Transcript Overview of Circuits 2

Circuits 2 Overview
January 11, 2005
Harding University
Jonathan White
General Overview of
Class
• 3 tests and a comprehensive final
– The first test should be easy if you remember last
semester.
• Homework for each chapter
• Small quizzes to reinforce new concepts or if I think
you are sleeping
• Lab every Thursday except tomorrow
– Some labs will be for presentations
– Some may be needed for test review
• Final projects:
– Team build of an FM transmitters
– Team presentation and report on any circuits topic
• After the first 3 chapters, the material covered is
more difficult due to the math involved.
– Also, some memorization of formulas will be required.
Chapter 9 – Sinusoids and Phasors
• Impedance: ratio of phasor voltage to
phasor current.
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Z = V/I -- similar to Ohm’s Law, R=V/I
Impedances are combined exactly like resistors.
For resistors, Z = R
For inductors, Z = jwL
For capacitors, Z = 1/(jwC)
– To solve AC circuits, convert every element to an
impedance value and treat like a resistor.
• We will practice some phasor mathematics,
and how to use your calculator to solve.
Chapter 9 - Problems
Simplify and write in
rectangular and polar form:
 24075  160  30   60  j80
• Find I0 in the circuit
below:
 67  j84  2032 
 5  j 6    2  j8 
 3  j 4  5  j    4  j 6 
Obtain Zin for the circuit below:
Chapter 10 – AC Steady-State Analysis Techniques
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Nodal analysis
Mesh analysis
Superposition
Source transformation
Thevenin/Norton equivalents
• Should be a good review of last semester.
Make sure you can do nodal analysis.
Ch. 10 Problems:
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Use nodal analysis to find vo in
the circuit below:
Find the Thevenin equivalent from a to b
Find the mesh currents if v1 = 10cos(4t) V and v2 = 20cos(4t – 30o) V
Ch. 11 – AC Power Analysis
• Power in a circuit is still p = v*I
– However, the power in an AC circuit
changes continually. We use average
power.
• PAVG = ½ VmImcos(θv – θi)
• Resistive loads absorb power all the
time. Reactive loads don’t.
• RMS values of currents/voltages
• Power factors
Ch. 11 Problems:
Find the average power
absorbed by each element if
vs = 8cos(2t – 40o) V
Find the RMS value of the waveform below:
Ch. 12 – Three Phase
Circuits
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Used in high power applications
Used in power generation plants
Used in alternators/generators
Typically consists of 3 voltage sources
spread out by 120o in phase
– Wye or Delta Connections
• Table 12.1 (page 518) summarizes
about everything about 3 Phase
circuits.
Ch.12 Problems
For the - circuit below, calculate the phase and line currents:
Ch. 13 – Magnetically Coupled Circuits
• Also known as transformers
• You’ll be spending about 2 months on
this in physics
• The number of windings in the coils
affect the produced voltage and
current.
– This is the summary for this chapter.
Ch. 13 Problems
Find the average power delivered to the 4 Ohm resistor:
Ch. 14 – Frequency Response and Filters
• Variation in behavior of a circuit with a change in
signal frequency.
• Bode plots
– Only a little
• Resonance
– We’ve done this before in lab
• Quality factor and bandwidth
• Passive filters:
– Lowpass/HighPass/Bandpass/Bandstop
• Active filters with Op Amps
• This is a very long, but very important chapter.
– It is also very understandable and useful.
Ch. 14 - Problems
Calculate the resonant frequency, the quality factor, and the bandwidth for the
circuit below:
Chs. 15 & 16 – Laplace Transforms
• A way of solving sinusoidal and nonsinusoidal problems
• Lets use do algebra instead of calculus
– Make the RLC problems just a few steps instead
of 15.
• Works by transferring the whole problem
from the time domain into the frequency
domain, solving the problem algebraically,
and then doing an inverse Laplace
transform at the end to get back to the time
domain.
– Laplace makes solving complex problems much
easier
• Covered in the differential equations class.
Chs. 15 & 16 problems
Find the Laplace Transform of:
f(t) = te-2tu(t – 1)
Find the inverse Laplace transform of:
1
2
F ( s)  
s s 1
Find v0 using the Laplace Method:
Chs. 17 & 18 – Fourier Transforms
• These are difficult, and we will only cover
them if we have time at the end of class
– They are covered in the differential equations
class and in control systems.
• Fourier transforms are used to express nonsinusoidal sources as an infinite sum of
sinusoids.
– We can then apply the methods we’ve used in
AC analysis.
• Page 764 has a great picture of what the
Fourier transform does.