EIT Circuits Review

7/29/2019 EIT Circuits Review

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EIT Review

Electrical Circuits DC Circuits

Lecturer: Russ Tatro

Presented by TauBeta Pi

The Engineering Honor Society


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Session Outline

Basic Concepts Basic Laws

Methods of Analysis

Circuit Theorems

Operational Amplifiers

Capacitors and Inductors Summary and Questions


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Basic Concepts

Linear, Lumped parameter systems.

Linear response is proportional to V or I(no higher order terms needed)

Lumped ParameterElectrical effects happen instantaneously in the system.

Low frequency or small size (about 1/10 of the wavelength).


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Basic Concepts


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Basic Concepts - Units

Volt The Potential difference is the energy required to move a unitcharge (the electron) through an element (such as a resistor).

Amp Electric current is the time rate of change of the charge,measured in amperes (A).

A direct Current (dc) is a current that remains constant with time.An alternating current (ac) is a current that varies sinusoidallywithtime.

Ohm the resistance R of an element denotes its ability to resist the

flow of electric current; it is measured in ohms ().


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Basic Concepts - Units

Farad Capacitance is the ratio of the charge on one plate of acapacitor to the voltage difference between the two plates, measured infarads (F).

Henry Inductance is the property whereby an inductor exhibits

opposition to the charge of current flowing through it; measuredinhenrys (H).


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Basic Concepts - Volts

Symbol: V or E (electromotive force)

Circuit usage: V

or v(t) when voltage may vary.

Voltage is a measure of the DIFFERENCE inelectrical potential between two points.

I say again!

Voltage ACROSS two points.


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Basic Concepts - Amps

Symbol: A (Coulomb per second)

Circuit usage: I

or i(t) when current may vary with time.

Amperage is a measure of the current flow past apoint.

I say again!Current THRU a circuit element.


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Basic Concepts - Ohms

Symbol:

Circuit usage: R

Resistance is the capacity of a component tooppose the flow of electrical current.

R = V/I


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Basic Concepts - Farad

Symbol: F

Circuit usage: C for capacitor

Capacitor resists CHANGE in voltage across it.

Passive charge storage by separation of charge.

Electric field energy.


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Basic Concepts - Henrys

Symbol: H

Circuit usage: L for inductor

Inductor resists CHANGE in current thru it.

Passive energy storage by creation of magneticfield.


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Basic Concepts Passive Sign Convention

Use a positive sign when:

Current is the direction of voltage drop.


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Basic Concepts Power

p = (+/-) vi = i2R = v2/R

p = the power in wattsv = the voltage in volts

I = the current in amperes

I.A.W. with Passive Sign Convention

+ (positive) element is absorbing power.- (negative) element is delivering power.


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Basic Concepts - Example

Power delivered/absorbed.


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Basic Concepts

End of Basic Concepts.

Questions?


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Basic LawsCircuit Connections:

Nodes point of connection of two or more

branches.

Branches single element.

Loops any CLOSED path in a circuit.


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Basic Laws Ohms LawOhms Law: v = iR

R = v/i

1

= 1 V/A

Short Circuit when R = 0

Open Circuit when R =


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Basic Laws - Kirchhoffs Laws

KVL: Kirchhoffs Voltage Law

Sum of all voltages around a closed path iszero.

KCL: Kirchhoffs Current Law

Sum of all currents = zero

sum all currents in = sum all currents out

Based on conservation of charge:


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Basic Laws Series/Parallel

......

111

21

++=RRReq

21

21

RR

RRReq

+

=

For Two Resistors in Parallel:

Parallel Resistors:

Series Resistors:Req= R1 + R2 +


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Basic Laws Voltage Divider

Voltage Divider for Series Resistors:

vRR

Rv

21

11

+=

vRR

R

v 21

2

2 +=


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Basic Laws Current Divider

Current Divider for Parallel Resistors:

iRR

Ri

21

21

+=

iRR

R

i21

12 +=


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Basic Laws ExampleKCL/KVL Example


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Basic Laws ExampleCalculating Resistance

Req = ?

Req = ?


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Basic Laws ExampleVoltage Divider


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Basic Laws ExampleCurrent Divider


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Basic Laws

Questions?

f


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Break for 5 minutes.

Chinese Proverb: This too shall pass.

Or as the Kidney stone patient hopes:This too shall pass,

but not soon enough!

M th d f A l i


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Methods of Analysis

Nodal Analysis

assign voltages in branches and find currents.

Mesh Analysis

assign currents in a loop and find voltages.

M th d f A l i


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Methods of Analysis

Node Analysis:

1. Select a reference node.2. Apply KCL to each of the nonreference

nodes.

3. Solve the resulting simultaneous equations.Number of equations = #of nodes - 1

M th d f A l i


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Methods of Analysis

Node Analysis:

Select a reference node.This becomes the zero reference.

All voltages become a rise in voltage fromthis reference node.

M th d f A l i


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Methods of Analysis

Node Analysis:

Apply KCL:There are a number of slightly differentapproaches in applying KCL.

The approach you use MUST be consistent!

IMHO assume voltage drop away from node.This means the current is leaving the node.

IMHO in my humble opinion

M th d f A l i E l


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Methods of Analysis Example

Let us work a node problem.

M th d f A l i


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Methods of Analysis

Supernode: when a voltage source connects tononreferencenodes.

Recall that a ideal voltage source providesWHATEVER current the circuit requires.

Procedure:

1. Short the voltage source. That is: form a singlenode of the ends of the voltage source.

2. Write the constraint equation for the voltages.3. Write the standard node equations for the

supernode.

Methods of Anal sis


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Methods of Analysis

Remember the constraint equation!

v1 2V = v

2

Methods of Analysis


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Methods of Analysis

Mesh Analysis:

A mesh is a loop which does not contain any otherloops within it.

1. Assign mesh currents to the n meshes.

2. Apply KVL to each mesh. Express thevoltages in terms of Ohms law.

3. Solve the resulting n simultaneous equations.



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Let us work a mesh problem.

Methods of Analysis


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Methods of AnalysisSupermesh: when two meshes share a current

source.

Recall that a ideal current source providesWHATEVER voltage the circuit requires.

Procedure:

1. Open the current source. That is form a singlemesh for the two mesh sharing the currentsource.

2. Write the constraint equation for the currents.3. Write the standard mesh equation for the

supermesh.

Methods of Analysis


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Methods of Analysis

Remember to write the constraint equation!i1 6A i2 = 0

Methods of Analysis


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Methods of Analysis

Supermeshor Supernode?

1. Do what the test tells you!

2. Pick the approach with the least equations.

3. Node equations are usually easier.

Methods of Analysis


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Methods of Analysis

End of Methods of Analysis.

Questions?

Circuit Theorems


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Circuit Theorems

1. Superposition

2. Source Transformation

3. Thevenins Theorem4. Nortons Theorem

5. Maximum Power Transfer

Circuit Theorems - Superposition


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Determine the contribution of each independent

source to the variable in question. Then sumthese responses to find the total response.



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1. Turn off all independent sources except one.

Voltage source V = 0 when shorted.

Current source A = 0 when opened.2. Solve the circuit.

3. Repeat until all sources handled.

4. Sum the individual responses to get the totalresponse.

Circuit Theorems S T f


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Source TransformsA source transformation exchanges a voltage

source with a series resistor with a currentsource and a parallel resistor.

Riv ss =

Rvi ss =

Circuit Theorems Example


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Let us work a source transformation problem.



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Let us work a source transformation problem.

Circuit Theorems Th i Th


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Thevenins Theorem

Thevenins Theorem: a linear two-terminal

network can be replaced with an equivalentcircuit of a single voltage source and a seriesresistor.

VTH is the open circuit voltage

RTH is the equivalent resistance of the circuit.

Circuit Theorems Th i Th


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Thevenins Theorem



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Let us work a Thevenin problem.



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Let us work a Thevenin problem.

Circuit Theorems Nortons Theorem


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Norton s Theorem

TH

THN R

V

I =

Nortons Theorem: a linear two-terminal network can bereplaced with an equivalent circuit of a single current sourceand a parallel resistor.

IN is the short circuit current.

RTH is the equivalent resistance of the circuit.



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Let us work a Norton problem.



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p

Circuit Theorems Maximum Power Transfer


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Maximum Power TransferThe maximum power delivered to a load is when

the load resistance equals the Theveninresistance as seen from the load.

THL RR=

Circuit Theorems Maximum Power Transfer


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Maximum Power TransferWhen

Then

THL RR =

TH

THR

Vp 4

2

max =

Circuit Theorems


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End of Circuit Theorems.

Questions?

Break for 5 minutes.


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Nerves and butterflies are fine - they're aphysical sign that you're mentally ready

and eager. You have to get the butterfliesto fly in formation, that's the trick.

~Steve Bull



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p p

OP Amp name derived from this circuits abilityto perform various mathematical operations.

Why us? Another chance to use Node Analysis!

When not? Op Amp with capacitor or inductor?No Laplace skills? Then guess an answer and

move along.



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p p

Ideal Op Amp assumptions:

1. in = ip = zero

2. vn = vp

3. Vout is equal to or less than the input powervoltage.

CCout VV



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Use node analysis to solve the problem. If yourecognize the type and like to memorize:

Inverting Op Amp:

NoninvertingOp Amp:

input

input

feedback

out VR

RV =

inputinput

feedback

out VR

R

V

+=

1

Operational Amplifiers Example


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Let us work an Op Amp problem.



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End of Operational Amplifiers.

Questions?

Capacitors and Inductors


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A Capacitor consists of two conducting platesseparated by an insulator.

Capacitance is the ratio of the charge on one plate

of a capacitor to the voltage difference betweenthe two plates. Capacitance is measured inFarads.



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The voltage across a capacitor cannot changeabruptly.

A capacitor is an open circuit to dc.

dt

dvCi =



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Capacitors add in parallel - CAP

Series Capacitance

...21++=

CCCeq

...111

21

++=

CCCeq



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An Inductor consists of a coil of conducting wire.

Inductance is the property where an inductoropposes change to current flow. Inductance is

measured in Henrys.



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The current thru an inductor cannot changeabruptly.

An inductor is a short circuit to dc.

dt

diLv=



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Inductors add in series.

Parallel Inductance

...21++=

LLLeq

...111

21

++=

LLLeq

Capacitors and Inductors Example


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Overall behavior of an inductor



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Overall behavior of an inductor



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Overall behavior of a capacitor



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End of Capacitors and Inductors.

Questions?

Summary


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Passive Sign

Power: p = vi

Ohms Law v = ir = i2R = V2/R

KCL Sum of currents = zero

KVL Sum of voltage in loop = zero Series/Parallel Elements

Voltage/Current Divider

Summary


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Source Transformation

Thevenin Equivalent

Norton Equivalent

Ideal Op Amp

Capacitor Inductor

Summary


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What we did not cover:

Response of 1st order RC/RL circuits

Unbounded response

Response of 2nd order RLC circuits

Sinusoidal Steady-State analysis 3 Phase AC power

Be sure to study these areas as timepermits.


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Good Luck on the EIT Exam! It is a timed exam. Answer what you

know. Mark what you might know andcome back later. Do not get bogged downon a few questions. Move along!

Remember that it is a multiple choiceexam. Look for hints in the answers.

If totally in doubt Guess by using yourintuition and science.


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EIT Review

Electrical Circuits DC Circuits

Lecturer: Russ Tatro

Presented by TauBeta Pi

The Engineering Honor Society

Documents

EIT Circuits Review