Electric Circuit and Component

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

Electric Circuit and Component

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