Transcript Resistance - XAMK Moodle

Resistance
 Resistance is a natural feature of materials.
 Metals are good conductors and non-metals are usually insulators.
 Most conductors follow Ohm’s law (I=V/R) where R is the same
constant at any voltage. Voltage dependent resistors (VDR) are nonlinear components, where R changes when voltage changes. VDRs
can be used e.g. in over-voltage protectors.
 The resistance depends on the length l and area A of the conductor
and the resistivity ρ of the material:
l
R
A
Picture from Wikipedia
Typical resistivities
Material
Resistivity
Material
Resistivity
Silver
1,64 E-8
Nichrome
100E-8
Copper
1,72E-8
Silicon
2500
Aluminium
2,83E-8
Paper
10E10
Iron
12,3E-8
Mica
5E11
Constantan
49E-8
Quarz
1E17
In temperature dependent resistors (NTC or PTC resistors) the resistance
changes, when the temperature changes. They can be used for measuring the
temperature or for limiting the current of a circuit in overload situations.
PTC (Positive Temperature Coefficient) cables can be used as self-regulating
heating cables. The heating power decreases automatically when temperature rises.
Ohm’s law and
Kirchhoff’s laws
 The voltages and currents in a
circuit containing resistors and
voltage or current sources can
be calculated by using Ohm’s
law (I =V/R) and Kirchhoff’s
laws (two laws in the picture,
but which two …)
 For some cases there are simple
calculation formulas, which are
based on these basic laws.
Examples of this kind of rules
(on next slide) are
 resistors in parallel
 resistors in series or
 voltage division using
resistors.
Resistors in parallel and in series
1
1
1
1
 

 ...
Rtot R1 R2 R3
Rtot  R1  R2  R3  ...
Voltage divider:
Vout = Vin * Z2 /(Z1 + Z2)
Capacitors
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Capacitors are components that can store charge.
Q
The capacitance C tells how much charge Q is in the
C
capacitor, when the voltage over the capacitor is V.
V
Parallel-plate capacitor is the simplest type of capacitor.
The capacitance C of parallel-plate capacitor can be
A
calculated from the permittivity of the insulating material
C

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
0 r
= 0 r , area A and distance d between the plates.
d
Some dielectric materials like ceramic materials, tantalum
oxide or aluminium oxide have a high value of relative
permittivity r . These materials can be used as an
insulation for capacitors that have a big capacitance in
small size.
Capacitance can be made higher by using thinner
Picture from Wikipedia
insulation (smaller value of d), but this makes the
breakdown voltage of the capacitor smaller.
Capacitors in parallel and in series
(Note: For parallel capacitors the capacitances are added. But for
resistors and inductors the opposite is true: For serial resistors or inductors
the resistance or inductane values are added.)
Ctot  C1  C2  C3  ...
1
Ctot  1 1 1
C1  C2  C3 ...
The unit of inductance is
As/V. It is called Farad,
but usual values are
micro- or nanoFarads…
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There are many types of
capacitors
Pictures from Wikipedia
Big aluminium electrolyte
capacitor
Tantalum capacitors
Capacitors in the picture below
(from left to right):
- Multilayer ceramic
- Ceramic disk
- Multilayer polyester film
- Tubular ceramic
- Polystyrene
- Metallized polyester film
- Small aluminium electrolyte
Aluminium electrolyte
capacitors
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In this picture
you can see
an exploded
electrolytic
capacitor.
Cylindrical shape and big size
They are polarized: DC voltage must be connected to correct direction.
Otherwise the capacitor may be damaged or even explode. (There is a + or –
sign close to one of the terminals.)
Typical values are big, e.g. 100 nF to 4700μF. Used in power supply circuits
in order to keep the output voltage stable.
Typical maximum voltage values 12V,16V, 32V, 64V (but can be even
hundreds of Volts).
Made of long sheet of aluminium that is coated by a very thin layer of
aluminium oxide. The capacitance can be very high, because the insulating
oxide layer is very thin (small d) and has a high value of r
The electrical connection to the other capacitor terminal happens through a
conducting liquid (electrolyte).
Pictures from Wikipedia
Tantalum capacitors
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Low voltage devices
Smaller mechanical size than in aluminium electrolyte capacitors
Capacitances 1μF – 150μF
Stable capacitance and very low impedance in low frequencies
Dont like voltage spikes
They are polarized: DC voltage must be connected to correct direction.
(There is a + or – sign close to one of the terminals.) Can explode if
connected to the opposite direction.
Picture from Wikipedia
Picture from Wikipedia
Plastics capacitors
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Typical materials polystyrene, polyester, polypropylene or teflon
The insulation is plastics foil.
Some plastics capacitors are mechanically very small, because they use very
thin foils. These capacitors are for low voltages only.
Other plastics capacitors are mechanically bigger, because they use thicker
foils. These capacitors can be used for higher voltages, too.
Capacitance values are small or medium (1 nF – 50μF), but the eletrical
values are good and stable. These are good capacitors for small-signal
electronics. For example operational amplifier circuits like active filters,
integrators and differentiators use most often plastics foil capacitors.
Ceramic and mica capacitors
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Ceramic insulation materials can have a high value of permittivity, which
makes it possible to make capacitors that have very small mechanical size
but still a reasonably high capacitance value. Many ceramic capacitors can
also be used at high voltages.
Signal conditioning ceramic
capacitors at the higher left
corner (and some tantalum
and one small electrolyte
capacitor):
In the tantalum capacitors
you can see that maximum
voltages are small (e.g. 20V
or 16V or 10V). The polarity
is marked with + or – sign
at one end.
Picture from Wikipedia
Coils or Inductors
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The DC current through a coil creates a magnetic field.
A coil is a short circuit for DC. Low frequency currents go
easily through inductors, but high frequency currents are
attenuated or completely blocked.
Series and parallel connections are calculated as in resistors.
The voltage v of the inductor L is proportional to the rate of
increasing (or decreasing) the current i:
The inductor stores in its magnetic field an energy that is
proportional to the square to the current. It is not possible to
increase (or decrease) the current of the inductor without
bringing more energy to (or taking away some energy from)
the inductor.
wL 
1 2
Li
2
The unit of inductance is
Vs/A. It is called Henry,
but usual values are
milli- or microHenrys…
di
vL
dt
Resistance resists current. Inductance makes it more difficult
to decrease or increase the current. Big capacitance means that
a lot of current is needed for changing the the voltage.
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The 2nd man in the picture cannot
stop eating. A circuit with big
inductance cannot stop (or start)
the current before enough energy
is taken away from (or brought to)
the circuit.
The 3rd man can eat a lot without
feeling tension (”too high voltage”) in
his stomach. Big capacitance makes
it more difficult to change the
voltage accross the capacitor. A lot
of current must be fed to a big
capacitor to increase its voltage.
Hydraulic analogy
of C, L and R
Pictures from Wikipedia
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In the hydraulic analogy, a capacitor is analogous to a rubber membrane
sealed inside a pipe. The membrane stops continuous flow to one direction
(DC), but it allows short time flow that is changing direction often (like AC).
The membrane is repeatedly stretched and un-stretched by the flow of
water, which is analogous to a capacitor being repeatedly charged and
discharged by the flow of charge.
In the same analogy, an inductor is analogous to a heavy paddle wheel
rotating in the flow (or a liquid that has a high mass). It is difficult to make it
moving, but it is also difficult to stop it.
The resistor is analogous to a very narrow pipe that resists the flow.
Transformers
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When two coils are put close to each other  by mutual inductance the energy
is transferred from one coil to the other. If the coils have different number of
turns (N), the transformer can make the voltage higher and the current smaller
(or voltage smaller and current higher):
VP / VS = NP / NS
IP / I S = N S / NP
Picture from Wikipedia
RLC-circuits as filters
RLC-circuits can be used as filters:
- High-frequency current can easily
go through a capacitor. Low-frequency
or DC currents are stopped by the
capacitor.
- Low-frequency or DC currents can easily
go through an inductor. High-frequency
currents are stopped by the inductor.
-RLC-circuits are called passive filters.
In electronics we usually prefer active
RC-filters that consist of operational
amplifiers, resistors and capacitors but
no inductors (because inductors are big
components and sensitive to magnetic
interference).
Material types
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Conductors (resistivity about 10E-7 Ωm)
Insulators
Semi-conductive materials (resistivity over 1010Ωm)
 Germanium was the material of the first transistors.
 Silicon has replaced germanium in modern electronics.
 Compound semiconductors (GaAs) are used e.g. in optical components
like LEDs.
 The fabrication process can chemically change different parts of the
semiconductor component into a different type:
 P-type semiconductors (holes are the majority current carriers)
 N-type semiconductors (electrons are the majority current carriers)
Diodes
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P-type end is anode and n-type is cathode
Current is possible only in one direction.
AC-current will be rectified by a diode, because the current in opposite
direction is not possible. The rectified half-sinusoid pulses can be filtered
into DC current by using big capacitors.
Voltage-stabilizing circuits use special diodes, that conduct also to the
opposite directions at a certain voltage. This voltage over zener-diode does
not depend on the current passing the component.
Light emitting diodes (LED) work like diodes, but when they have a
current, part of the power is released as light. In most other components the
power lost in the component is turned into heat.
NPN and PNP transistors
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Transistor is a current controlled current source. The bipolar NPN
transistor has two n-type areas and a thin p-type area between them. In
PNP transistors there are two p-type areas and one n-type area.
The transistor can be used as a switch or as an amplifier.
There is also a second group of transistors. They are FETs (Field-effect
transistors) which are voltage-controlled current sources.
Integrated circuits (ICs)
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ICs include many integrated components, especially transistors
 SSI small-scale integrated ICs (operational amplifiers, voltage regulators,
basic digital circuits) have tens of transistors in one IC. This technology is
about 50 years old but some SSI components are still commonly used.
 MSI (medium scale integration) had hundreds of transistors in one IC
 LSI (large scale integration) had thousands of transistors in one IC. For
example the first microprocessors 40 years ago were LSI circuits.
 VLSI (very large scale integration) has at least tens of thousands of
transistors in each IC, but many todays digital ICs like microprocessors or
memories have hundreds of millions of transistors.
The use of ICs can make the design on electronic circuits much easier than the
design of circuits using separate (discrete) transistors. Especially in analog
electronics the operational amplifier ICs are used a lot.
Operational amplifiers (OpAmps)
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OpAMPs are used to amplify or process
analog signals in e.g.
 Filtering circuits
 Summing or subtracting of analog
signals
 Integrators and differentiators
The basic idea of OpAmp is very high
amplification (gain) and the use of
negative feedback. The OpAmp has two
inputs. The output voltage is the
difference of the input voltages
multiplied with the gain.
The gain is an extremely big number, e.g.
100 000 or 1 000 000. We can simplify
calculations by thinking that the gain is
infinite.
Negative feedback in OpAmp circuits
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Negative feedback is created to an OpAmp circuit by connecting a resistor (or
sometimes a capacitor) between the output and the inverting input (-).
The negative feedback can be used to set the gain of an OpAmp circuit to the
wanted level (see the circuits and gain formulas on the next slides).
The negative feedback also creates a situation, where both inputs (+) and (-)
have almost the same voltage. (If these voltages were different, the output voltage
should be infinite.) This fact is used in many simplified OpAmp calculations.
 An exemption to the above rule is the situation, where the OpAmp cannot
give enough voltage or current. In that case the output voltage is smaller
than the theoretical value and the input voltages are not equal.
 For many OpAmps the highest possible output voltage is about 1 or 2 volts
smaller than the supply voltage. (about +14 V if supply voltage is +15 V)
 The highest possible output current can be e.g. 20 mA or 50 mA. This means
that the resistors loading the output should be typically kilo-ohms. OpAmps
are used for signal processing. They cannot be used as power amplifiers for
driving e.g. motors or loudspeakers.
The input current of the OpAmp is very small. It can usually be considered to
be practically 0. This fact can also be used for simplifying the calculations.
Inverting amplifier
Rf
vout
G

vin
R1
If you want to make the gain a positive number,
you can add a second amplifier, where Rf=R1
The input current that is taken from vin is not 0. It flows first
through R1 and then through Rf to the output of the amplifier.
The negative feedback makes both OpAmp inputs to have equal
voltage. Also the inverting input (-) must have a voltage of 0 V. It is
called a virtual ground.
Non-inverting amplifier
Rf
vout
G
 1
vin
R1
The gain a positive number. It is always bigger that 1.
The input current that is taken from vin is practically 0. This means
that the amplifier has a very high input impedance.
Unity-gain buffer
 If the feedback resistor of an non-inverting amplifier is replaced with
a short-circuit (Rf=0), the gain will be G=1. (The R1 can now have any
value, and so we can also leave it away.)
 This unity-gain amplifier has a very high input impedance, because
the input current is practically 0. This circuit can be used as a buffer
amplifier. It prevents the voltage drop that usually happens, when a
load is connected to a transducer. (Compare to Electronics assignments
3: task 4)
Inverting summing amplifier, DAC
- vout 
Rf
R1
 v1 
Rf
R2
 v2 
Rf
R3
 v3  ...
The gain is always a negative number. If you want to make the gain
a positive number, you can add an inverting amplifier, where Rf=R1
The input currents that are taken from v inputs are not 0. All these
currents go through Rf and create a voltage that is proportional to the sum
of the currents.
In simplest case all the resistors have equal values and the output is
a usual sum. By using different resistors, the inputs can have
different weights. Compare to the Summing amplifier DAC in
http://electronics-course.com/digital-analog-converter#summing
Differential amplifier
If all resistors are equal, the output voltage is simply V2 – V1
Differential amplifiers are used in signal processing.
In instrumentation systems electronic signals are often transmitted in long
wires as a difference of two voltages. This method can cancel interfering
voltages.
Integrator
Differentiator (derivative amplifier)
Comparator, AD-converters
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Comparator is an OpAmp without negative feedback. There are only two
possible values for the output voltage: either its maximum value or minimum
value. Typical values are 1 or 2 volts below the supply voltage.
If supply voltages are +15 V, the comparator works like this:
 Vout = +14 V if V1 > V2
Vout = -14 V if V2 > V1
The output signal can be considered as a digital signal (binary signal), because it
has only two levels.
 Comparators can e.g. be used for switching the heating ON or OFF
depending on the voltage of a temperature transducer.
 Analog signals can be represented as digital numbers by using Analog-toDigital converters like the Flash ADC in http://electronics-course.com/flash-adc
 Flash ADC is a simple and fast circuit, but it requires a big number of
comparators, if many comparison levels (many different possible numbers)
are needed. There are other ADC principles that need less comparators, but
more digital circuits.
Comparator with Hysteresis
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As mentioned earlier, a comparator can be used for switching some
equipment (e.g. a heating resistor) ON or OFF depending on a voltage (that is
measured e.g. from a temperature transducer).
This simple circuit causes a practical problem. The heating can be switched all
the time between ON and OFF. This can damage the switching component
and causes unnecessary electric interference.
The problem can be solved by using a comparator with positive feedback.
The positive feedback changes the voltage level at the other input of the
comparator. Switching from low to high happens at different voltage than
switching from high to low. This is called a hysteresis.
 E.g. the heating could be swithed ON when temperature drops under +20
C and switched OFF when temperature rises above +21 C.
Electronics assignment 6 is an example of a comparator with hysteresis, which
is based on positive feedback.