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2017-05-23
Analog Electronics
http://www.miun.se/personal/kent.bertilsson/Courses/AnalogElectronics.htm
•
Thomas L. Floyd, "Electronic Devices - Conventional Current Version"
ISBN: 0-13-615581-2
•
Don Manchini, "Op Amps for Everyone" -Free downloadable pdf
Lecturer
Lab teacher
Kent Bertilsson
Krister Hammarling
[email protected]
S-Building Office S206
Phone 060-148915
[email protected]
S-Building Office S207
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Examination
This analog electronics is given as a stand alone course
but also as one part of the Measurement System course.
• 12 x 2h scheduled lectures
– 10 Lectures
– 2 times for solving problems
• As appeared in the plan (Not as shown in schedule)
• 4 x 4h scheduled laboratory classes completing 3 tasks
that should completed and handed in to the laboratory
teacher.
• A written exam will be held 27th October
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Introduction
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Block Diagram
• Electronic systems is often described by block diagram
Antenna
Amplifier
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Filter
Analog to
digital conversion
Time domain vs Frequency domain
• Every signal can be described both in the time domain
and the frequency domain.
• A periodic signal (in the time domain) can in the frequency
domain be represented by:
– A peak at the fundamental frequency for the signal, fs=1/T
– and multiples of the fundamental f1,f2,f3,…=1xfs ,2xfs ,2xfs
V
V
T=1/fs
t
fs
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2 fs
3 fs
4 fs
5 fs
f
Time domain vs Frequency domain
• Every signal can be described both in the time domain
and the frequency domain.
• A non periodic (varying) signal time domain is spread in
the frequency domain.
• A completely random signal (white noise) have a uniform
frequency spectra
V
V
fs
2 fs
3 fs
4 fs
5 fs
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f
Noise
f
Transfer function
• The transfer function is the relation between the amplitude for the
output and input in the frequency domain.
U Out  f 
Hf 
U in  f 
– H(20kHz)=10 mean that for a 20kHz signal the output is ten times larger
than the input.
– H(f) is of course continuous function
H
10
5
0
f
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Filter
• A filter is a circuit that let some frequencies pass and
H
block others.
– Low pass
f
H
– High pass
f
H
– Band pass
f
H
– Band stop
f
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jω-method
• The jω-method is a very powerful tool making it possible
performing advanced frequency dependent (alternating
current, AC) functions using the same rules that applies for
direct current (DC)
Resistor
Capacitor
Inductor
X R
1
X
jC
X  jL
Symbol
Reactance
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jω-method
• Impedance calculations can be performed in the same
way as for normal resistances.
R
L
R
L
Z  Z R  Z L  R  jL
1
R
Z R  ZC
R
j C
Z  Z R // Z C 


Z R  ZC R  1
1  jRC
jC
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RC - filter
Calculate the transfer function H(ω)
R
VIn
C
What is the output voltage and
power level at the cut-off frequency?
VOut
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Amplifier
• Voltage amplification
PIN
IIN
IOut
VIn
VOut
POut
VOut
AV 
VIn
• Current amplification
I Out
AI 
I In
• Power amplification
POut
AP 
PIn
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Decibel, dB
decibel, dB is very useful expressing amplification (and attenuation)
APdB
APdB
POut
 10 log AP  10 log
PIn
V2
P V I 
(Under assumption
R
that RInAmp=RLoad)
2
VOut
2
 VOut 
POut
VOut
R


 10 log
 10 log 2  10 log 
 20 log

VIn
PIn
VIn
 VIn 
R
VOut
AVdB  20 log AV  20 log
VIn
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dB
AV
AP
20
10
100
10
3.16
10
6
2
4
2  1.414
3
0
1
1
-3
2
-20
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2
1
 0.707
0.5
0.1
0.01
Bode Diagram
• Absolute decibel value and phase of the transfer function
is plotted against a logarithmic frequency axis
H  f  dB
  angle H  f 
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RC-filter example
Draw an asymptotic bode
diagram for the RC filter.
R
VIn
C
VOut
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Bode diagram
• Complicated expressions can be factorized into
sub-expressions as
Const
Differentiator
Zero
C
j

1 j
0
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1
j
1

1 j
0
Integrator
Pole
Bode diagram
• According to logarithmic laws
Atot  A1  A2  A3
Atot dB  A1dB  A2 dB  A3 dB
angle Atot   angle A1   angle A2   angle A3 
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Example
R
VIn
R2
Draw an asymptotic bode
diagram for the shown filter.
C
R3
VOut
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Amplifier model
• The amplifier model is often sufficient describing
how an amplifier interacts with the environment
ROut
VIn
RIn
AVVIn
VOut
• RIn – Input impedance
• AV – Voltage gain
• ROut – Output impedance
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Bandwidth
• The bandwidth is the frequency range where the
transferred power are more than 50%.
AP  0.5 AP max
H(f)
AVmax
0.707AVmax
AV  2 AV max  0.707 AV max
B  f 2  f1
f1
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f2
f
Distortion
• A nonlinear function between UIn and UOut distorts the
signal
– An amplifier that saturates at high voltages
– A diode that conducts only in the forward direction
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Noise
• Random fluctuation in the signal
• Theoretically random noise contains all possible
frequencies from DC to infinity
• Practical noise is often frequency limited to an upper
bandwidth by some filter
• A limited bandwidth from the noisy reduce the noise power
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