Handbook for Sound Engineers

1184 Chapter 32

3. Electromagnetic waves travel through space or air
   at the speed of light. The physical distance trav-
   eled by a wave during one cycle is called wave-
   length. The equation is

(32-5)

where,

M is wavelength in feet,

f is frequency in MHz.

For 1 MHz AM radio, 100 MHz FM radio, and

2 GHz cell phone signals, wavelengths are about

1000 ft, 10 ft, and 6 inches, respectively.

4. Any wire will behave as an antenna at frequencies
   where its physical length is a quarter-wavelength or
   multiples thereof. This is responsible for the
   impedance peaks and dips seen at 25 MHz inter-
   vals in Fig. 32-5.

32.2.5 Cables and Transmission Lines

A cable consists of two or more conductors that are kept
in close proximity over their length. Cables, such as
those for ac power and loudspeakers, are generally used
to convey power to a load. In a pair of such conductors,
because the same current flows to and from the load in
opposite directions, the magnetic fields have the same
intensity but are of opposite polarity as shown in
Fig. 32-6. In theory, there would be zero external field,
and zero net inductance, if the two conductors could
occupy the same space. The cancellation of round trip
inductance due to magnetic coupling varies with cable
construction, with typical values of 50% for zip cord,

70% for a twisted pair, and 100% for coaxial

construction.

At very high frequencies, a cable exhibits very

different characteristics than it does at, say, 60 Hz

power frequencies. This is caused by the finite speed,

called propagation velocity, at which electrical energy

travels in wires. It is about 70% of the speed of light for

typical cables making wavelengths in cable correspond-

ingly shorter. A cable is called electrically short when

its physical length is under 10% of a wavelength at the

highest frequency of interest. Wavelength at 60 Hz for

typical cable is about 2200 miles (mi), making any

power cable less than 220 mi long electrically short.

Likewise, the wavelength at 20 kHz for typical cable is

about 34,500 ft, making any audio cable less than about

3500 ft long electrically short. Essentially identical

instantaneous voltage and current exists at all points on

an electrically short cable and its signal coupling

behavior can be represented by lumped resistance,

capacitance, and magnetically coupled inductance as

shown in Fig. 32-7. Its equivalent circuit can then be

analyzed by normal network theory.

When a cable is longer than 10% of a wavelength,

signals must be considered to propagate as electromag-

netic waves and the cable can properly be called a

transmission line. This includes typical cables longer

Figure 32-5. Wire is low-impedance current path only at
low frequencies.

M^984

f

---------=

100 1k 10k 100k 1M 10M 100M

Impedance of 10 ft of #12 Straight Wire

10k

3k

1k

300

100

30

10

3.0

1.0

0.3

0.1

0.03

0.01

Frequency—Hz

Ohms

Figure 32-6. Cancellation of field in circuit pair.

Figure 32-7. Lumped-circuit model of electrically short

coaxial cable.

+

Lc

Ls

Rc

Rs Ccs

S S