Objectives for Lecture #1
- Derive the one-sided Laplace transform for a function of
time
- Apply standard Laplace transform properties to
compute the transform of a time-varying function
Objectives for Lecture #2
- Understand how the frequency domain is useful to solving
ordinary differential equations
- Convert nth-order ordinary differential equations into the
frequency domain
- Define the impulse function and establish its Laplace
transform
- Apply the initial and final value theorems to determine
initial and final values of a time-varying function
- Apply time periodicity theorem to derive the Laplace
transform of a periodic time function
- Recognize standard Laplace transform pairs
- Explain the concept of partial fraction expansion and how
it relates to the Inverse Laplace transform
- Define a strictly proper rational polynomial and show how
one may be derived by long division
Objectives for Lecture #3
- Define frequency-domain poles and zeros
- Explain the concept of partial fraction expansion and how
it relates to the Inverse Laplace transform
- Define a strictly proper rational polynomial and show how
one may be derived by long division
- Identify the proper partial fraction expansion for
rational polynomials with simple poles and repeated simple poles
- Calculate the partial fraction expansion coefficients for
terms with simple and repeated simple poles
- Inverse Laplace transform a rational polynomial that has
been partial fraction expanded
Objectives for Lecture #4
- Identify the proper partial fraction expansion for
rational polynomials with non-repeated complex poles
- Calculate the partial fraction expansion coefficients for
terms with complex poles
- Inverse Laplace transform a partial-fraction-expanded
rational polynomial containing complex poles
Objectives for Lecture #5
- Derive the s-domain representation of resistors,
inductors, and capacitors, including initial conditions
- Analyze circuits with zero initial conditions and an
arbitrary input to derive the complete response (natural + steady-state
response) using Laplace transform techniques
- Analyze circuits with initial conditions and an arbitrary
input to derive the complete response (forced + initial-condition response)
- Use circuit analysis techniques to solve for time-domain
inductor and capacitor initial conditions
Objectives for Lecture #6
- Apply standard circuit analysis techniques (nodal, mesh,
superposition, source transform) to derive the complete circuit response
using Laplace transform techniques
- Identify the natural, forced, steady-state, and initial
condition responses
Objectives for Lecture #7
- Define the transfer function for a Linear-Time-Invariant (LTI)
circuit
- Derive transfer functions for circuits using circuit
analysis techniques
- Show how a transfer function may be used to find the
forced response
Objectives for Lecture #8
- Explain what constitutes a 2nd-order circuit
- Derive the solutions for unforced series and parallel RLC
2nd-order circuits using the Laplace transform
- Define the damping factor, damping frequency and undamped
natural frequency for 2nd-order circuits
- Define the conditions for over-damped, under-damped, and
critically-damped responses
- Solve for the step response of a 2nd-order series RLC
circuit
- Solve for parameters in a series RLC circuit that will
result in an over-damped, under-damped, or critically-damped step response
Objectives for Lecture #9
- Solve for the step response of a 2nd-order parallel RLC
circuit and for general 2nd-order RLC circuits
- Solve for parameters in a parallel RLC circuit that will
result in an over-damped, under-damped, or critically-damped step response
Objectives for Lecture #10
- Explain the physical meaning of the unit impulse response
and how it connects with the transfer function
- Derive the impulse response expression from an s-domain
transfer function
- Derive the convolution integral from the transfer function
definition and Laplace transform properties
- Explain when numerical convolution might be required or
preferred
- Evaluate the convolution integral using mathematical
integration, determining the correct integration limits and assigning the
proper time interval for the solution
Objectives for Lecture #11
- Evaluate the convolution integral using graphical
techniques
Objectives for Lecture #12
- Derive the sinusoidal steady-state response from a
transfer function and an assumed sinusoidal input
- Define frequency response and explain what information a
frequency response plot conveys
- Explain the purpose of logarithmic frequency scales in
frequency response plots
- Define absolute gain and gain in decibels and explain the
advantage of decibels
- Derive the magnitude and phase expressions from a transfer
function
Objectives for Lecture #13
- Define a Bode plot
- Manipulate a transfer function to identify poles, zeros,
and gain factor
- Show how to factor a transfer function into terms to
generate the Bode plot (gain factor + real poles and zeros)
- Derive how the Bode plot can be assembled from individual
terms of the factored transfer function
- Derive the Bode plot characteristics for real poles and
zeros
Objectives for Lecture #14
- Derive a Bode plot by combining the effects of multiple
terms
- Derive the Bode plot characteristics for non-repeated
complex poles and zeros
- Show the impact of the damping factor on straight-line
approximations for complex poles and zeros
- Derive transfer functions from straight-line Bode plot
approximations
Objectives for Lecture #15
- Define resonance and determine the conditions necessary
for resonance in a 2nd-order series or parallel circuit
- Explain the use of circuits that exhibit resonance
- Define the characteristics of a circuit in resonance in
terms of power factor, impedance/admittance, and current/voltage
- Manipulate the transfer function to compute the resonant
frequency, bandwidth, cutoff frequencies, and Q
Objectives for Lecture #16
- Explain the frequency response characteristics of ideal
low-pass, high-pass, band-pass, and band-stop filters and compute the output
of an ideal filter given its frequency response and an assumed input
- Distinguish between passive and active filters
- Explain the characteristics of non-ideal filters and
define the terminology passband, transition band, and stopband
- Derive the transfer functions for simple 1st-order passive
filters
- Recognize standard passive filter transfer functions
- Analyze a circuit or transfer function to determine its
filter type
Objectives for Lecture #17
- Derive the transfer functions for simple 2nd-order passive
filters
- Recognize standard passive filter transfer functions
- Analyze a circuit or transfer function to determine its
filter type
- Choose circuit parameters to implement a desired passive
filter transfer function
Objectives for Lecture #18
- Explain the advantages and disadvantages of active filters
- Derive active filter transfer functions using ideal op-amp
analysis
- Derive wide-band band-pass/band-stop active filter design
equations through analysis of cascaded low-pass and high-pass circuits
- Choose circuit parameters to implement a desired passive
filter transfer function
Objectives for Lecture #19
- Explain the purpose of impedance and frequency scaling
- Derive the effect of impedance and frequency scaling on
the cut-off frequency, bandwidth, and Q
- Design filters using prototype circuits and combined
impedance and frequency scaling
Objectives for Lecture #20
- Determine the period and fundamental frequency for a
periodic signal
- Explain the purpose of the trigonometric Fourier series
and derive the equivalent magnitude/angle form
- Distinguish between the fundamental and harmonics
- Derive expressions for the Fourier series coefficients
- Derive the Fourier series for a simple periodic waveform
Objectives for Lecture #21
- Derive the Fourier series for more complex periodic
waveforms
- Use the Fourier series to make circuit calculations
Objectives for Lecture #22
- Identify even, odd, and half-wave symmetry in periodic
waveforms
- Utilize symmetry to simplify the determination of Fourier
series
- Use the Fourier series to make circuit calculations
Objectives for Lecture #24
- Solve for the real, reactive, apparent, and complex power
of a circuit and determine the power factor (leading or lagging)
- Use the power triangle to relate the power components of a
given circuit
- Explain the purpose of performing power factor correction
- Determine the reactive power and capacitance required to
obtain a specified power factor
Objectives for Lecture #25
- Define three-phase wye and delta connections
- Define a balanced three-phase voltage source and a
balanced three-phase load impedance
- Define line-to-neutral, line-to-line, and phase
voltages and delta, line, and phase currents
- Determine the phasor diagram representation for a given
balanced set
- Define phase sequence and given a phase quantity,
calculate the remaining terms of a desired balanced phase sequence
- Determine the transformation between a balanced Y
impedance connection and a balanced delta impedance connection
- Define a neutral wire and explain its purpose
- Analyze a balanced Y-Y circuit with a zero-impedance
neutral
- Analyze a balanced Y-Y circuit with a non-zero-impedance
neutral
Objectives for Lecture #26
- Define a neutral wire and explain its purpose
- Analyze a balanced Y-Y circuit with a zero-impedance
neutral
- Analyze a balanced Y-Y circuit with a non-zero-impedance
neutral
Objectives for Lecture #27
- Analyze a 3-phase circuit with a balanced Y-source and
delta-load, delta-source and delta load, and delta-source and Y-load
- Derive relationships between line and phase quantities for
a Y-source and a delta-load
Objectives for Lecture #28
- Define the purpose of a per-phase equivalent circuit and
establish the steps necessary to convert a general three-phase circuit into
its per-phase equivalent
- Analyze a balanced three-phase circuit using its per-phase
equivalent circuit and general circuit analysis techniques
- Derive line and delta quantities from per-phase analysis
results
Objectives for Lecture #29
- Show that the instantaneous power of a balanced
three-phase source is constant and explain why this is desirable
- Establish expressions for 3-phase real, reactive,
apparent, and complex power in terms of phase and line quantities
- Compute the various types of three-phase circuit power
- Given a transmission system and information about load
power and voltage, calculate the required sending voltage and transmission
efficiency
Objectives for Lecture #30
- Given a balanced source, line impedance, and load
impedance, calculate the load power and transmission efficiency using
per-phase equivalent circuit analysis
Objectives for Lecture #31
- Define magnetic field, flux density, flux, field
intensity, Ampere's law, permeability, reluctance and mmf
- Derive a magnetic equivalent circuit given the parameters
of a core and winding
- Explain the advantages of a magnetic equivalent circuit
containing mmf sources and reluctances
- Make calculations for a simple magnetic equivalent circuit
Objectives for Lecture #32
- Explain the construction of a single-phase transformer and
define the terminology primary and secondary
- Define the assumptions for an ideal single-phase
transformer
- Derive the voltage and current relationships for an ideal
single-phase transformer
- Derive how voltages, currents, and impedances are
reflected across an ideal transformer
- Solve for current, voltage and power on the source and
load sides of a transformer using reflected quantities
- Calculate the efficiency of a circuit using step-up and
step-down ideal transformers
- Explain why transformers are used in power distribution,
circuit isolation, and impedance matching
Objectives for Lecture #33
- Define flux linkage, self inductance, leakage inductance,
magnetizing inductance, and mutual inductance
- Define Faraday's law and relate it to flux linkages
- Derive a magnetic equivalent circuit of two coupled coils,
each with leakage flux
- Derive the T-equivalent circuit for a real transformer
including winding resistance, leakage reactance, magnetizing reactance, and
core loss
- Use the open-circuit and short-circuit tests to
calculate transformer parameters
- Discuss aiding and opposing coupling
Objectives for Lecture #35
- Define the concepts of torque, speed, and induced voltages
in rotating machines
- Define the Lorentz force Law and correctly apply the
right-hand rule
- Explain the elements of a rotating machine, including
stator, stator windings, rotor, and rotor windings
Objectives for Lecture #36
- Define the attributes of a symmetrically-wound AC machine
stator
- Explain how a balanced-set of stator current results in a
rotating magnetic field -- illustrate the strength of the resultant field
and the speed and direction of rotation
Objectives for Lecture #37
- Illustrate how a 4,6,8,...-pole machine stator is
constructed and derive the speed of the resulting rotating field
- Explain the construction of a 3-phase synchronous machine
- Explain the operation of slip rings and brushes
- Explain the operation of synchronous motors and generators
in terms of interacting magnetic fields on the stator and rotor
- Explain power flow and efficiency in motors and generators
- Derive the expression for the induced torque produced by
the interaction of two rotating magnetic fields
Objectives for Lecture #38
- Derive the per-phase equivalent circuit for a synchronous
machine
- Derive the expression for the induced voltage in the
stator of a 3-phase synchronous machine
- Define the rotor angle, synchronous reactance, and
excitation voltage
Objectives for Lecture #39
- Explain the flow of real power through a synchronous
machine for motor and generator operation
- Derive an expression for the mechanical power given a
loss-less machine
- Work steady-state problems using the synchronous machine
equivalent circuit and steady-state power/torque relationships
- Define the phasor diagram for generator and motor
operation
Objectives for Lecture #40
- Define naval shipboard power distribution terminology:
ring bus, switchboard, circuit breaker, ungrounded distribution, delta
distribution, split plant, vital and non-vital loads, load shedding
- Introduce the concept of Integrated Power Systems and
the use of electric drive for propulsion and the integration of new high
energy weapons