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ELEC-E5650 Electroacoustics ELEC-E5650ELECElectroacoustics-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Lecture 2: SteadyRaimundo -GonzalezState Analysis / Dynamic Analogies Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering Raimundo2 2GonzalezFebruary 2018 Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering March 7, 2019 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 1 Aalto, Signal Processing & Acoustics ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 LectureRaimundo Gonzalez 2: Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 I. Steady State Analysis ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 2 Aalto, Signal Processing & Acoustics Steady state sinusoidal response When designing Electroacoustics systems we are usually more interestedELEC in the-E5650 steady state behavior of the system. This will ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 lead into Raimundomostly Gonzalez working in the frequency domain. Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 3 Phasors to represent sinusoidal signals ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez In audio, we are interested in signals which are Department of Signal Processing and Acoustics Aalto University School sinusoidal, meaning the its frequency components of Electrical Engineering always have a magnitude and phase. 22 February 2018 x(t) = !"#$%"#& = !"#$%'& where is a phasor ! = ! "#& which solely contains the amplitude and phase. ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 4 Complex Number From physics and signal processing we know that it is easier to work with complex numbers for solutions to systemsELEC with- E5650sinusoidal behavior. ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 5 A time domain attempt would require solving…. ELECRC circuit-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 with our solution being… But we are not interested in the transients response, the homogenous solution, therefore we can try an easier approach. ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 6 Our solution RC circuit – steady state solution Solving ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 Steady state solution Our governing equation magnitude phase ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 7 Phasor Domain – Voltage-Current Relation The imaginary basis j equals 90 degree shiFt counterclockwise in the complex plane which will aFFect the phase oF the output signal. ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 ResistorsRaimundo Gonzalez Inductor Capacitor Department of Signal Processing and Acoustics Aalto University School ! V = Iof RElectrical Engineering V = I jωL V = I 22 February 2018 jωC ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 8 RLC Circuit 2nd order form !"#(%) ( !#(%) #(%) 1 + + = - /01234 !% ) !% )* ) . ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Electrical Impedance Raimundo Gonzalez -. 1 Department of Signal Processing and Acoustics Aalto University School = ( + + /0) = 78 of Electrical Engineering # /0* 22 February 2018 Natural Frequency Damping coefficient 1 ( * Governing equation 00 = )* : = 1 !#(%) 2 ) - % = (# t + 6 # % !% + ) . * !% And if… Forced Frequency where " 234 : < 1 0! = 00 1 − : -. % = -. 1 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 9 ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 LectureRaimundo Gonzalez 2: Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 II. Dynamic Analogies ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 10 Aalto, Signal Processing & Acoustics Transducers ELEC-E5650 Rectilinear Lecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 ElectroacousticsElectronics Mechanics Acoustics Raimundo Gonzalez Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering Differential Differential 22 February 201Algebra8 Analytic tools: Equations Equations To work with all three we need a common denominator. Hopefully one that makes things easier! ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 11 Method: Dynamic Analogies • Use the simplicityELECof-E5650electronic circuit analysis to model problems in ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 mechanicalRaimundoand Gonzalezacoustics domains as Department of Signal Processing and Acoustics Aalto University School well as moreof ElectricalcomplexEngineering domain-coupled systems. 22 February 2018 • We can do this because the equations of motion for each domain are equivalent. From “Dynamical Analogies”, Harry F. Olson (1943) ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 12 Benefits ELEC-E5650 • Model domain-coupled systems under single paradigm ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez • Math: AlgebraicDepartment of Signal Processingtools and Acousticsavailable Aalto University Schoolfor electronics can be applied to systems of other domainsof Electrical Engineering. 22 February 2018 • Analysis: the physical behavior of each element in the system is conserved. • Boundaries of electric elements are clearly defined. • We can apply well-known representation methods (Circuit Diagrams). • Easier visualization. ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 13 Physical and Mathematical Meaning of Electronic Quantities and Circuit Elements ElementsELEC-E5650 • ElectroacousticsLectureResistance 1: Overview, Electroacoustics-type introduction & Circuit Elements pt1 • RaimundoCapacitance Gonzalez-type Department of Signal Processing and Acoustics Aalto University School • ofInductance Electrical Engineering-type • 2Transformation2 February 2018 -type • Gyration-type Quantities • Potential across the circuit element ("!) • Flow through the circuit element ($#) • Magnitude of the circuit element (&̃) Figure adapted from [2] ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 14 Resistance Property of an element which dissipates energy. ELEC-E5650 Electrical Mechanical Acoustical Resistance (RE ) Resistance (RM ) Resistance (RA ) ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez Frictional Viscosity DepartmentElement of Signal Processing… and AcousticsResistor Aalto University School of Electrical Engineering Surface/Element property of air 22 February 2018 $ ' * Defined by… ! = ! = ! = " % & ( ) + (1 Representation… (2 Figures from [1] ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 15 Inductance, Mass, Inertance Property of an element which opposes change in flow. ELEC-E5650 Inductance (L ) Mass (MM ) Inertance (MA ) ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Raimundo Gonzalez Uncompressed DepartmentElement of Signal Processing… and AcousticsInductor Aalto University School Mass of Electrical Engineering volume of air 22 February 2018 $% $* $- Defined by… ! = # ' = ( + = ( $& ) $& , $& ' Representation… * Figures from [1] ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 16 Electrical Capacitance, Compliance, Acoustic Capacitance Property of an element which opposes change in potential. ELEC-E5650 Electrical Mechanical Acoustic Compliance (C ) Capacitance (CA ) ElectroacousticsLecture 1: Overview, Electroacoustics Capacitanceintroduction & Circuit Elements (CE pt1 ) M Raimundo Gonzalez Compressive DepartmentElement of Signal Processing… and AcousticsCapacitor Aalto University School Spring of Electrical Engineering property of air 22 February 2018 1 1 1 Defined by… ! = & ' () * = & , () - = & / () $% $+ $. ,1 Representation… ,2 Figures from [1] ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 17 Mechanical and Acoustic Sources (ideal) MechanicELEC- E5650Sources Acoustic Sources ElectroacousticsLecture
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