ENSC 320
Lecture Notes
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0. What is This Course About?
1.
Circuits in the Time Domain
1.1 Linearity, Time
Invariance and Consequences
superposition, sketch solution, derivative and integral properties,
impulses
1.2 Analysis of
Linear Circuits by Differential Equations
[DC&L, Chapter 9]
cap
voltage, inductor current as state variables; coupled first order DEs;
conversion to single DE; conversion of initial conditions at time 0- to time
0+; properties of time domain solution related to roots of characteristic
equation
1.3 Additional
Topics in Differential Equation Solution
impulse
response; decomposition to zero state and zero input responses; effect of right
hand side derivatives; standard parameterization for 2nd order
(damping factor, natural frequency)
1.4 The Convolution
Input-Output Relation [DC&L, Chapter 16]
“flip, slide and integrate”; sketch solutions; properties
1.5 Some Useful
Circuits
lowpass
for averaging; high pass for edge detection; resonance for tone detection;
notch for tone elimination
2.
The
2.1 Plausibility of Integral
Transforms
generalization of matrix transforms, invertibility
2.2 The
one-sided
2.3 Inverting the
inversion
by residues, pole-zero diagrams related to time domain behaviour
2.4 Selected
Properties of the
multiplication/convolution, time differentiation, time shift,
time/frequency scaling
2.5 Solving
Differential Equations by
including initial conditions, zero state and zero input responses
2.6 More Properties
of the
initial and final value theorems, frequency
differentiation, convolution in s, time/frequency scaling, time/frequency
shift, series and parallel decompositions.
3.
The
3.1
circuits in the
s-domain: transfer function, impedance, circuit reduction, many examples
3.2 Circuits With
Non-Zero Initial Conditions
fictitious
sources to represent initial conditions
3.3 Circuits With Switching
use
of fictitious initial condition sources to solve circuits containing switches
4.
Frequency Response [DC&L, Chapter 15]
4.1 Frequency Response by
steady-state response
to cosine input, transfer function on imaginary axis, link to Fourier
transform, elementary frequency responses.
4.2 Frequency Response By Pole-Zero Diagram
sketch
solutions relating pole and zero locations to frequency response, use in
design, lowpass-bandpass transformation
4.3 Parameters Derived From Frequency Response
bandwidths of
lowpass and bandpass filters, group delay
4.4
Bandpass Filters and Resonance
[DC&L, Chapter 17] (pp. 4.4.1-4.4.17) (pp. 4.4.18-4.4.28)
natural
frequency and damping factor; quality factor; passive RLC series and parallel
circuits; active filter resonance; design from application specs; energy and Q;
effect of imperfect L and C.
4.5 Bode Plots of Frequency Response [DC&L,
Section 15.8] – not covered in class,
read it if you need it.
rationale for
Bode plots; asymptotic approximations; Bode plots of resonant systems
5.
Filter Design
5.1 General Approach
general discussion: passband, stopband specs; filter classes; design procedures; implementation structures
5.2 Butterworth Design [DC&L 21.3, 21.4]
selection of filter order, cutoff frequency from attenuation specs; frequency scaling normalized filters
5.3 Chebyshev Design
selection of filter order, ripple from attenuation specs; frequency scaling normalized filters
5.4 Filter Implementation With Passive Components [DC&L 21.5]
normalized Butterworth and Chebyshev I filter structures, frequency scaling and impedance scaling
5.5 Sallen-Key and Related Active Filters
embedded voltage controlled voltage sources; impedance scaling of controlled sources; normalized Sallen and Key second order lowpass structures; scaling to desired specs; multifeedback filter; decomposition of high order filters to quadratic sections.
5.6 State Variable Filters
realization for arbitrary order; state variable quadratic sections
5.7 Lowpass to Highpass/Bandpass Transformation
generation of highpass and bandpass filters from lowpass prototypes
Appendix 5A: About Chebyshev Polynomials
Appendix 5B: Operational Amplifiers (from the extinct course ENSC 222) (sections 5.B.1 to 5.B.4) (sections 5.B.5 to 5.B.7)
6.
Mutual Inductance and Transformers [DC&L Chapter 18]
6.1 Review of Inductors
elementary physics of magnetic fields; inductance; stored energy
6.2 Coupled Coils
Mutual inductance. Coupling coefficient. Analysis of coupled coils. Dot rule. Energy in a pair of coupled coils.
6.3 Coupled Coils as Circuit Elements.
6.4 Ideal Transformers
Unity coupling, infinite permeability. Reflected impedance, reflected source.
6.5 Less-Than-Ideal Transformers
Partial coupling, finite permeability, winding resistance. Models with embedded ideal transformers.
7. Two-Port Networks [DC&L Chapter 19]
7.1 Review of One-Ports
Thevenin,
Norton equivalents; partitioned matrix method of reduction.
7.2 Admittance Parameter Analysis
calculation
of y parameters from circuit diagram; admittances and gain of terminated
two-port
7.3 Impedance Parameter Analysis
calculation
of z parameters from circuit diagram; impedances and gain of terminated
two-port
7.4 Elementary Connection of Two-Ports
parallel,
series and cascade connection of common-ground two-ports. z and y parameters only, motivation for h and
t parameters
7.5 Mixed Variables: the h- and t-Parameter Sets
h-parameters:
relation to z- and y-paramers; input and output impedances, voltage gain for
terminated network; relation to transistor parameters. t-parameters: use in cascade connections;
relation to z- and y-parameters; input, output impedances, voltage gain for
terminated network.
7.6 Reciprocal Networks
definition;
interchange of current source and voltage response; interchange of voltage
source and current response; T-equivalent and Pi-equivalent of reciprocal
networks.
8.
Polyphase Circuits
8.1 Review of AC Power.
Power in time domain.
Power in sinusoidal steady state. Average or real power. Reactive power. Power
factor improvement. Maximum power transfer.
8.2 Measuring AC Quantities
AC ammeter and
voltmeter; wattmeter.
8.3 Three-Phase Systems in Y Format
Motivation for 3
phase. Y format three-phase generation,
transmission, transformation and consumption of power. Four-wire and three-wire transmission. Line-line voltages. Rotating magnetic field. Single line analysis of balanced system.
8.4 Three-Phase Systems in Delta Format
Generation of delta
quantities, relation to Y counterparts.
Y-delta, delta-Y transformations, mixed systems.