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Engineering Math and Circuit Analysis Enrichment Activity 2004 NASA SHARP Program California State University, Los Angeles Presented by: Dr. Tabrizi Reported by: Travis Antoniono
This presentation was given to the NASA Sharp students, as part of an orientation on Engineering Math and Circuit Analysis. It was given in the Engineering building. All the students were present and the presentation started at 9:30 A.M.
The presentation was presented by Dr. Tabrizi in lecture form and covered a vast amount of topics. The presentation touched on many of the basic components of four introductory Electrical Engineering courses. The topics that were introduced to the students were as followed:
Engineering Math
1) Important Engineering Signals & Functions: Unit-Step, Impulse, Sinusoidal 2) Complex Number Algebra 3) Introduction to Linear Algebra: Vector & Matrix 4) Introduction to Boolean Algebra: Introduction, Logic Functions
Introduction to Circuit Analysis 1) Important Electric Circuit Quantities, Definitions & Units 2) Active & Passive Elements 3) Branch, Node, Loop, Reference Node, Grounding, Open/ Short Circuit 4) Kirchhoff's Voltage Law (KVL) & Kirchhoff's Current Law (KCL) 5) Ohm's Law, Resistors, and DC Circuits 6) Karnaugh-Map, Logic Gates & Digital Logic Circuits (Combinational or memory less circuits)
Engineering Math When using Engineering Math there are a few basic ideas to apply. One should know that Engineering Math is practiced when one investigates systematically. Within any Engineering Math problem there is a system in which an input is taken in and an outcome comes out. In any problem one should first analyze and then design. One can test the system through simulation. Engineering Math embraces mathematical models, which are the validations of ideas.
1) Important Engineering Signals & Functions: Unit-Step, Impulse, Sinusoidal
Unit -Step
The unit-step is the integral of an impulse function from negative infinity up through time t. Impulse
· The function is zero whenever t is not zero · When t is zero, the function is unity
Sinusoidal A sinusoidal function is like a sine function because it can be produced by shifting, stretching or compressing the sine function. It transmits our waves via electromagnetic signals.
2) Complex Number Algebra Complex numbers are used to analyze real numbers. The complex domain is Z= a+jb. In the complex domain a and b are real numbers and j= (-1)1/2 Within complex numbers there are polar and rectangular forms of numbers which are interchangeable. In rectangular z=a+jb= r<angle. In polar form r = (a2+b2)1/2
3) Introduction to Linear Algebra: Vector & Matrix Linear algebra is the study of linear sets of equations and their transformation properties. Vectors are quantities that have magnitude and associated direction. A matrix is composed of columns and rows. One may use a matrix to solve for unknowns of and equation. One can find a determinant and an inverse to a matrix.
Vectors
Matrix
4) Introduction to Boolean Algebra: Introduction, Logic Functions
In Boolean algebra there are only two elements, 0 and 1. One sets up a Boolean algebra problem in a truth table.
Introduction to Circuit Analysis 1) Important Electric Circuit Quantities, Definitions & Units
Digital circuits can take on only a finite number of states.
Analog circuits have voltages and other quantities that vary in a continuous manner. Analog is the DC resistive circuit.
2) Active & Passive Elements Passive elements are positive and absorb power. Active elements are negative and give off power.
3) Branch, Node, Loop, Reference Node, Grounding, Open/ Short Circuit Branch- Wiring that runs from a service panel or sub-panel to outlets. Branch circuits are protected by fuses or breakers at the panel.
Node - A point of connection between multiple links.
Loop - Fastener consisting of a metal ring for lining a small hole to permit the attachment of cords or lines
Reference Node - The node that is the immediate parent of all nodes.
Grounding - Establishing a connection between an electrical circuit or equipment and earth ground or electrical ground.
Open Circuit - An electrical circuit that is not "made". Contacts, switches or similar devices are open and prevent the floe of current.
Closed Circuit - An electrical circuit that is "made". Contacts, switches or similar devices are closed and allow the floe of current.
4) Kirchhoff's Voltage Law (KVL) & Kirchhoff's Current Law (KCL) Kirchhoff’s Voltage Law (KVL)- Around a closed loop, the total voltage should be zero.
Kirchhoff's Current Law (KCL): As a direct consequence of the conservation of charge, namely charge can neither be created nor destroyed, the node, being of negligible physical size, holds no charge. For instance, referring to Figure 1.6, the sum of, I1, I2, and I3 must equal zero.
Figure 1.6: Kirchhoff's current law
5) Ohm's Law, Resistors, and DC Circuits
Ohm’s Law- V
= I x R V = Voltage I = Current R = Resistance
In this algebraic expression, voltage (E) is equal to current (I) multiplied by resistance (R). Using algebra techniques, we can manipulate this equation into two variations, solving for I and for R, respectively:
Resistors Resistors limit current. In a typical application, a resistor is connected in series with an LED:
Enough current flows to make the LED light up, but not so much that the LED is damaged. DC Circuits DC is electricity that directly flows through a conductor, such as a metal wire.
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