Storing Audio and Video Data

There are two ways of storing sound and light information. For sound, this information is the time dependence of the pressure (how much it differs from atmospheric pressure). For light, the information is the time dependence of the intensity of the light (for black and white) or the intensity of each of three primary colors (for color imaging). Let’s call these the “primary signal”.

In an analog representation, some property of the storage medium (e.g.magnetization in a magnetic tape, depth of grooves in a vinyl disk) is directly proportional to the primary signal. It is stored as a continuous function of time; that is, both time and the stored signal are continuous variables. (Similarly, AM and FM radio waves are analog carriers of the sound signal.) This means that the stored signal can, in principle, have excellent fidelity, since no information is lost. However, any defects (scratches in the vinyl or tape, accidental demagnetizations of the tape, stray electrical signals for AM or FM transmissions) can easily cause distortions (“noise”) or even destructions of the signal. (As we discussed, this is a bigger problem for AM than FM broadcasts.) In addition, because the signals are continuous functions (of intensity and time), they require a lot of storage space, e.g. to store a song or movie.

In a digital representation, the signal is stored as a set of numbers at set time intervals. That is, compared to an analog representation, both the time and the signal are discretized; they are no longer continuous variables. Therefore there may be less “extraneous” information, described below, in the digital representation so less storage space is needed to store the “useful” information (i.e. that we can see or hear). “Extraneous”: one hopes that in discretizing the information, the information that is lost is not important. For example, for a sound recording, if the time interval is shorter than 0.05 ms (1/fmax, the maximum frequency we can hear), we might not notice the difference (although some musicians prefer analog to digital recordings). For light, the fastest interval we can see is ~ 10 ms, so information does not need to be stored more densely than this.

In the digital recording, the intensity signal is also discretized. For example, suppose the signal is stored as an integer between 0 and 1000. If the primary signal = 636.7, it will be rounded up to 637 – i.e. there are round-off errors in the digital signal. However, since the signal is stored as a number, it is immune to noise; i.e. an interfering signal won’t change this number (although the signal can be removed by gross mishandling of the storage medium).

So in summary, an analog representation is a more faithful representation of the primary signal because it is a continuous function of the intensity as a function of time, but it is sensitive to defects and stray signals and takes a lot of storage space. A digital representation rounds-off both the time and intensity, so may lose some information and fidelity, but it is immune to stray signals and takes much less storage space (so more things can be stored in the same area).

Digital information is stored as number, and we are most used to numbers in “decimal format”. In decimal format, there are ten possible values (0,1,2,3,4,5,6,7,8,9) for each place in the number, and each place is a factor of 10 times larger than the place next to it. For example, the number “105”means that there are five “ones” plus zero “tens” plus one “hundred”. [Similar arguments hold for fractions in decimal notation.]

For storing information (and also doing logical transformations), it is more useful to use a “binary format”, in which each digit can be 0 or 1 and each place is a factor of 2 times the place next to it. So the decimal number “105” would be represented as “1101001” which means that there is one “one” plus zero “twos” plus zero “fours” + one “eight” + zero “sixteens” + one “thirty two” + one “sixty four”. The advantage of using binary is that “one” and “zero” can be represented easily by different electrical, magnetic, optical signals (or logical symbols), such as:• Capacitor charged or discharged (or + or – polarity of charge)• Magnetization up or down• Current on or off (or clockwise or counterclockwise through a circuit)• Light on or off (or reflected or not reflected)• True of false• Heads or tales (if you want to use coins to store your data!)

Exercise: What is the decimal equivalent of the binary number 10011?

What is the decimal equivalent of the binary number 10011?

This number is 1x1 + 1x2 + 0x4 + 0x8+ 1x16 = 19

Exercise: What is the binary equivalent of the decimal number 65?

What is the binary equivalent of the decimal number 65?

65 = 1x64 + 0x32 +0x16 +0x8 + 0x4 + 0x2 + 1x1, so its binary representation is 1000001.

In a CD, the digital information is stored as a set of small pits along circular tracks in the disk. Light from an infrared diode laser is focused along these tracks as the CD turns. If the light hits a pit, the reflected signal is weak (because the surface of the pit is not flat and because the depth of the pit is such that there is destructive interference between the light hitting the pit and that hitting its border). However, if the light hits the track where there is no pit, the reflected signal is large. Therefore, “1” and “0” correspond to a strong reflected light signal and a weak reflected light signal. (Of course, the location of the tracks, timing of the disk rotation, and separation of sets of pits that correspond to different numbers have to be carefully arranged and controlled.)

DVD players have red diode lasers, with a shorter wavelength than CD players. Because the smallest spot to which light can be focused is approximately the wavelength (see March 30 lecture), DVD players can have more tightly focused light spots than CD players, and therefore smaller and more densely packed pits (and can even put the pits in different levels of the plastic). Therefore, a DVD can hold more information than the CD, e.g. visual as well as audio information.

A blue-ray player has a blue laser, with an even shorter wavelength, so blue-ray disks can hold even more information, e.g. light signals for more display pixels to give a sharper picture.[Even more dense storage disks may come when appropriate ultraviolet diode lasers are developed.]

Total internal reflection is not only used for communications, but for carrying light through fibers in lams and endoscopic surgery.

Just as digital storage devices can hold more “useful” information, with less noise, than analog devices, more “useful” information can be transmitted digitally. We do this by sending light pulses as a function of time (e.g. pulse = 1, no pulse = 0). These are sent through transparent, glass optical fibers. The glass fiber is surrounded by another glass “cladding” with a smaller index of refraction than the inner glass. Light rays that hit the cladding material at an oblique angle undergo total internal reflection: 100% of the light is reflected and stays inside the cable.

Of course, light rays that bounce back and forth between the cladding will travel further than those that go straight through, so take more time to travel, spreading out the light pulse. To minimize this pulse spreading, the diameter of the core is kept very small (9 μm), to minimize the variation in path lengths, and the cladding is “graded”, i.e. changes gradually, in the best optical fibers.

[The text describes other aspects of optical communication and the optical systems of CD players that we won’t get into.]

Optical communication, optical storage disks, and electronic image sensors in cameras all depend on an electronic device that can sense the light signal and put out a voltage and/or current. A simple device for doing this is a photodiode, essentially the “inverse” of a light-emitting diode, shown here.

In an LED, electrons in the conduction band can “recombine” (i.e. fall into) holes in the valence band near the pn junction, emitting light at the gap energy, i.e. with frequency f = Egap/h. (In regular diodes, the recombination energy is turned into heat.)

In a photodiode, if light with frequency f ≥ Egap/h is incident on the diode, it can excite electrons across the gap, i.e. from the valence band into the conduction band, creating an electron-hole pair. Generally, these will recombine (usually turning their energy into heat) but if the pair is in the depletion region, the internal electric field may separate them before they have a chance to recombine: since the p-region is negative and the n-region is positive, there will be an electric field pointing to the left. This will drive the holes to the left (through the p-region) and the electrons to the right (through the n-region). If the photodiode is connected to a resistor, it will send current through the resistor. If it is connected to a capacitor, it will charge up the capacitor. If it is connected to a storage battery, it can recharge the battery. In any case, it converts the energy of the photons into other forms of energy.

photons

A useful memory device (used in cameras) is a charge-coupled device (CCD) which is a combination of a photodiode and MOSFET (discussed next class) – there is a CCD for each pixel in the display.

Another important application of photodiodes is as a solar cell:

Sunlight has a continuous range of frequencies and photon energies. This graph shows the spectrum of solar energy (as a function of wavelength, λ = c/f). The black curve is the theoretical spectrum (which we will discuss when we go back to Chapter 7.) The yellow is the measured spectrum at the top of the atmosphere and the orange is what reaches earth. (Some light is removed by Rayleigh scattering and some by absorption by water and carbon dioxide molecules in the atmosphere; fortunately, nitrogen, oxygen, and argon, which make up most of the atmosphere, don’t absorb much at these wavelengths.)[ozone absorbs in the ultraviolet]

photons from sunAlthough a photodiode can capture photons with frequencies f ≥ Egap/h, it is most efficient at absorbing frequencies right at the gap. A higher frequency photon might be absorbed, putting an electron in a high energy state, but it falls back down to the bottom of the conduction band (“wasting” this extra energy as heat). Furthermore, photons with frequencies f < Egap/h won’t be absorbed at all.

So the challenge is to find semiconductors that can match their absorption to the solar spectrum.

[The theoretical maximum output voltage of the photodiode is Vmax = Egap/e, where e = electron charge and Egap is the difference in energy of the electron and hole, but the output voltage is always somewhat smaller than this due to internal losses.]

This shows a diagram of a solar cell that contains three different photodiodes, that absorb in different parts of the spectrum.

• The maximum efficiency (ratio of output energy to input solar energy) attained by a solar cell with multiple materials is 46%.

• The maximum efficiency attained with an experimental single material solar cell is 30%.• The typical efficiency of commercial solar cells is ~ 15% (but increasing).

Exercises:23. As it passes through the lens that focuses it onto a CD’s aluminum layer, the player’s laser beam is

more than 1 mm in diameter. Why does its large size as it leaves the lens allow the beam to focus to asmaller spot?

24.Why can light from a blue laser form a narrower beam waist than light from an infrared laser?26.When you look into the front of a square glass vase filled with water, its sides appear to be mirrored.

Why do the sides appear so shiny?28.Why does the surface of a DVD look so colorful in white light?31.What numbers do the two binary bytes 11011011 and 01010101 represent?32. How is the number 165 represented in binary?Problems• A gallium arsenide LED emits light with a wavelength of 870 nm. What would be the theoretical

maximum output voltage of a gallium arsenide photodiode?• What should be band gap of a semiconductor to match the peak wavelength in the solar spectrum?