Circuits II EE221 Instructor Kevin D Donohue Course Introduction Website Resources and Phasor Review Course Policies Procedures Introduce Instructor and Teaching Assistant Review Syllabus Expectations and Workload Team Project Relevance of Course Course goal Develop problem solving skills useful for designing electrical systems involving information power Circuits A connection of components with electrical properties typically arranged to process information or transfer power Entropy and Enthalpy Circuits in your head Circuit elements used to describe neural membrane 15 20 mH Z 10 http www mindcreators com NeuronModel htm Relevance of Course Electromagneti cs Antennas Circuit Boards Remote Sensors Optics and Lasers Electronics Amplifiers Filters Signal Processors Sensors Digital Computer EE221 EE211 Circuits Power Motors Generators Transmission lines Conversion Signals and Systems Communications Control Signal Processing Computer Course Outcomes 1 2 3 4 5 6 Perform AC steady state power analysis on singlephase circuits Perform AC steady state power analysis on threephase circuits Analyze circuits containing mutual inductance and ideal transformers Derive transfer functions variable frequency response from circuits containing independent sources dependent sources resistors capacitors inductors operational amplifiers transformers and mutual inductance elements Derive two port parameters from circuits containing impedance elements Use SPICE to compute circuit voltages currents and transfer functions Course Outcomes 7 8 9 Describe a solution with functional block diagrams top down design approach Work as a team to formulate and solve an engineering problem Use computer programs such as MATLAB and SPICE for optimizing design parameters and verify design performance Web Sites of Interest Matlab Resources Manuel on Matlab Basics http www mathworks com access helpdesk help pdf doc matlab getstart pdf Download PDF on Getting Started and read sections on Introduction through Matrices and Arrays Pages 1 1 to 2 19 MATLAB Tutorials http www mathworks com academia student center tutorials index html A graphic description to step through basic exercises in Matlab Should have Matlab open while going through this so you can try the examples Consider it homework this week to go through the interactive tutorial about 2 hours Nothing to hand in for it Octave a Free Matlab Clone http www gnu org software octave Web Sites of Interest B2SPICE Demos and Free Lite Version http www beigebag com demos htm Students can download a free Lite Version on their own PCs The Lite version has some functional limits but saved files that can be opened with university s full version Within the B2SPICE program itself are simple tutorial under the help menu to get student started with using the basic function of the program Phasor Review What is a complex number and why is it used to solve electrical engineering problems What is a phasor Who introduced it to the profession Why is it popular The Sinusoidal Function Terms for describing sinusoids x t X m sin t X m sin 2 ft Maximum Value Amplitude or Magnitude Frequency in cycles second or Hertz Hz Radian Frequency in Radian second 1 1 0 8 0 8 sin 2 t 4 0 6 0 4 0 4 0 2 0 2 0 2 sin 2 t 5 0 2 0 4 0 6 0 0 2 0 4 0 6 0 8 0 8 1 1 1 2566 0 2566 0 7434 1 7434 2 7434 Radians 3 7434 4 7434 2 0 6 Amplitude Amplitude Phase 0 4 0 2 0 0 2 0 4 0 6 0 8 Seconds 1 1 2 1 4 1 6 Trigonometric Identities cos t sin t 2 cos t cos t or 180 sin t cos t 2 sin t sin t or 180 Radian to degree conversion sin sin cos cos sin multiply by 180 Degree to radian conversion multiply by 180 cos cos cos sin sin X m sin t X m cos sin t X m sin cos t 1 B A cos t B sin t A B cos t tan A 2 2 Complex Numbers Each point in the complex number plane can be represented in a Cartesian or polar format IM a jb r exp j r r a2 b2 a r b RE 1 b tan a a r cos b r sin Complex Arithmetic Addition a jb c jd a c j b d Multiplication and Division r v rv r r v v Simple conversions j 1 90 1 j j 1 180 Euler s Formula Show exp j cos j sin A series expansion j 2 j 3 4 j 5 exp j 1 1 2 3 4 5 2 4 6 cos 1 2 4 6 3 5 7 sin 1 3 5 7 Complex Forcing Function Consider a sinusoidal forcing function given as a complex function X m exp j t X m cos t jX m sin t Based on the concept of orthogonality it can be shown that for a linear system the real part of the forcing function only affects the real part of the response and the imaginary part of the forcing function only affect the imaginary part of the response For a linear circuit excited by a sinusoidal function the steady state response everywhere has the same frequency Only the magnitude and phase of the response can change A useful factorization X m exp j t X m exp j exp j t Mechanical Analogy Electrical Energy transfers between electric field capacitor and magnetic field inductor Mechanical Energy transfers between gravitational field and elasticity of spring http www youtube com watch v T7fRGXc9SBI Note Every part of the spring moves at the same frequency only the phase and magnitude of the oscillation changes The same is true for a linear RLC circuit Phasors Sinusoidal function notation for linear circuits can be more efficient if the exp j t is dropped leaving the magnitude and phase quantities maintained via phasor notation Tim e Dom ain x t A cos t x t A sin t Examples Frequency Dom ain X A X A 90 Phasors Examples Find the equivalent impedances Z for the circuits below at a frequency of 60 Hz 15 20 mH Z 10 Show Z 8 1 j 5 5 9 83 34 33 1 mF
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