhoffs voltage law. A mesh is a closed circuit. The
voltage drop over a resistor has plus where the current
enters.
Voltage divider. Divided voltage over R1.
∑I = 0
Nod
∑U = 0
Mesh
U1 = E
I1 = I
R1
R1 + R2
Current branching. Branch current through R1.
R2
R1 + R2
P =U ⋅I
P=
OHM’s law. R resistance G Conductance.
Series circuit.
Paralell circuit.
U2
R
P = I2 ⋅R
DC power in resistor.
Electrical fields
F =k
Q1 ⋅ Q2
r2
E=k
a
ε = εr ⋅ε0
d
Q
U
E=
U=
C
d
2
C ⋅U
We =
2
C =ε
Q1 ⋅ 1
r2
Coulumbs law force F between charged
particles. Elektric field E is the force upon an
unit charge. Constant k = 9⋅109.
Plate capacitor. ε capacitivity
(Polarizability). ε0 is for air/vacuum.
Capacitor voltage U charge Q and electric
field E.
Electrostatic energy.
5
Magnetical fields
Φ
a
Fm = N⋅I
1 l
Rm = ⋅
µ = µr ⋅ µ0
µ a
Fm = Φ⋅Rm
F = B⋅I⋅l
dΦ
e=N
dt
di
u=L
dt
L⋅I2
Wm =
2
Flux Φ (number of force lines) flux density B.
B=
”mmf” Magneto motoric force.
Reluctance Rm magnetic resistance. µ permabily,
µ0 = 4π⋅10-7 for vacuum. (µr relative vacuum)
OHM’s law for magnetic circuit.
Motor principle.
Induction law. (Lenz law, that e is counteracting).
Self induction. Inductance L.
Elektromagnetic energy.
Transients
x (t ) = x ∞ − ( x ∞ − x 0 ) e
t = τ ⋅ ln
−
Quick formula.
t
x0 = entity start value
x∞ = entity value after long time
τ = time constant of the process
τ
”all the swing” through the ”rest”
" all"
" rest"
Capacitor: τ = RC Inductor: τ =
L
R
Time constant τ.
Alternating current AC
Periodical functiond
x(t ) = Xˆ sin(ω ⋅ t + ϕ ) ω = 2π ⋅ f
T
X med = X =
1
x(t )dt
T ∫0
T
X RMS = X =
∫x
2
(t )dt
0
T
jω-method
Z = R + jX
X L = jω L X L = ω L
1
1
XC =
XC = −
jω C
ωC
Sine with phase ϕ.
Mean value of one period. All pure sine
functions has mean value 0.
Effective value (RMS). For sine functions:
X̂
X =
2
Impedance Z, resistance R and reactance X.
Inductive reactance.
Capacitive reactance.
6
Resonance circuits
1
f0 =
2π LC
2πf 0 L
R
Q=
Q=
r
2πf 0 L
Resonance frequency.
Definition of the inductor Q-value (Q-factor)
with series resistance r, and alternatively with
parallell resistance R.
Transformation between series resistance r
and parallell resistance R. (if Q > 10)
Band width BW, ∆f .
R
= Q2
r
∆f
1
=
f0 Q
Maximum power theorem
RL = RI
ZL = Z
Maximum power DC.
Maximum power AC. Complex two terminal
circuit and complex load. (* conjugate)
Maximum power AC. Complex two terminal
circuit and resistive load.
*
I
RL = Z I
Ideal transformerr
P1 = P2
U 1 N1
=
U2 N2
Ideal transformer.
Voltage ratio.
Current ratio.
I1 N 2
=
I 2 N1
Z 1←2
N
=  1
 N2
2
Impedance transformation ratio.

 ⋅ Z 2

Inductive coupling
U1 = r1 I1 + jω L1 I1 + jω MI 2 U 2 = r2 I 2 + jω L2 I 2 + jω MI1
k=
M
L1 L2
LSER = L1 + L2 ± 2 M
LPAR =
L1 ⋅ L2 − M 2
L1 + L2 ± 2 M
7
Equation system with
r1 L1 r2 L2 M
Coupling coefficient k mutual
inductance M
k =1 100% identical flux k = 0
independent
Series connection (”-” for
counteracting)
Paralell connection (”+” for antiparalell).