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8/12/2019 Electric Circuit and Component
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Electric Circuits andComponents
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Introduction review of the fundamentals of basic electrical components and discrete circuitanalysis techniques
important in understanding and designing all elements in a mechatronic system
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Voltage and Current
Voltage (electromotive force, emf) measure of the electric field's potential
imposing an electrical field that imparts energy by making electrons move production of electrical current
"across" variable between two points in the electric field
in order to measure a voltage
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Voltage and CurrentCurrent
time rate of flow of positive charge
ampere (A), coulombs (C)
"through" variable that moves through the field
direct current (DC) when voltage and current in a circuit are constant
alternating current (AC) when they vary with time, usually sinusoidally
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Electrical Circuit
closed loop consisting of several conductors connecting electrical components voltage source: provides energy to the circuit, e.g. power supply, battery,generator
load: a network of elements that may dissipate or store electrical energy
ground: reference point in the circuit where the voltage is assumed to be zero
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Basic Electrical Elements three basic passive electrical components
passive elements require no additional power supply
defined by the voltage-current relationship
two types of ideal energy sources
the ideal sources contain no internal resistance, inductance, capacitance
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Resistor
dissipative element that converts electrical energy into heat Ohm's law ( V = I R ) defines the voltage-current characteristic of an ideal resistor
real resistors: nonlinear due to temperature effects; failure due to the limitation inthe power dissipation
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Resistor wire resistance
r : resistivity, specific resistance of the material
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Resistor
resistors packaged in various forms DIP and SIP: multiple resistors
in a package
axial-lead resistor's value and tolerance
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ResistorExample: resistance color codes
Red-Red-Orange-Gold
Yellow-Violet-Brown-Gold
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Resistor
Variable resistor resistance values controlled by a mechanical screw, knob, or linear slide
potentiometer (pot): the most common type
trim pot: a pot in a circuit to adjust the resistance in the circuit
A typical single-turnpotentiometer
axial-lead resistors, trim pot & rotary pot, DIP
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Capacitor passive element that stores energy in the form of an electric field
the field is the result of a separation of electric charge
dielectric material: insulator that increases capacitance as a result of permanent orinduced electric dipoles in the material
DC does not flow through a capacitor
charges are displaced from one side to the other side thru the conducting plate,establishing the electric field
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Capacitor
ceramic capacitors (pF range)mylar capacitors
electrolytic capacitors (polarized)
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Capacitor voltage-current relationship
voltage across a capacitor is proportional to the integral of the displacement current
C : capacitance measured in farads (F)
capacitance: property of the dielectric material and the plate geometry andseparation, typically 1 pF ~ 1000 mF
In case of parallel plate model, C = e A/d (e: permittivity)
capacitor's value: the first two digits are the value and the third is the power of 10multiplied times pF
e.g. 102: 10 10 2 pF
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Capacitor
voltage cannot change instantaneously
used for timing purposes in electricalcircuits, e.g. RC circuit
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Inductor passive energy storage element that stores energy in the form of a magnetic field
characteristics based on Faraday's law of induction: V (t ) = d l /d t
l : total magnetic flux thru the coil windings due to the current
ideal inductor: l = L I
L : inductance measured in henry (H = Wb/A)
inductance: typically from 1 mH to 100 mH
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Inductor
voltage-current relationshipvoltage across an inductor is proportional to the rate of change of the current thru the
inductor
the current through an inductor cannot change instantaneously
important to consider in motors, relays, solenoids, some power supplies, and high-frequency circuits
e.g. large inductance of electric motor
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Kirchhoff's Laws essential for the analysis of circuits
KVL
sum of voltages around a closed loop is 0
How to apply KVL to a circuit
1. assume a current direction on each branch of the circuit
2. assign the appropriate polarity to the voltage across eachpassive element (assumed voltage drops must be consistentwith the assumed current directions)
3. starting at any point in the cir cuit, form the sum of thevoltages across each element
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Kirchhoff's Laws
Example of KVL find the current in the circuit
1. assume the current direction
2. assign the voltage drop polarity
3. starting at A, form
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Kirchhoff's LawsKCL
sum of the currents flowing into a closed surface or node is 0
currents leaving a node or surface are assigned a negative value
What if the calculated result for a current or voltage is negative?
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Kirchhoff's Laws
Series resistance circuit the current through each of the components is the same
resistors in series add to the equivalent resistance
check!
Applying KVL
- V S + V R 1 + V R 2 = 0
I = V S / (R 1 + R 2)
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Kirchhoff's LawsVoltage divider
a circuit containing two resistors in series
in general, for N resistors connected in series
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Kirchhoff's Laws
Parallel resistance circuit each resistor experiences the same voltage
I 1 = V S / R 1 and I 2 = V S / R 2
Applying KCL
I I 1 I 2 = 0
I = V S (1/R 1 + 1/ R 2)
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Kirchhoff's LawsCurrent divider
a circuit containing two resistors in parallel
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Kirchhoff's Laws
Example find I out and V out
1. combine resistors
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Kirchhoff's LawsExample
find I out and V out
2. Apply KVL
Note!
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Sources and Meters
Voltage source ideal voltage source has zero output resistance and can supply infinite current
real voltage source model: ideal voltage source in series with output impedance
Vout Vs
output impedance is very small usually neglected for most applications
output impedance can be important when driving a circuit with small resistance
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Sources and MetersCurrent source
ideal current source has infinite output resistance and can supply infinite voltage
real current source model: ideal current source in parallel with an outputimpedance
the output impedance is very large minimize the current division effect
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Sources and Meters
Meters ideal ammeter has zero input resistance and no voltage drop across it
real ammeter model: ideal ammeter in series with an input impedance
the input impedance is very small
ideal voltmeter has infinite input resistance and draws no current
real voltmeter model: ideal voltmeter in parallel with an output impedance
the input impedance is very large, usually 1~10 M W
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Sources and MetersExample
effects of source and meter output and input impedance on makingmeasurements in a circuit
What if the source and meter were ideal?
In reality
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Sources and Meters
Example effects of source and meter output and input impedance on makingmeasurements in a circuit
voltage measured by the actual meter
V m = V s when Z in = and Z out = 0
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Sources and MetersExample
effects of source and meter output and input impedance on makingmeasurements in a circuit
e.g. If R 1 = R 2 = 1 k W
If Z in = 1 M W and Z out = 50 W
If V s = 10 V
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AC Circuit Analysis
When linear circuits are excited by alternating current (AC) signals of a givenfrequency, the current through and voltage across every element in the circuit are AC signals of the same frequency
sinusoidal AC voltage V (t )
w: radian frequency
f : phase angle leading or lagging waveform
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AC Circuit AnalysisDC offset
vertical shift of the signal from the reference sinusoid
Example
AC voltage V (t ) = 5.00 sin( t + 1) V
- amplitude = ?
- radian frequency = ?
- frequency = ?
- phase angle = ?
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AC Circuit Analysis
Principal reasons for using AC power instead of DC power more efficient to transmit over long distances
easy to generate with rotating machinery (e.g., an electric generator)
easy to use to drive rotating machinery (e.g., an AC electric motor)
provides a fixed frequency signal that can be used for timing purposes andsynchronization
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AC Circuit AnalysisPhasor analysis
phasor (vector): vector representation of the complex exponential
using complex numbers to represent sinusodial signals based on Euler's formula
for the voltage across and current through each element in the steady state
- same frequency as input
- constant amplitude
- maybe different phase from the input
Here V m is the amplitude and f is the phase angle ofthe signal
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AC Circuit Analysis
Phasor analysis math relations for manipulating phasors
phasor magnitude
phasor angle
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AC Circuit Analysis extension of Ohm's law to the AC circuit analysis of resistor, capacitor, inductor
Z : impedance
voltage will lead the current by 90
for DC, w = 0 Z = ? for AC at very high frequency, Z = ?
voltage will lag the current by 90
for DC, w = 0 Z = ?
for AC at very high frequency, Z = ?
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AC Circuit Analysis
Example find the steady state current I through the capacitor
phasor form of the voltage source
V in = 5 V = (0 + 5j) V
phasor form of the capacitor impedance
Z C = -j / wC = -1666.67j W = 1666.67 W
phasor form of the inductor impedance
Z L = jwL = 1500j W = 1500 W
combining all the impedances
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AC Circuit AnalysisExample
find the steady state current I through the capacitor
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Power in Electrical Circuitsinterpretation of power
consumed or generated by an electric element infinitesimal work (d W ) done when an infinitesimal charge (d q) moves through an electricfield resulting in a change in potential represented by a voltage V
power is the rate of work done
P is negative if the element dissipates or stores energy, or positive if
instantaneous power in a resistive circuit
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Power in Electrical Circuits for AC signals, the power changes continuously over a period of the AC waveform
average power over a period is a good measure
q: difference between the voltage and current phase angles
using the rms (root-mean-square) values of the voltage and current
for AC networks including inductance and capacitance
P avg = I rms V rms cos q = I 2rms |Z | cos q = (V 2rms / |Z |) cos q
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Transformer
device used to change the relative amplitudes of voltage and current in an ACcircuit
composed of primary and secondary windings whose magnetic fluxes are linkedby a ferromagnetic core
relationship between the primary and secondary voltages
f : magnetic flux linked between the two coils
step-up transformer, step-down transformer, isolation transformer
power is equal if we neglect losses due to winding resistance and magnetic effects
Note: only AC is transformed
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SummaryElectric circuits and components
Basic electrical elements: resistor, capacitor, inductor
Kirchhoff's laws
Sources and meters
AC circuit analysis
Power in electrical circuits
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Preview
Semiconductor electronics Junction diode
Transistor
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LabLab 1
Power supply
Multimeter
Measuring the resistance of resistors
Verification of Ohm's law
Measuring for circuits with a serial or parallel connection of resistors
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Question:
Proper car jump start?
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Grounding