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 20 mH 10  15  Z

Relevance of Course EE221, EE211 Circuits Electronics: Amplifiers, Filters, Signal Processors, Sensors, Digital, Computer Electromagnetics: Antennas, Circuit Boards, Remote Sensors, Optics and Lasers Power: Motors, Generators, Transmission lines, Conversion Signals and Systems: Communications, Control, Signal Processing, Computer

Course Outcomes: 1.Perform AC steady-state power analysis on single-phase circuits. 2.Perform AC steady-state power analysis on three-phase circuits. 3.Analyze circuits containing mutual inductance and ideal transformers. 4.Derive transfer functions (variable-frequency response) from circuits containing independent sources, dependent sources, resistors, capacitors, inductors, operational amplifiers, transformers, and mutual inductance elements. 5.Derive two-port parameters from circuits containing impedance elements. 6.Use SPICE to compute circuit voltages, currents, and transfer functions.

Course Outcomes: 7.Describe a solution with functional block diagrams (top- down design approach). 8.Work as a team to formulate and solve an engineering problem. 9.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  Download PDF on “Getting Started” and read sections on Introduction through Matrices and Arrays (Pages 1-1 to 2-19). MATLAB Tutorials:  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)

Web Sites of Interest B 2 SPICE Demos and Free Lite Version 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 : Maximum Value, Amplitude, or Magnitude Radian Frequency in Radian/second Frequency in cycles/second or Hertz (Hz) Phase.2.4 

Trigonometric Identities Radian to degree conversion multiply by 180/  Degree to radian conversion multiply by  /180

Complex Numbers Each point in the complex number plane can be represented in a Cartesian or polar format.

Complex Arithmetic Addition: Multiplication and Division: Simple conversions:

Euler’s Formula Show: A series expansion ….

Complex Forcing Function Consider a sinusoidal forcing function given as a complex function:  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:

Mechanical Analogy Electrical: Energy transfers between electric field (capacitor) and magnetic field (inductor) Mechanical: Energy transfers between gravitational field and elasticity of spring. 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: Examples …

Phasors Examples Find the equivalent impedances Z for the circuits below at a frequency of 60 Hz: Show Z = 8.1+j*5.5 = 9.83   20 mH 10  15 .1 mF Z