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Powers of 2

Powers of 2. Metric Prefixes (whole numbers). Metric Prefixes (fractions). y = log(x) with x and y axes equal linear scale. y = log(x) with x and y axes linear scale y axis expanded. y = log(x) with x axis logarithmic scale and y axis linear. Bels and deciBels (positive).

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Powers of 2

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  1. Powers of 2

  2. Metric Prefixes (whole numbers)

  3. Metric Prefixes (fractions)

  4. y = log(x) with x and y axes equal linear scale

  5. y = log(x) with x and y axes linear scaley axis expanded

  6. y = log(x) with x axis logarithmic scale and y axis linear

  7. Bels and deciBels (positive)

  8. Bels and deciBels (negative)

  9. dB references • dBW – dB Watts (0dBW = 1 Watt) • dBm – dB milliWatts (0dBm = 1/1000 Watt) • dBi – antenna gain (0dBi = the field intensity of an isotropic antenna at a given input power and frequency) • An isotropic antenna is a simple straight wire antenna without any physical modifications. • A differently shaped antenna’s field intensity is measured and compared to the isotropic antenna at the same input power and frequency. The ratio is expressed in deciBels as dBi.

  10. Wave Crests

  11. Heinrich Hertz

  12. Speed of Light Radio waves travel through space at a speed of approximately 300,000,000 meters per second. Electricity travels through a wire and light travels through fiber optics at a speed of approximately 200,000,000 meters per second.

  13. Electromagnetic Waves

  14. Range of Frequencies

  15. Traditional Classification of BandwidthsStill heard quite often, but less meaningful in today’s world.

  16. Usually we talk directly in terms of actual Bands used. Microwaves Television & FM Radio AM Radio 802.11b & 802.11g Wireless LANs Visible Light & X-Rays

  17. Calculating frequency and wavelength Example 1 A radio wave has a wavelength of 2 meters. Calculate the frequency in hertz. f = C l f (hertz) = 300,000,000 (meters/second) 2 meters (wavelength or l) f = 150,000,000 hertz (continued)

  18. Calculating frequency and wavelength Example 2 A radio wave has a frequency of 10,000,000 hertz. Calculate the wavelength in meters. Since we know the formula for calculating frequency, we can solve it for the wavelength as follows: l = C f l (meters) = 300,000,000 (meters/second) 10,000,000 (hertz) l = 30 meters

  19. Fourier’s Theorem Fourier's theorem states that any complex wave is the sum of a fundamental sine wave and its multiples (also called its harmonics). The same idea, but in more detail: Fourier's theorem states that any complex waveform is the sum of sinusoids (sine waves, the simplest kind of waveform). The complex waveform will be composed of a fundamental frequency of a sine wave, to which are added other sine waves of various amplitudes that are all multiples of the fundamental frequency.

  20. Fourier Example – Square Wave green: y = sin(x) + 0.333333 sin(3x) + 0.2 sin(5x) + 0.142857 sin(7x) pink + white + red + cyan yellow: y = sin(x) + 0.333333 sin(3x) + 0.2 sin(5x) pink + white + red blue: y = sin(x) + 0.333333 sin(3x) pink + white pink: y = sin(x)

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