isc0100 cyberelectronicsisc.ttu.ee/materials/martin/isc0100/kyberelektroonika12019-eng-3.pdf · an...
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ISC0100
CYBERELECTRONICS
Fall 2018
The 3rd lecture
Martin Jaanus NRG-308
[email protected] 56 91 31 93
Learning environment : http://isc.ttu.ee
Materials : http://isc.ttu.ee/martin
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Topics
1. Voltage, current
2. DC, AC
3. Values, calculations
4. Capacitor, Inductor
Alternative current
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Voltage, electric potential difference, electric pressure or
electric tension (formally denoted ∆V or ∆U, but more often
simply as V or U, for instance in the context of Ohm's or
Kirchhoff's laws) is the difference in electric potential energy
between two points per unit electric charge. The voltage
between two points is equal to the work done per unit of
charge against a static electric field to move the test charge
between two points and is measured in units of volts (a joule
per coulomb).
The volt (symbol: V) is the derived unit for electric potential, electric potential
difference (voltage), and electromotive force. The volt is named in honour of the
Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile,
possibly the first chemical battery.
.
Voltage
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An electric current is a flow of electric charge. In electric
circuits this charge is often carried by moving electrons in a
wire. It can also be carried by ions in an electrolyte, or by both
ions and electrons such as in a plasma.
The SI unit for measuring an electric current is the ampere
(A), which is the flow of electric charge across a surface at the
rate of one coulomb per second.
Current
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The electrical resistance of an electrical conductor is a
measure of the difficulty to pass an electric current through
that conductor. The inverse quantity is electrical conductance,
and is the ease with which an electric current passes.
Electrical resistance shares some conceptual parallels with
the notion of mechanical friction. The SI unit of electrical
resistance is the ohm (Ω), while electrical conductance is
measured in siemens (S).
An object of uniform cross section has a resistance
proportional to its resistivity and length and inversely
proportional to its cross-sectional area. All materials show
some resistance, except for superconductors, which have a
resistance of zero.
Electrical resistance and conductance
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DC, Direct current Direct current (DC) is the unidirectional
flow of electric charge. It is not changing during observation.
0
0,5
1
1,5
2
2,5
3
3,5
4
0 0,5 1 1,5 2
V
t
0
0,5
1
1,5
2
2,5
3
3,5
4
0 0,5 1 1,5 2
V
t
Direct Current
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AC, Alternative current is an electric current in which the flow
of electric charge (periodically) reverses direction. Different
signal values.
-350
-250
-150
-50
50
150
250
350
0 0,5 1 1,5 2
V
t -20
-15
-10
-5
0
5
10
15
20
0 0,5 1 1,5 2
V
t
Periodic Non periodic
Alternative Current)
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Alternative Current
How AC can be produced.
Image :wikipedia Image :circuitlab.com
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Alternative Current - values
-350
-250
-150
-50
50
150
250
350
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2
V
t
amplituded (A)
Max (V)
amplitude (A)
Min (V)
p-p
Perod (T)
Periodic signal, amplitude, peak to peak, period
Example:
u(t)=A*sin(2πt+φ)
Signal has several values
• Amplitude
• Peak value (max,min)
• Mean value:
• Absolute mean value
• rms,
root mean square value
𝑈𝑚𝑘 =1
𝑇න0
𝑇
|𝑢 𝑡 |𝑑𝑡
𝑈0 =1
𝑇න0
𝑇
𝑢 𝑡 𝑑𝑡
𝑈𝑚𝑘 =1
𝑇න0
𝑇
𝑢2 𝑡 𝑑𝑡
frequency f=1/T , unit hertz (Hz)
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Alternative Current - RMS
𝑈𝑚𝑘 =1
𝑇න0
𝑇
𝑢2 𝑡 𝑑𝑡Effective value
Root mean square (RMS) amplitude is used especially in electrical engineering:
the RMS is defined as the square root of the mean over time of the square of the
vertical distance of the graph from the rest statei.., the RMS of the AC waveform
(with no DC component).
RMS value equals with DC value whitch has the same energy..
RMS value describes a power of signal .
The power is proportional with root of the signal..
All measurement devices (meters) are showing RMS value.But actually most of them are showing absolute mean value !!!!
If we use RMS values, the formulas are same than in DC values..
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Alternative Current - measurement
How AC can measured
Scale is graduated using RMS
Value. Real difference is 1,11x
Correct result only when
Measuring sine wave
𝑈𝑚𝑘 =1
𝑇න0
𝑇
|𝑢 𝑡 |𝑑𝑡
Below 1V unlinear !
Recifier Filter Amplifier
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Alternative Current - true RMS
True RMS multimeter
x2 𝑋 V
It is expencive realization in analogue electronics (toot and square root)
In digital meters, real time sampling is required.
All measurement devices (meters) are showing RMS value.
But actually most of them are showing absolute mean value !!!!
𝑈𝑚𝑘 =1
𝑇න0
𝑇
𝑢2 𝑡 𝑑𝑡
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Input: 2 V sine
Alternative Current - measurement
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Input: 6 V sine
Alternative Current - measurement
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Input: 6 V sine ???
Keskväärtus on 0
Alternative Current - measurement
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Input: 6 V triangle
Alternative Current - measurement
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Input: 6 V rectangular
Alternative Current - measurement
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Alternative Current - calculations
Calculation (look also waveform.pdf)
A
t
Part of signal mean value RMS value
A
t
A
t
B
𝐴 ∗ 𝑡 𝐴2 ∗ 𝑡
𝐴 + 𝐵
2∗ 𝑡
𝐴2 + 𝐴𝐵 + 𝐵2
3∗ 𝑡
𝐴2
π∗ 𝑡
𝐴2
2∗ 𝑡
Mean value
Xk=𝑋1+𝑋2+𝑋…𝑡1+𝑡2+𝑡…
RMS value
Xrms=𝑋1+𝑋2+𝑋…𝑡1+𝑡2+𝑡…
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Alternative Current - calculations
Example :
RMS
V=25∗02+25∗
42
2+25∗
(−4)2
2+25∗02
100=
02+42
2+(−4)2
2+02
4= 2 𝑉
AVG
V=25∗0+25∗4∗
2
π+25∗ −4 ∗
2
π+25∗0
100=
0+4∗2
π+ −4 ∗
2
π+0
4= 0 V
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Alternative Current - calculations
Example :
RMS
V=25∗
42+4∗ −1 + −1 2
3+25∗ −1 2+25∗
−1 2+ −1 ∗0+ 0 2
3+25∗
02+0∗4+42
3
100=1.66 𝑉
AVG
V=25∗
4+ −1
2+25∗ −1 +25∗
−1 +0
2+25∗
0+4
2
100= 0.5 V
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Alternative Current - calculations
Example :
RMS V=3262
2+
1832
2=264.3𝑉
Periods are different !
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Capacitor
Capacitor prysical quantity - capacitance C, unit farad (F)
Energy is tored into electrical field 𝐸 =𝐶𝑉2
2
Integrates current , voltage misses current a quater period.
Conductance reactive 𝑌𝑐 = 𝑗ω𝐶 𝑍𝑐 =1
𝑗ω𝐶ω = 2π𝑓 ω−angular frequency(rad/s)
In case of series or parallel connection , use conducance formulas !!!
Concuctance is proportional with frequency.
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Capacitor•Capacitors:
• state variable: voltage
• Fundamental circuit equation:
• The capacitance gives an indication of electric inertia. Compare the
above equation with Newton’s
• Capacitors will tend to hold its voltage fixed.
• For a finite current with an infinite capacitance, the voltage must be
constant. Hence, capacitors tend to behave like voltage sources
(the larger the capacitance, the closer they resemble a voltage source)
• A capacitor’s energy is
CC
dvi C
dt
dvF m
dt
21
2CW Cv
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Inductor
Physical quantity – inductivity L, unit henry (H)
Energy is stored in magnetic field 𝐸 =𝐿𝐼2
2
Integrate voltage , current misses a quater period .
Resistance is reactive ZL= 𝑗ω𝐿 𝑌𝐿 =1
𝑗ω𝐿ω = 2π𝑓 ω− angular freq.(rad/s)
In parallel or series connection use resistance formulas.
Resistance is proportional with frequency.
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Inductor• Inductors
• state variable: current
• Fundamental circuit equation:
• The inductance gives an indication of electric inertia. Inductors will
tend to hold its current fixed.
• Any attempt to change the current in an inductor will be answered with
an opposing voltage by the inductor. If the current tends to drop, the
voltage generated will tend to act as an electromotive force. If the
current tends to increase, the voltage across the inductor will drop, like
a resistance.
• For a finite voltage with an infinite inductance, the current must be
constant. Hence, inductors tend to behave like current sources (the
larger the inductance, the closer they resemble a current source)
• An inductor’s energy is
LL
div L
dt
21
2LW Li
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Inductors and capacitors..
• …are present even if we do not want it !!.
• Also the resistance
• Parasite (invisible) (components)
• In the rise of frequency , will apply parasite L and C
If you are designig electronics you must accept it !!!
You buy this:
But you get this:
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Since capacitors behave like constant voltage sources you shall never connect a
switch in parallel with a capacitor. Any attempt to violate this load will lead to high
currents. Likewise, you shall never connect a switch in series with an inductor. Any
attempt to violate this rule will lead to high voltages.
Inductors and capacitors
500kV Substation arc.
Screenshot from video https://www.youtube.com/watch?v=hIkNY5xjy5k
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R, L, C..
Low-pass filter
High-pass filter
𝐹𝐶=1
2𝜋𝑅𝐶
𝐹𝐶=1
2𝜋𝑅𝐶
RC- time constant
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R, L, C..
Images:wikipedia
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Resonance
Resonance is a condition in an RLC circuit in which the capacitive and reactive
reactance are equal in magnitude, thereby resulting in a purely resistive impedance.
Resonance circuits are useful for constructing filters and used in many application.
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Series resonance
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Series resonance
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Parallel resonance
At resonance, the impedance consists only
conductance G.
The value of current will be minimum since the total
admittance is minimum.
The voltage and current are in phase.
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RC transfer calulation
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L
+
–R V
+
R=600Ω
L=300mH
=2krad/s
Find transfer ratio in dB
1. Find the transfer function.
Using Ohm’s law
I=V/Z , where Z total resistance of
inductor and resistor Z=R+jωL. Voltage, applied to resistor
equals
Vr=I*R . We get
Vr/V=R/(R+jωL) or K=R
R+jωL. Since we are interested in amplitude,
We need length of the vector
Kv=20log (R
R2+(ωL)2
)
RC transfer calulation 1
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L
+
–R V
+
R=600Ω
L=300mH
=2krad/s
Kv=20log (R
R2+(ωL)2
)
Kv=20log (600
6002+6002
) =20log(0.707)=-3dB
RC transfer calulation 1
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L
+
–C V
+
C=1nF
L=400mH
=49krad/s
Kv=20log 1
1-490002*400*10-3*1*10-9=20log(1/0.0396)=20log(25)=27.9dB
Transfer function:
K=1/j ωC
jωL+1/jωC=
=1
j (ωL-1/ωC) * jC=
1
1- 2LC
j*j=-1 1/j=-j
RC transfer calulation 2