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 Laplace Transform [DC&L, Chapter 13]

            2.1  Plausibility of Integral Transforms

generalization of matrix transforms, invertibility

            2.2  The Laplace Transform

one-sided Laplace transform, region of convergence, examples: exponentials, trigonometric functions, monomials, impulses

            2.3  Inverting the Laplace Transform 

                        inversion by residues, pole-zero diagrams related to time domain behaviour

            2.4  Selected Properties of the Laplace Transform

multiplication/convolution, time differentiation, time shift, time/frequency scaling

            2.5  Solving Differential Equations by Laplace Transform

including initial conditions, zero state and zero input responses

            2.6  More Properties of the Laplace Transform

initial and final value theorems, frequency differentiation, convolution in s, time/frequency scaling, time/frequency shift, series and parallel decompositions. 

3.  The Laplace Transform in Circuit Analysis

            3.1  Laplace Analysis of Circuits at Rest

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 Laplace Transform

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.

Laplace analysis of magnetically coupled circuits.

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.