Electrical and Computer Engineering: An Introduction with Examples

1. Electrical and Computer Engineering:An Introduction with Examples Neil Goldsman, Zeynep Dilli, Latise Parker GE-TIME: Teachers Integrating Mathematics and Engineering July 2004 University of Maryland, College Park

2. Electrical and Computer Engineering (ECE): Things We Shape • Electrical and electronics engineering: Designs by shaping the concrete and the non-concrete • Electrical currents • Electromagnetic waves: • From radio to light • Semiconductors • Sound • Images • Information

3. Mathematics in ECE • Mathematics is a language for ECE  • Mathematics is how we represent and manipulate information  

4. A Look Inside • CD Player: • Digital data read by laser • Converter from digital data to analog audio • Equalizers and amplifiers to process audio and send to speakers • AM Radio Receiver: • Radio waves from antenna • Digital circuits to select channel • Analog circuits to convert radio signals to audio signals • Digital Camera: • Photonic sensor converts light signal into electrical signal • Analog image information stored in individual pixels • Converter from analog light intensity to digital data • Digital circuits to do image processing like sharpening, color correction, zoom

5. A Look Inside, 1: CD Player Audio information is “analog”: It can have any value within a range. It is stored on a compact disc in “digital” format: Reduced to a limited number of values, set at certain levels, and stored in a pattern of 0s and 1s. Example: For a signal varying from -1 to 1, a three-bit system can have eight discrete levels: A laser in the CD player shines light on the CD surface. The 1s and 0s reflect light differently from each other. A light sensor near the laser catches the reflection and detects the 1s and 0s etched upon the spinning disc surface.

6. A Look Inside, 1: CD Player The CD surface has a sequence of three-bit numbers. The detection circuit reads the sequence and the D/A converter pulls out the analog audio data from it. Example Sequence: 011 101 110 111 110 101 011 001 000 000 000 001 011 101 110 111 110 101 011 … The amplifier might be designed to amplify treble and bass at different levels. The amplification level is also set by the volume control.

7. A Look Inside, 1: CD Player Aside: SOUND, 1 Sound is formed by periodic vibrations of a material medium, usually air. The faster the vibrations, the higher the vibration frequency, and the higher the pitch of the sound we hear. We measure vibration speed in Hertz: how many times per second does the medium or source vibrate? Example: Telephone dial tones are tuned to the musical note A. This is, by standard, at 440 Hz. The musical note E is a “major fifth” above A. By definition, this means that the ratio of the frequency of E to that of A is 3/2. So the E right above the central A is at 660 Hz. A: E:

8. A Look Inside, 1: CD Player Aside: SOUND, 2 A: E:

9. A Look Inside, 1: CD Player Aside: SOUND, 3 Real instruments do not have pure sinusoidal vibrations. Their vibrations include harmonics: whole-number multiples of the fundamental frequency of the note. The full tone of the instrument is the sum of the fundamental and certain harmonics, added at varying strengths. The difference between how two instruments sound even while playing the same note comes from which particular harmonics they include, and the particular strength each is at. Ex.: For an A note, the tone of an instrument might be the sum of components at 440 Hz, 880 Hz, 1320 Hz, 1760Hz, … n*440Hz where n is an integer. Ex: An instrument like a guitar or violin will only have odd harmonics (fundamental, 3*fundamental, 5*fundamental…) in its tone. Other instruments might include even harmonics.

10. A Look Inside, 1: CD Player Aside: SOUND, 4 Example: Fictional Instrument 1, only odd harmonics Example: Fictional Instrument 2, only even harmonics INSTRUMENT 1: sin(2π*440*t)+0.5*sin(2π*3*440*t)+0.25*sin(2π*5*440*t)+0.25*sin(2π*7*440*t)+0.25*sin(2π*9*440*t) +0.1*sin(2π*11*440*t)+0.1*sin(2π*13*440*t)+0.1*sin(2π*15*440*t); INSTRUMENT 2: sin(2π*440*t)+0.5*sin(2π*4*440*t)+0.25*sin(2π*6*440*t)+0.1*sin(2π*8*440*t);

11. A Look Inside, 2: AM Radio Receiver Stations broadcast individual signals… The radio receives all of them together Goldsman, Dilli, Parker

12. A Look Inside, 2: AM Radio Receiver The antenna receives a weak signal. The amplifier increases the amplitude of the signal. A digital circuit sets the filter to separate the signal we want from the others. The filter lets only radio signal of a certain frequency to pass.

13. A Look Inside, 2: AM Radio Receiver The audio signal is the “envelope” of the radio frequency signal. The demodulator, an analog electronic circuit, extracts this envelope.

14. A Look Inside, 2: AM Radio Receiver The final amplifier is designed to be able to “drive” the speakers of the radio, which convert the final electrical signal to sound.

15. A Look Inside, 2: AM Radio Receiver The signal arrives as a mixture of radio and audio frequency signals, multiplied together. We need to extract the audio signal (ωAUD2) carried by the radio frequency of the channel we want (ωRF2). The mathematics 1, incoming signal from antenna: 2, after amplification: 3, after filtering for channel 2: 4, after demodulation: 5, after amplification:

16. A Look Inside, 3: Digital Camera • Digital cameras combine photonics with signal processing and electronics… • Converting light to electrical charge: Photonics • Converting electrical charge to images: Electronics, Image processing • Manipulating and storing the images: Image processing

17. A Look Inside, 3: Digital Camera Converting Light to Electricity Semiconductors can be designed into devices that will convert light that falls on them into electrical charges. These devices can be put in circuits that will use the resulting charge to create voltage or current signals. Example:Fiber optic communication circuits use photodetectors at the receiving end to sense and interpret the communication signal light coming through the fiber. Example: The photodetectors in our game sense the laser light falling on them and the circuit they are in passes the information to the game control program in the computer.

18. A Look Inside, 3: Digital Camera Converting Electrical Signal to Digital Images Nearly any amount of light can fall on a single photodetector. This information is analog. To store and manipulate this information digitally, we have to the opposite of what the CD player does and convert the analog information to digital levels. Example: In the figure below, the darker the color, the more charges gathered on the corresponding pixel represented by a higher number.

19. A Look Inside, 3: Digital Camera Converting Electrical Signal to Digital Images There is a two-dimensional array of photodetectors as the light sensor in a digital camera. The larger number of sensors in this array, the better the camera. Here is why.

20. A Look Inside, 3: Digital Camera Color Images White light is a combination of colors. A combination of red, green and blue light can be used to represent all colors. Computer graphics programs also use this principle. We can put red, green or blue filters on individual pixels and make the pixel store brightness information only of that color. Then the digital processor combines the information to form the full color picture. Goldsman, Dilli, Parker

21. Goldsman, Dilli, Parker A Look Inside, 3: Digital Camera Color Images