Freedom University Tutorial Videos

Video Galleries from the University of New South Wales

doctorj — Sun, 09 Oct 2011 15:53:38 +0000

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VIDEO GALLERIES: List of Video Playlist from the University of New South Wales (UNSW)

Here are video galleries from UNSW’s You’ll find various collections of video courses from that program. Many of the videos are about one hour or so in length.

Below is a list of video galleries from the University of New South Wales:

Below is a sample of their lesson from their course, Programming For Designers:

COMP1400 - Week 1, Lecture 2

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Title: COMP1400 - Week 1, Lecture 2

Title: COMP1400 - Week 3, Lecture 2

Title: COMP1400 - Week 3, Lecture 1

Title: COMP1400 Week 5, Lecture 1

Title: COMP1400 Week 5, Lecture 2

Title: COMP1400 Week 6, Lecture 1

Title: COMP1400 Week 6, Lecture 2

Title: COMP1400 Week 7, Lecture 2

Title: COMP1400 - Week 8, Lecture 1

Title: COMP1400 - Week 8, Lecture 2

Title: COMP1400 Week 9, Lecture 2

Title: COMP1400 Week 9, Lecture 1

Title: COMP1400 Week 10, Lecture 2

Title: COMP1400 Week 10, Lecture 1

Title: COMP1400 Week 11, Lecture 1

Title: COMP1400 Week 7, Lecture 1

Title: COMP1400 - Week 2, Lecture 1

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University of New South Wales Issues Call for Tax Research Fellows (taxprof.typepad.com)
U.S. Biotech Firm Synedgen and University of New South Wales Partner to Improve Bone Regeneration (prweb.com)
International Research Candidate Scholarships at the University of New South Wales, Sydney, Australia (warpweftandway.wordpress.com)

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A Collected Set of Playlists of MIT Videos

doctorj — Mon, 19 Sep 2011 23:02:21 +0000

Playlists of MIT Videos Collected from YouTube

The last posting gave you video playlists from the Khan Academy. Here’s another one that will increase your higher level of thinking and challenge in pursuing these highly technical topics.

You’re probably aware of Massachusetts Institute of Technology’s (MIT’s) Open Courseware. You’ll find here various collections of video courses from that famous institution. Many of these videos are about one hour or less in length and can be found on Youtube and at MIT’s website: http://ocw.mit.edu. But I’ve collected the sets of videos for your convenience and are found here and shown below: Playlists of MIT videos.

Also, I’m testing some new software with these video lists so occasionally it gets buggy and you get errors. Just keep refreshing the browser page and it should work after a few times of doing this.

I know you’ll find these hundred of videos useful in your studies of interests.

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Video Playlists from the Khan Academy

doctorj — Sun, 18 Sep 2011 05:14:00 +0000

Video Playlists from Khan Academy

One of the most valuable resources is from the Khan Academy.
For your convenience, I used their playlist from YouTube and are
found in the right.

Some of the topics is what I plan to do but since Salmon Khan did
them, this will save me time to develop other courses.
When I have time, I plan to do some of these topics as well.

I know you will find them useful and this is what I envision
on the future of education about ten years ago!

Playlists from Khan Academy

Algebra

Calculus

Differential Equations

Here are sample videos from the Khan Academy

Salman Khan talk at TED 2011 (from ted.com)

12 3 4 5... 14 15 next »

Title: Salman Khan talk at TED 2011 (from ted.com)

Title: SOPA and PIPA

Title: Simple Equations

Title: Khan Academy on the Gates Notes

Title: Basic Addition

Title: Krebs / Citric Acid Cycle

Title: The Khan Academy

Title: Introduction to the atom

Title: Balancing Chemical Equations

Title: DNA

Title: Algebra: Linear Equations 4

Title: Basic Trigonometry

Title: Introduction to Limits

Title: Liar Truthteller Brain Teaser

Title: Calculus: Derivatives 1

Title: Introduction to Evolution and Natural Selection

Title: Equations 2

Title: Adding and subtracting fractions

Title: Algebra: Linear Equations 1

Title: What is a differential equation

12 3 4 5... 14 15 next »

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Semiconductor Tutorial: Drift and Diffusion Currents

doctorj — Tue, 13 Sep 2011 23:07:34 +0000

In a semiconductor, there are holes and electrons being created. These charged holes and electrons are also known as carriers. The movement of these carriers in the semiconductor is due to two processes.

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Drift Current Density

One process concerns drift movement results from an electric field. The other is known as diffusion resulting from varying concentrations or gradient concentrations.

In an n-type material there are a large number of electrons. The electrons will react to an external electric field applied in one direction. This field produces a force on the negatively-charged electrons in the opposite direction. The electrons acquires a drift velocity given as

(Equation 1)

where

with units of cm^2/V-s.

The mobility is a measure how well an electron travels through a semiconductor material. The above minus sign means that the velocity is opposite direction to the applied electric field.

The electron drift creates a drift current density [latex] \frac{A}{m^2}[/latex] given as

(Equation 2)

where n is the electron concentration (#/cm^3) and e is the magnitude of the electronic charge.

For a p-type material having a large number of holes, there are similar relationships. The drift velocity of holes is

(Equation 3)

where is the hold mobility. The positive sign means that the velocity is in the same direction as the applied field.

The hold drift creates a drift current density given as

(Equation 4)

The total drift current contains both electrons and hole resulting in the total drift current density, J given by

(Equation 5)

where

is the conductivity and where is the resistivity of the semiconductor.

The above relationships show that controlling the conductivity of a semiconductor can be controlled by selective doping. This approach allows us to build a variety of electronic devices currently available.

We also note that Equations 1 and 3 show that the carrier drift velocity is a linear function of the applied electric field. Increasing the electric field will increase the drift velocity of the carriers but there will be a point when carrier velocities will no longer increase. That is, the velocities reach a saturation point known as drift velocity saturation.

Also, mobility values are functions of carrier concentrations. In this case, as the carrier concentrations increase, then mobilities will decrease which affects the conductivity or resistivity of the semiconductor material.

Diffusion Current Density

The diffusion process occurs when particles flow from regions of high concentrations to regions of low concentrations. When electrons and holes flow in a semiconductor, they go in random directions as a result of interactions with crystal atoms of the semiconductor lattice structure. Average carrier speeds are also affected by the temperature. The net result however, is that the flow of carriers move away from high-concentration region to one that has lower concentration.

Now, the diffusion current density due to the electron diffusion is given as

where e is the magnitude of the electron charge, dn/dx is the gradient of the electron concentration with respect to the distance x, is the electron diffusion coefficient.

Similarly, the diffusion current density to the hole diffusion is given as

where dp/dx is the gradient of the hole concentration, Dp is the hole diffusion coefficient.

Einstein relation shows the relationship between drift and diffusion currents. In this case, the mobilities to describe drift currents and diffusion coefficients to describe diffusion currents are not independent to each other. Einstein relation is given as

at room temperature.

We note that the total current density is the sumo of the drift and diffusion current densities. Usually, one of the two processes dominate the other.

Excess Carriers

The above discussion assumes the semiconductor crystal is in thermal equilibrium. A crystal will not be in equilibrium when a voltage is applied or a net current exists.

As valence electrons acquire enough energy to break the covalent bonds, they become free electrons and interact with photons of high0enrgy incident in the semiconductor. This interaction produces an electron and a hole pair resulting in excess electrons and excess holes. The creation of excess holes and electrons produces a non-equibrium condition of increasing concentrations of holes and electrons.

This phenomenon cannot increase indefinitely such that a free electron will recombine with a hole known as electron-hole recombination. The recombination process and excess concentration will reach a steady-state value.

The time when excess carriers exists before recombination is called the excess carrier lifetime. Solar cells and photodiodes involve excess carrier mechanisms.

Below is a collection of videos on semiconductors and will serve as a good review on semiconductor theory.

Semiconductors Theory 1 Segment 2A - Doped Silicon Crystal

Title: Semiconductors Theory 1 Segment 2A - Doped Silicon Crystal

Title: Description of the Silicon Atom

Title: Current Flow and the Electric Circuit, Theory 2D Segment 2B

Title: Semiconductor Theory 7 Segment 5 - J-FET Schematic Symbols

Title: Semiconductor Electronics Module 1 Theory Lesson 1 Segment 8

Title: Semiconductor Electronics Theory Lesson 1 Segment 1 - Semiconductor Atoms

Title: Theory 2D Opening - Current Flow and the Electric Circuit

Title: Semiconductor Electronics Module 1 Theory Lesson 1 Segment 7

Title: Bipolar Transistors - Semiconductor Devices Theory 5 Segment 1

Title: Introduction to Semiconductor Materials (2)

Microelectronics Tutorial: Extrinsic Semiconductors Concentrations of electrons and hole are small found in intrinsic...
Microelectronics Tutorial: Semiconductor Materials and Properties Electronic devices such as transistors and diodes are fabricated using...

Microelectronics Tutorial: Extrinsic Semiconductors

doctorj — Tue, 13 Sep 2011 05:05:14 +0000

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Concentrations of electrons and hole are small found in intrinsic semiconductors. As a result, the currents are small as well. We can increase these concentrations by adding some impurities to the semiconductor crystal. We’d like to have the impurity atom have a different number of valence electron than the semiconductor crystal.

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Also, we want the impurity atom replace one of the semiconductor atoms. For silicon which has four valence electrons, then an impurity atom like phosphorus with five valence electrons will replace a silicon atom in the silicon crystal. The extra or fifth valence electron is loose bound to the phosphorus atom such that at room temperature, the electron has enough energy to break the bond. These electrons are free to move about and contribute to the current in the semiconductor crystal. Using phosphorus as a the dopant material forms an n-type semiconductor material (for negatively charged electrons). Also, phosphorus is known as a donor impurity since it donates an extra electron.

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To get an p-type material (for positively charged holes), we’ll use either boron or aluminum which has three valence electrons. Its three valence electrons are used to form three of the four covalent bonds nearest to the silicon atoms. This leaves one bond position open easily filled by adjacent silicon valence electrons creating a hole and contributing to hole current.

The video below will help further explain the concept of doping as briefly discussed above.

Doping of semiconductors

This video describes the mechanism of current conduction inside of a p-type respectively n-type semiconductor. Using aluminum as a dopant for a silicon crystal creates holes inside of the crystal structure. Additional conduction electrons are provide…

Semiconductor materials containing impurity atoms are called extrinsic semiconductors. They are also known as doped semiconductors. By controlling this doping process, the concentrations will determine conductivity and currents associated with the semiconductor material.

At thermal equilibrium, we have a relationship between the electron and hole concentration

(Equation 1)

where

is the thermal equilibrium of free electrons

is the thermal equilibrium of hole electrons

and is the intrinsic carrier concentration.

Suppose the donor concentration is much larger than the intrinsic concentration . then

(Equation 2)

Using Equation 2, yield the hole concentration as

(Equation 3)

Similarly, if the acceptor concentration is much larger than the intrinsic concentration . then

(Equation 4)

Using Equation 4, yield the hole concentration as

(Equation 5)

The above development assumes the concentrations are at room temperature.

For an n-type semiconductor, the majority carriers are the electrons since they outnumber the holes and are referred as minority carriers. In p-type semiconductor, the holes are the majority carriers while the electrons are the minority carrier.

Microelectronics Tutorial: Semiconductor Materials and Properties Electronic devices such as transistors and diodes are fabricated using...

Microelectronics Tutorial: Semiconductor Materials and Properties

doctorj — Mon, 12 Sep 2011 23:57:36 +0000

Electronic devices such as transistors and diodes are fabricated using semiconductor materials. Here, we briefly look at the properties and characteristics of semiconductors. We’ll introduce some terminology associated with semiconductors.

Below is a short video on the crystal structure of silicon, carbon, and germanium

_____________________________________________________

The crystallization of silicon, carbon (in the modification diamond) and germanium is treated at this video. The procedure of hybridization of orbitals leads to the formation of face-centered cubic crystal structures. Computer animations using the ball-and-stick model as well as the calotte model (also called space filling model) demonstrate the construction of the crystal lattice.

______________________________________________________

Below is a short video on the PN junction of a semiconductor video.

_____________________________________________________

PN junction of a semiconductor diode

The working principle of a diode is treated at the 3D animated part of the video. The voltage-current characteristic of a silicon diode is recorded in forward and reverse direction at the second part. See how the depletion layer is created between a …

______________________________________________________

Hopefully, the above video provided a basic understanding of a few semiconductor material properties. As you heard there are two types of charged carriers (electrons and holes) that exist in a semiconductor. In addition, there are two mechanisms that generate currents in a semiconductor.

The most common semiconductor found in integrated circuits is silicon. There are other semiconductor material to provide high speed and optical detection or generation such as gallium arsenide.

Intrinsic Semiconductors

In atoms, there are positively charged protons and neutral neutrons found in the nucleus. You’ll also find negatively charged electrons orbiting the nucleus. Electrons in the outermost shell or orbit are valence electrons. In fact, the periodic table is organized according to the number of valence electrons.

Below is a humorous video on the periodic table.

______________________________________________________

Elements by Tom Lehrer

***********************Its a great honor to have our little cartoon featured on Wired Magazine. (www.wired.com) As the number 5 top video about science. We would be pleased if you saw the other 9 videos featured. www.wired.com **************** A Usel…

The Periodic Table of Irrational Nonsense by Crispian Jago

See crispian-jago.blogspot.com/2010/07/periodic-table-of-irra…

Author:dullhunk

______________________________________________________

Germanium and silicon are usually known as elemental semiconductors while gallium arsenide is known as a compound semiconductor.

A silicon atom has four valence electrons. When they silicon atoms are close to each other, they form a crystal tetrahedral structure and lattice configuration. Each silicon atom has four nearest neighbors. The shared valence electrons between atoms form covalent bonds. These valence electrons in silicon atoms are available on the outer edge of the silicon crystal so larger single crystal structures are possible.

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At low temperatures however, the valence silicon electrons will not move for a small voltage since it is not enough energy to overcome the covalent bonds. In this case at low temperatures, the silicon material acts an insulator.

On the other hand, at higher temperatures, electrons can break hold from the covalent bond to move away from its original position and gain some minimum energy, called the bandgap energy, . Exceeding the bandgap energy means the valence electrons are now in the conduction band and are called free electrons. An electric field will attract these free electrons to form a current moving through the conduction band in the silicon crystal.

For semiconductors , the bandgap energy is about 1 electron volt while for insulators it ranges from 3-6 electron volt.

When an electron breaks its covalent bond and moves away from its original position, an empty state or “hole” results. More covalent bonds will be broken with increasing temperature resulting in an increase of positive “holes”. Also, the magnitude of the positive charge is the same as an electron charge.

The concentration of holes and electrons influence the magnitude of the current. When the electron and hole concentrations are equal (given as , then the crystal structure is intrinsic. The intrinsic concentration is given as

where B is a constant related to a particular semiconductor,

is the bandgap energy in eV,

T is the Kelvin temperature (K),

k is Boltzmann’s constant in eV/K,

and e is the exponential function.

The parameters B and deal with semiconductor materials and are not strong functions of temperature in the case of silicon (Si), gallium arsenide (GeAs) and germanium (Ge).

The intrinsic carrier concentration frequently appears in current-voltage equations.

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Signal Processing Tutorial: The Basic Sinusoids

doctorj — Mon, 12 Sep 2011 03:48:10 +0000

One common class of signals are sinusoids…that is they are either cosines or sines. The video shown below briefly reviews the definition of a sine, cosine, and tangent.

Basic Trigonometry Formula - SOH-CAH-TOA

Title: Basic Trigonometry Formula - SOH-CAH-TOA

Mathematically, the cosine signal is generally given as

(Equation 1)

where is the angular frequency (radians/sec), f is the frequency (cycles/sec or Hertz) t is the independent variable time, and is the phase shift, and A is the amplitude. With f as the frequency, then T=1/f is the time period of the sinusoid.

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The interactive graph below allows you to experiment with these parameters. The default function shown below is a combination of a sine and cosine function. It can be shown that the combination of sin(x)+cos(x) can be reduced to Equation 1. In fact, sin(x)+cos(x) can be viewed what is known as a rectangular form of asin(x)+bcos(x) or as a time function of

(Equation 2)

Equation 1 can be viewed as the polar representation of a sinusoid since the function has amplitude and phase while Equation 2 is the rectagular representation of a general sinusoid with a an b as the components of the function x(t). You can use conversion formulas similar used to going from one representation to another found in complex numbers.

In this case, the conversion formulas are

Again, using the interactive flash graph below, try changing the frequency, amplitude and phase to see how these parameters change.

[swf src="http://www.freedomuniversity.tv/resources/SimpleGraphExample/SimpleGraphExample.swf" width=671 height=452 ]

One reason why sinusoids are important has to do with physical systems since many can be modeled mathematically as sine or cosine functions of time. For example, we can hear audio signals, including sinusoidal ones. Tones from instruments have different pitches as a result of the different frequencies they produce.

With today’s technology, you can use a computer with an analog-to-digital converter (A-to-D) and a microphone, we can record digitally produced by an instrument. The mi9crophone is a transducer which converts mechanical sound into an electrical signal. This in turn takes the electrical signal coverts into a sequence of numbers that can now be stored in the computer. A typical plot is similar to the ones shown above.

The bottom line is that common physical systems produce signals whose graphical representations look like sinusoidal signals. You’ll learn that the sinusoidal functions (sine and cosine functions) are actually solutions to differential equations derived from the laws of physics to describe physical phenomena such as a tuning fork.

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Signal Processing Tutorial: Introduction to Signal Processing

doctorj — Fri, 09 Sep 2011 23:04:00 +0000

An Introduction to Signal Processing

Signal processing involves signals and systems.

Today, you have multimedia computers, entertainment systems and digital communications systems and you can be sure that signal processing functions are involved.

When it comes to the meaning of signals, you may be thinking of a signal as carrying information. Usually, that information is describing a physical quantity (e.g. temperature, pressure, or sound waves) that can be managed, stored, or delivered by physical processes.

Examples of signals from physical processes include speech, audio , video or image signals, radar, biomedical, and seismic are just a few of these physical pro

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cesses.

In speech signal that is produced as an acoustic signal, but it can be converted to an electrical signal by a microphone (a transducer), or it can be converted to a string of numbers found in digital audio recording.

Now, let’s turn our attention from signals to systems.

A system can mean many things to a number of different people and is therefore subject to a number of interpretations. For example, a “system” may refer to a large system such as the “Department of Defense”. In terms of signal processing, a system is one in which we can operate, change, record or transmit signals. A simple example would be an audio compact disk (CD), storing and representing a musical signal transcribed as a sequence of digital numbers. Now, a CD player (a system) converts the numbers stored on the disc to an acoustic signal we can hear.

Our use of the term system in signal processing will mean that an input signal will be operated on by a system to produce a new signal at the output of the system.

We will use mathematics to provide more precise statement of signals and systems. Mathematics will be used to show how signals and systems will interact.

How to Represent Signals Mathematically

As discussed earlier, signals carry information. That is, signals are variations represented or encoded patterns of information. They serve to measure or probe real-world physical systems, such as medical technology or wireless communications.

Signals can vary in time, space or both. We’ll initially focus on time since that it is natural to us. One example of a signal is speech which comes from changing pattern of air pressure in the vocal tract. The resulting pattern variation in time is what we call a time waveform.

The above photo shows various time waveforms. The vertical axis is usually the physical quantity such as air pressure and microphone voltage. The horizontal axis represents time. The signals in the above photo show one-dimensional continuous-time signal. Time is normally an independent variable since the signal is a function of time.

Thus, s(t) is a signal function s with an independent time variable t. So at each instant in time we can associate a value s.

Most signals originate as continuous-time signals. However, to increase the flexibility in processing signals, we can use a computer to help process the signal. Unfortunately, storing a continuous-time signal will require an infinite amount of computer memory. As a result, to make it more practical, a continuous-time signal needs to be converted into a discrete-time signal by sampling the signal function at isolated equally spaced points in time. This conversion process will result in a sequence of numbers that is characterized as a function of an index variable n.

Mathematically, where n is an integer and is the sampling period. The reciprocal of is known as the sampling frequency.

The resulting discrete signal from sampling becomes more manageable for the computer or signal-processing hardware.

Normally, we see signals as a function of time. However, there are other signals that do not vary in time. For example, a photo or image does not change in time. Thus, an image can be mathematically described as a function of two spatial variables (e.g. x and y). Here, the variables x and y are two independent variables. We can denote the picture p as a function p(x,y).

The bottom line here is that signals are mathematical functions. Think of functions as abstract symbols of functions. Thus, a speech signal is s(t) or a digitized (or sampled) photo p([m,n]. In this signal processing tutorial we can see that this is a first step to use mathematics to systematically describe signals and systems.

Below are some topics of signal processing videos that I’ve produced so far. More structured articles and videos will follow as well.

Matlab Tutorial - Amplitude Modulation

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Title: Matlab Tutorial - Amplitude Modulation

Title: Matlab Examples: Fourier Series of a Square Wave

Title: z-Transform Tutorial: z-Transform and inverse z-Transform Examples & Functions

Title: Signal Processing Tutorial: Sampling/Anti-Aliasing or the Nyquist Sampling Theorem

Title: Matlab Examples - Generating AM Using The Nyquist Sampling Theorem

Title: Matlab Examples - Amplitude Demodulation (synchronous detection)

Title: Signal Processing Tutorial: Nyquist Sampling Theorem and Anti-Aliasing (Part 1)

Title: Matlab Examples: Amplitude Modulation and Envelope Detection

Title: Inverse Laplace Transform Examples and Tutorial - Part 1

Title: Signal Processing Tutorial: Discrete-Time Convolution Examples (Inverse z-Transform)

Title: Overview and Introduction to the z-Transform (Polynomial & Rational Functions)

Title: Matlab Examples - Review of Discrete Convolution using Matlab

Title: Signal Processing Tutorial: Discrete-Time Convolution Examples (Part 1 - Intro)

Title: Inverse Laplace Transform Examples - Partial Fraction Expansion - Part 2

Title: Signal Processing Tutorial: Convolution Integral

Title: Signal Processing Tutorial: Continuous-Time Convolution Example (Inverse Laplace)

Title: Digital Signal Processing (DSP) Tutorial: Euler's Formula - Part 1

Title: Solving Linear Differential Equations: Common Laplace Transform & Examples - Intro (Part 1)

Title: Matlab Examples - Amplitude Modulation (shorter version)

Title: Digital Signal Processing (DSP) Tutorial: Geometric Series and Discrete-Time Fourier Transfrom

12 next »

Digital Signal Processing (DSP) Tutorial: Introduction to Geometric Series and the Discrete-Time Fourier Transform This is an introduction to digital signal processing. Here, we...
Overview and Introduction to the z-Transform (Polynomial & Rational Functions) We introduce the z-transform bringing polynomials and rational functions to...
Matlab Examples: Review of Discrete Convolution Sum Using Matlab Here is a review of the discrete convolution sum including...

Linear Algebra Tutorial: Online Linear Algebra Course

doctorj — Fri, 09 Sep 2011 20:16:28 +0000

TUTORIAL INTRODUCTION TO LINEAR ALGEBRA

Linear Algebra should be an essential tool for any engineer. Why? Because linear algebra has many application found in the behavior,

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natural, physical and social sciences, in engineering, in business, in computer science and in pure and applied mathematics.

A simple application of linear algebra is finding the solution of a system

of linear equations in several unknowns.

I’ve produced a couple of videos involving linear algebra. Here is a simple linear algebra tutorial on multiplying matrices using Matlab.

Matlab Video Tutorial: Multiplying Matrices and Vectors

Linear Algebra Tutorial Videos from the Khan Academy

Fortunately, the Khan Academy, a non-profit educational provider, offers over a hundred videos in linear algebra.
Below are the videos from the Khan Academy:

Introduction to matrices

12 3 4 5 6 7 8 next »

Title: Introduction to matrices

Title: Inverse Matrix (part 1)

Title: Matrix multiplication (part 1)

Title: Matrices to solve a system of equations

Title: Inverting matrices (part 2)

Title: Linear Algebra: Introduction to Vectors

Title: Matrix multiplication (part 2)

Title: Linear Algebra: Introduction to Eigenvalues and Eigenvectors

Title: Linear Algebra: Basis of a Subspace

Title: Inverting Matrices (part 3)

Title: Linear Algebra: Finding Eigenvectors and Eigenspaces example

Title: Linear Subspaces

Title: Linear Combinations and Span

Title: Linear Algebra: Eigenvalues of a 3x3 matrix

Title: Solving 3 Equations with 3 Unknowns

Title: Singular Matrices

Title: Linear Transformations

Title: Matrices: Reduced Row Echelon Form 1

Title: Linear Algebra: Vector Examples

Title: Linear Algebra: Introduction to Linear Independence

12 3 4 5 6 7 8 next »

The above set of linear algebra tutorial videos should give you a very good idea on what linear algebra is. Once you are comfortable with the above concepts in linear algebra you can proceed to more advanced applications on its use. Some of the key concepts given by these videos are: vectors, matrices, vector field, vector space and vector subspaces, eigenvalues, eigenvectors, linear transformations, singular matrices, and other linear algebra concepts.

Important concepts of linear algebra are vector spaces and linear maps between them. In more formal terms, a vector space is a set whose elements can be added together and multiplied by the scalars, or numbers.

In many physical applications, the scalars are real numbers. In general, the scalars may form any field F—thus one can consider vector spaces over the field Q of rational numbers, the field C of complex numbers, or a finite field Fq.

We’ll see in future courses in digital communications that the concept of vector spaces have been used in coding theory to correct errors in a digital message.

Vector operations of addition and scalar multiplication will have similar and usual addition and multiplication of numbers: addition is commutative and associative, multiplication distributes over addition, and so on.

Besides the mathematical formalism you need not to get to hung up on the technical details because there are many other applications in using linear algebra.

LINEAR ALGEBRA AND MODERN CONTROL THEORY

For example, Linear algebra concepts have been used in modern control systems. In modern control theory, you have matices A, B, C, D. Used in the following equation

x’=Ax+Bu (where x’ denotes first derivative of the state vector x)
y=Cx+Du

where A is the system matrix. When finding the eigenvalues of the system matrix A, you have basically the system poles or it has a physical meaning of vibrational modes of a system such as a building or bridge. the vector x is the state vector. You can think of the displacements at various locations of a bridge as its system state. The matrix B, is the input distribution of the system. Physically, this is how the actuators of a system affect or influence the system by the input u. The matrix C, describes how sensors are distributed in the system and relates the state vector with the output vector y. The matrix D, decsribes how the input u directly affects the output y.

Based on the above description of a system, you can apply a variety of feedback schemes to improve system performance. For example, you can feed back either the state vector x or the output vector y to alter the states and feedback of a system to more desirable ones.

However, the scope of feedback and modern control theory is beyond the scope of this short blog article but hopefully you get an idea of what you can do with linear algebra.

Linear Algebra Lecture 1.1: Vector Spaces An Introduction | Tutorial

If you are not in the United States, please come visit and replace 90% of our linear algebra professors. I am confident that these 7 minutes of your lecturing make more sense than an entire semester under their instruction. …

Publish Date: 08/30/2011 0:45

http://www.tutorialblogger.info/linear-algebra-lecture-1-1-vector-spaces-an-introduction/

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Circuit Analysis using the Thevenin Equivalent and Norton Equivalent

doctorj — Sat, 20 Aug 2011 18:05:08 +0000

One of the most important analytical tools used in circuit analysis is the Thevenin Equivalent. The Thevenin equivalent reduces an network of resistors and independent sources into a single resistor and a single voltage sources. The Thevenin equivalent can be transformed into a Norton equivalent consisting of a single resistor in parallel with a current source.

One simple application of the Thevenin equivalent is to maximize power transfer to a load by matching the load resistance with the Thevenin resistance.

Below is a collection of videos involving the Thevenin Equivalent.

Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 1

12 next »

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 1

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 3

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 2

Title: Circuit Analysis - Bipolar Junction Transistor Model (BJT) - Dependent Sources - Part 6

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 4

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 7

Title: Circuit Analysis - Operational Amplifier Model for Voltage Follower - Dependent Sources - Part 7

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 5

Title: Thevenin & Norton Examples - Thevenin Equivalent Circuit Theory - Part 6

Title: Electric Circuit Analysis - Linearity Properties - Superposition Principle and Circuits - Part 3

Title: Operational Amplifier Tutorial - Basic Op Amp (Part 1)

Title: Electric Circuit Analysis - Linearity Properties - Superposition Principle and Circuits - Part 1

Title: Operational Amplifier Tutorial - Basic Non-Inverting Op Amp (Part 2)

Title: Circuit Analysis: Node Analysis (Part 1 - Introduction)

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Here is an article that provides more information about electronics that briefly discusses the Thevenin Equivalent (Reference: http://www.articlealley.com/basic-electronics-2289057.html)

Basic Electronics

BASIC ELECTRONICS BY JITENDRA CHITNIS (B.E.- Electronics)
INTRODUCTION
As a child I was fond of electronic gadgets like Digital Wrist Watch cum stop watch, Colour Television, FM Radio, Walkman, Calculator and many more gadgets were on my want list. And I was lucky enough to get them for handling and after careful use for a year or two I used to open them for my study. All was possible due to my father, my maternal uncle and other family friends who knew about it. It was real fun to open and study though used to understand very little about the circuit inside.
Slowly when I completed my schooling I joined a Radio, Tape and Television Repairing classes and started understanding the real science and technology involved in these black boxes.
Here in this article I want to give a brief Introduction about the basics of the electronics and knowledge to help beginners or learners about what is the importance of this technology how we can use this knowledge to make a better life out of this.

Definition of Electronics
The branch of science which study the flow of electron through a semiconductors such as silicon or germanium is called electronics.
(Silicon and Germenium are the minerals from the Chart of Chemistry)
Conductors, Semiconductors and Insulators
Conductors
Conductors are nothing but the materials which allow the passage of current very easily. This is because they large number of free electrons available. Examples – Copper, Aluminium.
Insulators
These substances which do not allow the passage of electric current through them. In terms of energy band, the valance band is full while the conduction band is empty.
Semiconductors
Semiconductors are those substances which have conductivity inbetween the Conductors and Insulators. In terms of energy bands valence band is almost filled and conduction band is empty and gap between them is very thin.
Types of Semiconductors
1. P type and trivalent impurity to semiconductor
2. n type pentavalent impurity to semiconductor

pn Junction
When a p type semiconductor is joined to n type semiconductor it forms a pn junction.
Forward and Reverse bias of pn junction.
P type to positive and n type to negative is a forward bias condition of pn junction.
On the other hand if we connect p type to negative and n type to positive it becomes a reverse bias condition for pn junction.
Different semiconductor devices used in common electronic circuit
1. Diode- Use as Rectifier, Regulate current flow direction.

2. Transistors- pnp and npn type. Use as Aplifier, Switch

pnp npn
3. Field Effect Transistor- Use as Switch

4. Thyristor- High Voltage Switches for Power Circuits

5. Integrated Circuits- A composition of Different devices in small space to save space and electric consumption.(It consists thousands of diodes, transistors and resistors, capacitors in small size of 0.5 cm by 3 cm – many different combinations can be built as per requirement)
Other circuit devices
1. Resistor- To resist the current and drop voltage to the required level.

2. Capacitor- To maintain a electric charge at a point in circuit. Use Filteration of Voltage

3. Inductor- To oppose the fluctuating current. Use Filteration of current

BASIC LAWS and THEOROMS FOR LAYMAN
Ohm’s Law
When an applied voltage E causes a current I to flow through an impedance Z, the value of the impedance Z is equal to the voltage E divided by the current I
.
Impedance = Voltage / Current Z = E / I
Similarly, when a voltage E is applied across an impedance Z, the resulting current I through the impedance is equal to the voltage E divided by the impedance Z.
Current = Voltage / Impedance I = E / Z
Similarly, when a current I is passed through an impedance Z, the resulting voltage drop V across the impedance is equal to the current I multiplied by the impedance Z.
Voltage = Current * Impedance V = IZ
Alternatively, using admittance Y which is the reciprocal of impedance Z:
Voltage = Current / Admittance V = I / Y
Kirchhoff’s Laws
Kirchhoff’s Current Law At any instant the sum of all the currents flowing into any circuit node is equal to the sum of all the currents flowing out of that node: Iin = Iout Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero: I = 0 Kirchhoff’s Voltage Law At any instant the sum of all the voltage sources in any closed circuit is equal to the sum of all the voltage drops in that circuit: E = IZ Similarly, at any instant the algebraic sum of all the voltages around any closed circuit is zero: E – IZ = 0
Thévenin’s Theorem
Any linear voltage network which may be viewed from two terminals can be replaced by a voltage-source equivalent circuit comprising a single voltage source E and a single series impedance Z. The voltage E is the open-circuit voltage between the two terminals and the impedance Z is the impedance of the network viewed from the terminals with all voltage sources replaced by their internal impedances.
Norton’s Theorem
Any linear current network which may be viewed from two terminals can be replaced by a current-source equivalent circuit comprising a single current source I and a single shunt admittance Y. The current I is the short-circuit current between the two terminals and the admittance Y is the admittance of the network viewed from the terminals with all current sources replaced by their internal admittances.
Thévenin and Norton Equivalence
The open circuit, short circuit and load conditions of the Thévenin model are: Voc = E Isc = E / Z Vload = E – IloadZ Iload = E / (Z + Zload) The open circuit, short circuit and load conditions of the Norton model are: Voc = I / Y Isc = I Vload = I / (Y + Yload) Iload = I – VloadY Thévenin model from Norton model
Voltage = Current / Admittance Impedance = 1 / Admittance E = I / Y Z = Y -1
Norton model from Thévenin model
Current = Voltage / Impedance Admittance = 1 / Impedance I = E / Z Y = Z -1
When performing network reduction for a Thévenin or Norton model, note that: – nodes with zero voltage difference may be short-circuited with no effect on the network current distribution, – branches carrying zero current may be open-circuited with no effect on the network voltage distribution.
Joule’s Law
When a current I is passed through a resistance R, the resulting power P dissipated in the resistance is equal to the square of the current I multiplied by the resistance R: P = I2R
By substitution using Ohm’s Law for the corresponding voltage drop V (= IR) across the resistance: P = V2 / R = VI = I2R

Electronic students should learn the following units and formulae:
Units
Current (amp)
Resistance (ohm)
Voltage (volt)
Capacitance (farad)

Resistors in Series Rtotal = R1 + R2 + R3 etc.
Resistors in Parallel Rtotal =
or
1/Rtotal =
Time Period Time period = Resistance x Capacitance (T = R x C)
Ohm’s Law Voltage = Current x Resistance
(V = I x R)
Resistance = Voltage / Current
Current = Voltage / Resistance

List of Circuit Analysis and Design Blog Videos Below is my attempt to catalog the list of videos...
Thevenin & Norton Examples – Thevenin Equivalent Circuit Theory – Part 2 Here is Part 2 showing how to apply the Thevenin...
Thevenin & Norton Examples – Thevenin Equivalent Circuit Theory – Part 6 This example analyzes a summing circuit using the Thevenin equivalent...