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Last Modified : Tue, 26 Apr 16

ECE403-2016AudioEngineering

  • Instructor: Jont Allen (NetID: jontalle); ECE 403 Websites: 2016, 2013, 2012, 2011,2010, 2009; 2008;Text: Electroacoustics (Buy, TOC, Preface, Preface1, pdf), Beranek & Mellow (2012) is #1;
  • TA: Sarah Robinson (srrobin2@illinois.edu); Office hours: Wednesdays 2-3 PM, 2137 Beckman Institute (NO OFFICE HOURS 3/2); Allen Office hours: 2-3 Friday
  • Calendars: , University; Time: 12:30, Place: 3081-ECEB, etc: Time-Place, Official;
  • Topics: How to analyize a loudspeaker; acoustic wave phenomena; acoustics of rooms and auditoriums; artificial reverberation and sound localization/specialization; Transducer design (2-port networks, loudspeakers, microphones); Topics in digital audio.
  • Assignments: See {$Daily Schedule$} below;Software for Labs: software
  • Lab location: 5072 ECE (you should have card access to this room). Three MU boxes are kept in cabinet on the right hand side of the room when you walk in. NOTE: This lab is OCCUPIED Monday 1-2pm, Tuesday 2-4pm, Wednesday 2-4pm, Friday 2-3pm. ECE 420 students get priority for this lab space.
  • Final Report: Format for final report pdf, LaTeX example: zip
  • This week's schedule

Spring 2016 {$Daily Schedule$}

L W D Date m TOPIC
Part I: 1-port Network Theory (5 Lectures: L1-4,6; 1 Labs: L5)
M 1/18 MLK Day; no class
1 3 T 1/19 90 *Introduction to what you will learn this semester: You will understand how a loudspeaker works by learning the basic theory along with hands-on lab experiments.
*Everyone will work in a small group (ideally 4 students per group).
*Theory will be taught on Monday and Wed, while the Labs will be on Friday.
*Review of ECE-210: Fourier {$\cal F$} and Laplace {$\cal L$} Transforms; Impedance {$Z(s)$} and other complex functions of complex frequency {$s$}
*The Curious Case of {$\log(-1)$},{$j^j$}, {$(-1)^t$} and {$j^t$}
2 R 1/21 90 *Applications of the Laplace transform {$h(t) \leftrightarrow H(s)$} where {$t$} is time and {$s=\sigma+j\omega$} is complex-frequency
*A detailed comparison of the step function {$u(t)$} for each transform: Why {${\cal F} {\tilde u}(t) =\pi \delta(\omega)+1/j\omega$} and {${\cal L}u(t)=1/s$} are not the same.
*Impedance; Analytic functions;
*Detailed example using of a 1{$^{st}$}-order lowpass filter via the Laplace Transform method
*Convolution of vectors {$\leftrightarrow$} product of polynomials: {$a \star b \leftrightarrow A(z)\cdot B(z)$}, where
Time-domain: {$a \equiv [a_0,a_1,a_2, \cdots]^T$}, {$b \equiv [b_0,b_1, \cdots]^T$} Freq-domain: {$A(z)\equiv(a_0+a_1z+a_2z^2 \cdots)$}, {$B(z)\equiv(b_0+b_1z+ \cdots)$}
3 4 T 1/26 90 *Solving differential equations: The characteristic polynomial {$H(s)$}
*Properties of {$H(s)=N(s)/D(s)$}: Roots of {$D(s)$} in LHP.
*Simple example of a 2-port network and its formulation via the transmission matrix (ABCD) method
*Definition of the Inverse Laplace transform {$ {\cal L}^{-1} $}: {$f(t)u(t) = \int_{\sigma_0-j\infty}^{\sigma_0+j\infty} F(s)e^{st}\frac{ds}{2 \pi j}$}
*Homework 1: HWa (Discuss Feb 2, due Tues Feb 9, 2016)
4 R 1/28 30 *Definition of an impedance as an Analytic function {$Z(s)$}
Causal; stable; stable inverse; Conservation of Energy ({$\Re Z \ge 0$})
*Residue expansions and Inverse Laplace Transforms
*Inverse Laplace Transform {${\cal L}^{-1}$} definition: Residue Thm
5 R 1/28 60 Lab 1: 3081 ECEB: Define Student groups
*Learn about hardware; Demo of SysID
6 5 T 2/2 90 *Impedance functions: Minimum phase (MP), positive real (PR), and transfer functions as: all-pole (Strictly-IIR), all-zero (Strictly-FIR) and allpass (AP) functions
*Functions of a complex variable
*Calculus of Analytic functions: {$dH(s)/ds$}, {$\int_C H(s) ds$}.
2-port Linear System Theory (5 lectures: L7,9-12; 2 Labs: L8,L11; Exam I)
7 R 2/4 90 *Lab 2: 5072 ECEB: Setup of hardware; Learn how to make impedance measurements: Circuit Schematic
*Calibration of hardware
8 6 R 2/9 60 *2-Port networks; Definition of T [Pipes (53)] matrix and conversion method between Z and T matrix [Van Valkenburg (65)] (pdf)
*Carlin: 5+1 network postulates (pdf)
*Hunt's 2-port impedance model of the loudspeaker
9 T 2/9 30 *Discuss HWb Lab exercise (due: Feb 16)
10 R 2/11 90 *Lab 3: 5072 ECEB
*Measurement of 2-port RC example of HWb
*Implement Op-Amp circuit and remeasure 2-port of HWb
11 7 T 2/16 90 *Lecture 3081 ECEB:
*2-port networks: Transformer, Gyrator and transmission lines
*Moving coil vs. Balanced armature Loudspeaker
*Hunt 2-port {$Z$} impedance matrix equations: {$E=Z_e\, I|_{V=0}, F = B_0 l\, I|_{V=0}, E = -B_0l\, V|_{I=0}, F=Z_m\, V|_{I=0}$}
*Motional impedance (Hunt Chap. 2)
*The Maxwell Faraday Law of Induction in differential and integral form;Ampere's Law & Ampere's Force Law
*Homework 3: HWc due 3/3;Try HW in LaTeX
*Read: Kim and Allen (2013) pdf
12 R 2/18 90 Lab 4
*First measurement of a loudspeaker input impedance
13 8 R 2/23 60 *Reciprocal and reversible 2-port networks (T and Z forms)
*The Reciprocal calibrationmethod (i.e., cascaded loudspeakers)
*Thevenin & Norton parameters of a loudspeaker: {$P_0(f), U_0(f), Z_0(s)$}
*Forward, backward and reflected traveling waves
*Uniform Transmission lines & reflections at junctions
14 T 2/23 30 Review for Exam I, Lectures 1-12, HW-a,b,c
15 R 2/25 No class: Exam I, 7-9PM Room: 3081 ECEB, Thr Feb 25, 2016
Part II: Acoustic Waves and Horns (5 lectures+Exam II)
16 9 T 3/1 90 *Acoustic transmission lines
*Disc HWc-v1; Due: 3/3
17 R 3/3 90 *Lab 5: 5072 ECEB
*HWc Due Today; *Allen & Robinson out of town today
*HWd: Acoustics & Transmission Lines (due Mar 17)
18 10 T 3/8 90 *Review of Acoustic Basic Acoustics (Pressure and Volume velocity, dB-SPL, etc.)
*Acoustic Intensity, Energy, Power conservation, Parseval's Thm., Bode plots;
*Discuss HWd, due Mar 17
19 R 3/10 90 *Lab 6
F
S
3/11 90 Engineering Open House
20 11 T 3/15 90 *Acoustic wave equation.
*Acoustic horns: Tube acoustics where the per-unit-length impedance {${\cal Z}(x,s)\equiv s \rho_0/A(x)$} and admittance {${\cal Y}(x,s)\equiv s A(x)/\eta_0 P_0$} depend on space {$x$} (Horns);
21 R 3/17 90 *Spherical wave off of a sphere; Radiation (wave) impedance of a sphere
*Spectral Analysis and random variables: Resistor thermal noise (4kT).
*Wave equations and Newton's Principia (July, 1687); d'Alembert solutions in 1 and 3 dimensions of the wave equation
* HWd due; handout solution
12 M
F
3/19 90 Spring Break
22 13 T 3/29 90 *Radiation impedance of a Horn pdf
*Vacuum Tube guitar amplifiers pdf
*Transmission Lines discussion; Monster speaker cable
*Loudspeakers: lumped parameter models, waves on diaphragm
*Throat and Radiation impedance of horn
*HWe due 4/26; Starter files for middle ear simulation (txline.m,gamma.m); Similar to HW3 of ECE537

23 R 3/31 90 Lab 7; {$Z_{mot}$}" Measure Mass-loaded speaker impedance {$Z_e(f)$} & Speaker Faced-Up vs. Faced-Down
24 14 T 4/5 90 *Lecture: How does the middle ear work?
*Review for Exam II: HW-c,d,e
25 R 4/7 90 NO Class; Exam II, Thur @ 7 PM in 3081 ECEB
26 15 T 4/12 90 Review of the Fourier Transform [e.g.: {$\delta(t) \leftrightarrow 1$}, {$\delta(t-T) \leftrightarrow e^{-j\omega T}$}; {$1\leftrightarrow 2\pi\delta(\omega)$}, etc.]
*Notes on the Laplace {$\delta(t)$} function (i.e., {$u(t) \equiv \int_{-\infty}^t\delta(t)dt$} it a function? (pdf)
*Read: Kim and Allen (2013) pdf
Part III: Signal Processing (3 lectures L27,29-30; 2 Labs: L28,31;)
27 R 4/14 90 Lab 8 Reciprocity calibration (2 speakers F2F) & pressure measurement in cavity
*Work on lab report (Example LaTeX)
28 16 T 4/19 90 * Lecture: Middle ear as a delay line
This lecture is out of place, and needs editing for 2017
*Read Rosowski, Carney, Peak (1988) The radiation impedance of the external ear of cat: Measurements and applications (pdf)
29 R 4/21 90 *Lab
30 T 4/26 90 *Lab
31 R 4/28 90 *Lecture by Mary Mazurek, Audio Engineer WFMT Chicago
HWe due
32 Finish Lab Reports
33 18 T 5/3 90 Group presentations
34 W 5/4 90 Group presentations
R 5/5 Reading Day; Final project due by midnight: Please give me both a paper and pdf copy. NO DOC files
- F 5/6 Final Exams begin (Our final is the Lab project paper on loudspeakers)

Textbook

  • The textbook is Electroacoustics: The Analysis of Transduction, and Its Historical Background by Frederick V. Hunt. ISBN 0-88318-401-X.
  • Chapters 2 and 3 of the textbook are available pdf.

Final grade distribution:

  • The final grads were computed as follows: Each homework counted for 5 points. The two exams were each worth 25 points, for a total of 50 points. The final was broken down into 33 topics each worth 30/33 points, for a total of 30 points. This all adds to 100 points. Example: Score = 0.2*mean(HW)+.5*mean(Exams)+Final (within 1 point due to rounding and normalization).

Notes and References

  • Carlin Network postulates pdf
    *Conversion tables for 2-ports (page 1) and ABCD tables from Pipes (pages 2-3): pdf

General interest

Not fully proofed beyond here

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