Circuits IIEE221

Instructor: Kevin D. Donohue

Course Introduction, Website Resources, and Phasor Review

Course Policies Procedures

Introduce Instructor and Teaching Assistant

Review SyllabusExpectations and WorkloadTeam 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

http://www.mindcreators.com/NeuronModel.htm

Circuit elements used to describe neural membrane

20 mH

10

15

Z

Relevance of Course

EE221, EE211Circuits

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 InterestMatlab ResourcesManuel on Matlab Basicshttp://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

B2SPICEDemos and Free Lite Versionhttp://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?

-1.2566 -0.2566 0.7434 1.7434 2.7434 3.7434 4.7434

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Radians

Am

plitu

de

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Seconds

Am

plitu

de

The Sinusoidal Function

Terms for describing sinusoids:

)2sin()sin()( ftXtXtx mmMaximum Value,Amplitude, orMagnitude

Radian Frequencyin Radian/second

Frequencyin cycles/second orHertz (Hz)

Phase

)2sin( t

5

22sin

t

.2.4

Trigonometric Identities

2sin)cos(

tt

2cos)sin(

tt

)180or (cos)cos( tt )180or (sin)sin( tt

)sin()cos()cos()sin()sin(

)sin()sin()cos()cos()cos(

A

BtBAtBtA 122 tan cos) sin() cos(

) cos()sin( ) sin()cos( sin tXtXtX mmm

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.

RE

IM

a

b

r

rjrjba )exp(

)sin(

)cos(

tan 1

22

rb

ra

a

b

bar

Complex Arithmetic

Addition:)()()()( dbjcajdcjba

Multiplication and Division:

)())(( rvvr )(

v

r

v

r

Simple conversions: 1801- ,

1 ,901 jj

j

Euler’s Formula

Show:A series expansion ….

)sin()cos()exp( jj

!5!4!3!2!1

1)exp(5432 jjj

j

!6!4!2

1)cos(642

!7!5!3!1

)sin(753

Complex Forcing FunctionConsider a sinusoidal forcing function given as a complex function:

)sin()cos())(exp( tjXtXtjX mmm 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:

)exp()exp())(exp( tjjXtjX mm

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.

PhasorsSinusoidal function notation for linear circuits can be more efficient if the exp(-jt) is dropped, leaving the magnitude and phase quantities maintained via phasor notation:

Time Domain Frequency Domain )cos()( tAtx AX̂ )sin()( tAtx 90ˆ AX

Examples …

Phasors ExamplesFind the equivalent impedances Z for the circuits below at a frequency of 60 Hz:

Show Z = 8.1+j*5.5 = 9.8334.33

20 mH

10

15

.1 mFZ