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ing (RDF) equipment aboard a mobile vehicle facilitates determining the location of a transmitter.

An RDF receiver can also be used to find one’s own position with respect to two or more transmit-

ters operating on different frequencies.

In an RDF receiver for use at frequencies below about 300 MHz, a small loop or loopstick an-

tenna is used. It is shielded against the electric component of radio waves, so it picks up only the

magnetic part of the EM field. The loop is rotated until a sharp dip, or null, occurs in the received

signal strength, indicating that the axis of the loop lies along a line toward the transmitter. When

readings are taken from two or more locations separated by a sufficient distance, the transmitter can

be pinpointed by finding the intersection point of the azimuth bearing lines on a map.

At frequencies above approximately 300 MHz, a directional transmitting and receiving an-

tenna, such as a Yagi, quad, dish, or helical type, gives better results than a small loop. When such

an antenna is employed for RDF, the azimuth bearing is indicated by a signal peak rather than by a

null.

Navigational Methods

Navigation involves the use of location devices over a period of time, thereby deriving a function of

position versus time. This technique can be used to determine whether or not a vessel is on course.

It can also be used to track the paths of military targets, severe thunderstorms, and hurricanes.

Fluxgate Magnetometer

When conventional position sensors do not function in a particular environment for a mobile

robot, a fluxgate magnetometer can be used. This system employs sensitive magnetic receptors and a

Navigational Methods 531

30-14 A simple direction-finding scheme (A) and an ultrasonic

direction finder (B).

microcomputer to sense the presence of, and detect changes in, an artificially generated magnetic

field. Navigation within a room can be done by checking the orientation of magnetic lines of flux

generated by electromagnets in the walls, floor, and ceiling of the room. For each point in the room,

the magnetic flux lines have a unique direction and intensity. There is a one-to-one correspondence

between the magnetic flux intensity/direction and the points within the robot’s operating environ-

ment. This correspondence can be represented as a two-variable mathematical function of every lo-

cation in the room. The robot controller is programmed to know this function. This makes it

possible for the machine to pinpoint its position with extreme accuracy, in some cases to within a

few millimeters.

Epipolar Navigation

Epipolar navigation works by evaluating the way an image changes as viewed from a moving perspec-

tive. Suppose that you are piloting an aircraft over the ocean. The only land in sight is a small island.

The on-board computer sees an image of the island that constantly changes shape. Figure 30-15

shows three sample sighting positions (A, B, C) and the size/shape of the island as seen by a machine

vision system in each case. The computer has the map data, so it knows the true size, shape, and lo-

cation of the island. The computer compares the shape and size of the image it sees at each point in

time, from the vantage point of the aircraft, with the actual shape and size of the island from the

map data. From this, the computer can ascertain the altitude of the aircraft, its speed and direction

of movement relative to the surface, its latitude, and its longitude.

Log Polar Navigation

In log polar navigation, a computer converts an image in polar coordinates to an image in rectangular

coordinates. The polar radius is mapped onto the vertical rectangular axis, and the polar angle is

mapped onto the horizontal rectangular axis.

Radial coordinates are unevenly spaced in the polar map, but are uniform in the rectangular

map. During the transformation, the logarithm of the radius is taken to maximize the geographical

area that the system can observe. As a result of this logarithmic transformation (that’s where the

“log” comes from in the term), long-distance resolution is sacrificed, but the close-in resolution is

enhanced.

The so-called log polar transform distorts the way a scene appears to human observers, but

translates images and motions into data that can be efficiently dealt with by a computerized scan-

ning system.

Loran

The term loran is an acronym derived from the words long range navigation. Loran is one of the old-

est electronic navigation schemes, and is still used by some ships and aircraft. The system employs

RF pulse transmission at low frequencies from multiple transmitters at specific geographic loca-

tions.

In loran, a computer on board a vessel can determine the location of the ship by comparing the

time difference in the arrival of the signals from two different transmitters at known locations.

Based on the fact that radio waves propagate at the speed of light in free space (approximately

299,792 km/s or 186,282 mi/s), it is possible to determine the distance to each transmitter, and

from this, the location of the ship relative to the transmitters.

In recent years, loran has been largely supplanted by the Global Positioning System (GPS).

532 Transducers, Sensors, Location, and Navigation

Global Positioning System (GPS)

The Global Positioning System (GPS) is a network of radiolocation/radionavigation apparatus that

operates on a worldwide basis. The system employs several satellites, and allows determination of

latitude, longitude, and altitude.

All GPS satellites transmit signals in the microwave part of the radio spectrum. The signals are

modulated with codes that contain timing information used by the receiving apparatus to make

measurements. A GPS receiver determines its location by measuring the distances to several differ-

ent satellites. This is done by precisely timing the signals as they travel between the satellites and the

receiver. The process is similar to triangulation, except that it is done in three dimensions (in space)

rather than in two dimensions (on the surface of the earth).

Navigational Methods 533

30-15 Epipolar navigation is the optoelectronic counterpart of

human spatial perception.

There is some reduction in the propagation speed of EM microwaves in the ionosphere, as com-

pared with the propagation speed in free space. The extent of this reduction depends on the signal

frequency. The GPS employs dual-frequency transmission to compensate for this effect. A GPS re-

ceiver uses a computer to process the information received from the satellites. From this informa-

tion, it can give the user an indication of position down to a few meters.

Increasingly, automobiles, trucks, and pleasure boats come with GPS receivers installed as stan-

dard equipment. If you are driving in a remote area and you get lost, you can use GPS to locate your

position. Using a cell phone, citizens band (CB) radio transceiver, or amateur (ham) radio trans-

ceiver, you can call for help and inform authorities of your exact position, which is displayed on a

detailed map of the area in which you are located.

Quiz

Refer to the text in this chapter if necessary. A good score is at least 18 correct. Answers are in the

back of the book.

1. Which of the following devices would most likely be used for adjusting the frequency setting

of a digital radio transmitter or receiver?

(a) A piezoelectric transducer

(b) A dynamic transducer

(d) A capacitive proximity sensor

2. Collimation of IR rays can be done by means of

(a) an ordinary lens.

(b) a selsyn.

(d) any of the above.

3. A computer map

(a) can help a robot find its way around.

(b) requires the use of IR beacons.

(d) requires the use of a low-frequency RDF loop antenna.

4. The distance of a target from a radar station is called

(a) the resolution.

(b) the azimuth.

(d) the transform.

5. Which of the following devices is best for use as an ultrasonic pickup?

(a) A back-pressure transducer

(b) A piezoelectric transducer

534 Transducers, Sensors, Location, and Navigation

(d) A capacitive pressure transducer

6. What do loran and the GPS have in common?

(a) They both operate using IR energy.

(b) They both employ loop antennas at the transmitting and receiving stations.

transmitter.

(d) They both involve measurement of distances to determine the location of a receiver.

7. A bright spot close to, and directly to the left of, the center of a conventional radar display

indicates the presence of a target

(a) right over the observing station.

(b) at close range, west of the observing station.

(d) far from the observing station, azimuth unknown.

8. Which of the following systems enables a vessel to navigate entirely from its own frame of

reference, without the need for any electronic devices external to itself?

(a) An epipolar navigation system

(b) The GPS

(d) Forget it! There is no such thing.

9. Ultrasonic waves travel through a vacuum

(a) at the same speed as they travel in air.

(b) at a slightly higher speed than they travel in air.

(d) Forget it! No form of acoustic wave can travel through a vacuum.

10. Which of the following devices or techniques makes use of artificially generated magnetic

fields to facilitate location within a work environment?

(a) A dynamic transducer

(b) Epipolar navigation

(d) None of the above

11. Which of the following is not an example of a transducer?

(a) A microphone

(b) A radio antenna

(d) All of the above are examples of transducers.

Quiz 535

12. A foam-like material, having a resistance that varies depending on how much it is

compressed, is known as

(a) an elastomer.

(b) a fluxgate magnetometer.

(d) none of the above.

13. A stepper motor

(a) has torque that increases as its speed increases.

(b) resists applied torque when stopped with current going through its coils.

(d) is easily fooled by body capacitance.

14. A permanent magnet is a key component of

(a) an elastomer pressure sensor.

(b) a capacitive pressure sensor.

(d) a piezoelectric microphone.

15. An electric motor is an example of

(a) an electromechanical transducer.

(b) a pressure sensor.

(d) a texture sensor.

16. A capacitive proximity sensor should not be expected to detect the presence of

(a) a wooden chair.

(b) a metal desk.

(d) a steel post.

17. A well-designed photoelectric proximity sensor

(a) is easily fooled by loud noises.

(b) cannot detect the presence of objects that reflect light.

(d) is not easily fooled by stray sources of light.

18. An acoustic transducer can translate an ac electrical signal into

(a) visible light.

(b) sound or ultrasound.

(d) mechanical torque.

536 Transducers, Sensors, Location, and Navigation

19. Body capacitance can be a problem with

(a) electrostatic transducers.

(b) elastomer pressure sensors.

(d) all of the above.

20. Which of the following devices can be used to limit the torque or force applied by an

electromechanical device such as a robot?

(a) A back-pressure sensor

(b) A capacitive proximity sensor

(d) An optical shaft encoder

Quiz 537

538

CHAPTER

Acoustics, Audio,

and High Fidelity

IN SOUND RECORDING AND REPRODUCTION, ESPECIALLY WITH MUSIC, FIDELITY SUPERSEDES ALL

other considerations. In these applications, low distortion and “sound esthetics” are more important

than amplifier efficiency or gain. In this chapter, we’ll look at basic acoustics principles, and outline

some high-fidelity (hi-fi) components and design concepts.

Acoustics

Acoustics is the science of sound waves. Sound consists of molecular vibrations at audio frequency

(AF), ranging from about 20 Hz to 20 kHz. Young people can hear the full range of AF; older peo-

ple lose hearing sensitivity at the upper and lower extremes.

Audio Frequencies

In music, the AF range is divided into three broad, vaguely defined parts, called bass (pronounced

“base”), midrange, and treble. The bass frequencies start at 20 Hz and extend to 150 or 200 Hz.

Midrange begins at this point, and extends up to 2 or 3 kHz. Treble consists of the audio frequen-

cies higher than midrange. As the frequency increases, the wavelength becomes shorter.

In air, sound travels at about 1100 feet per second (ft/s), or 335 meters per second (m/s). The

relationship between the frequency f of a sound wave in hertz, and the wavelength λ

in feet, is as

follows:

= 1100/f

The relationship between f in hertz and λ

in meters is given by:

= 335/f

This formula is also valid for frequencies in kilohertz and wavelengths in millimeters.

A sound disturbance in air at 20 Hz has a wavelength of 55 ft (17 m). A sound of 1.0 kHz pro-

duces a wave measuring 1.1 ft (34 cm). At 20 kHz, a sound wave in air is only 0.055 ft (17 mm)

Acoustics 539

long. In substances other than air at sea level, such as air at extreme altitudes, freshwater, saltwater,

or metals, the preceding formulas do not apply.

Waveforms

The frequency, or pitch, of a sound is only one of several variables that acoustic waves can possess.

Another important factor is the shape of the wave itself. The simplest acoustic waveform is a sine

wave (or sinusoid ), in which all of the energy is concentrated at a single frequency. Sinusoidal sound

waves are rare in nature. A good artificial example is the beat note, or heterodyne, produced by a

steady carrier in a communications receiver.

In music, most of the notes are complex waveforms, consisting of energy at a specific funda-

mental frequency and its harmonics. Examples are sawtooth, square, and triangular waves. The

shape of the waveform depends on the distribution of energy among the fundamental and the har-

monics. There are infinitely many different shapes that a wave can have at a single frequency such

as 1 kHz. As a result, there is infinite variety in the timbre that a single musical note can have.

Path Effects

A flute, a clarinet, a guitar, and a piano can each produce a sound at 1 kHz, but the tone quality is

different for each instrument. The waveform affects the way a sound is reflected from objects.

Acoustics engineers must consider this when designing sound systems and concert halls. The goal is

to make sure that all the instruments sound realistic everywhere in the room.

Suppose you have a sound system set up in your living room, and that, for the particular place-

ment of speakers with respect to your ears, sounds propagate well at 1, 3, and 5 kHz, but poorly at

2, 4, and 6 kHz. This affects the way musical instruments sound. It distorts the sounds from some

instruments more than the sounds from others. Unless all sounds, at all frequencies, reach your ears

in the same proportions that they come from the speakers, you do not hear the music the way it

originally came from the instruments.

Figure 31-1 shows a listener, a speaker, and three sound reflectors, also known as baffles. The

waves reflected by the baffles (X, Y, and Z), along with the direct-path waves (D), add up to some-

31-1 Sounds from reflected

paths (such as X, Y,

and Z) combine with

direct-path sound (D)

to produce what a

listener hears.

thing different, at the listener’s ears, for each frequency of sound. This phenomenon is impossible

to prevent. That is why it is so difficult to design an acoustical room, such as a concert auditorium,

to propagate sound well at all frequencies for every listener.

Loudness and Phase

You do not perceive the loudness (also called volume) of sound in direct proportion to the power con-

tained in the disturbance. Your ears and brain sense sound levels according to the logarithm of the

actual intensity. Another variable is the phase with which waves arrive at your ears. Phase allows you

to perceive the direction from which a sound is coming, and it also affects perceived sound volume.

The Decibel in Acoustics

You have already learned about decibels in terms of signal voltage, current, and power. Decibels are

also used in acoustics, and in this application, they are considered in terms of relative power. If you

change the volume control on a hi-fi set until you can just barely tell the difference, the increment

is one decibel (1 dB). If you use the volume control to halve or double the actual acoustic-wave

power coming from a set of speakers, you perceive a change of 3 dB.

For decibels to have meaning in acoustics, there must be a reference level against which every-

thing is measured. Have you read that a vacuum cleaner produces 80 dB of sound? This is deter-

mined with respect to the threshold of hearing, which is the faintest sound that a person with good

hearing can detect in a quiet room specially designed to have a minimum of background noise.

Phase in Acoustics

Even if there is only one sound source, acoustic waves reflect from the walls, ceiling, and floor of a

room. In Fig. 31-1, imagine the baffles as two walls and the ceiling in a room. As is the case with

baffles, the three sound paths X, Y, and Z are likely to have different lengths, so the sound waves re-

flected from these surfaces will not arrive in the same phase at the listener’s ears. The direct path (D),

a straight line from the speaker to the listener, is always the shortest path. In this situation, there are

at least four different paths by which sound waves can propagate from the speaker to the listener. In

some practical scenarios, there are dozens.

Suppose that, at a certain frequency, the acoustic waves for all four paths happen to arrive in

exactly the same phase in the listener’s ears. Sounds at that frequency will be exaggerated in vol-

ume. The same phase coincidence might also occur at harmonics of this frequency. This is unde-

sirable because it causes acoustic peaks, called antinodes, distorting the original sound. At certain

other frequencies, the waves might mix in phase opposition. This produces acoustic nulls called

nodes or dead zones. If the listener moves a few feet, the volume at any affected frequency will

change. As if this isn’t bad enough, a new antinode or node might then present itself at another set

of frequencies.

One of the biggest challenges in acoustical design is the avoidance of significant antinodes and

nodes. In a home hi-fi system, this can be as simple as minimizing the extent to which sound waves

reflect from the ceiling, the walls, the floor, and the furniture. Acoustical tile can be used on the ceil-

ing, the walls can be papered or covered with cork tile, the floor can be carpeted, and the furniture

can be upholstered with cloth. In large auditoriums and music halls, the problem becomes more

complex because of the larger sound propagation distances involved, and also because of the fact

that sound waves reflect from the bodies of the people in the audience!

540 Acoustics, Audio, and High Fidelity