Handbook for Sound Engineers

Transmission Techniques: Wire and Cable 435

where,

h is the center to center conductor spacing,

Fb is very near 0. Neglecting Fb will not introduce

appreciable error.

14.26.1 Transmission Line Termination

All lines do not need to be terminated. Knowing when to
terminate a transmission line is a function of the fre-
quency/wavelength of the signal and the length of the
transmission line. Table 14-30 can be guideline, espe-
cially where the signal is long compared to the length of
the line. If the wavelength of the signal is small com-
pared to the transmission-line length, for instance a
4.5 GHz signal, a terminator is required to prevent the
signal from reflecting back toward the source and inter-
fering with forward traveling signals. In this case the
line must be terminated for any line longer than a quarter
of a wavelength.

Transmission-line termination is accomplished using

parallel or series termination. Parallel termination

connects a resistor between the transmission line and

ground at the receiving end of the transmission line

while series termination connects a resistor in series

with the signal path near the beginning of the transmis-

sion line, Fig. 14-20.

Resistive termination requires a resistor value that

matches the characteristic impedance of the transmis-

sion line, most commonly a 50ȍ or 75ȍcharacteristic

impedance. The termination resistance is matched to the

transmission line characteristic impedance so the elec-

trical energy in the signal does not reflect back from the

receiving end of the line to the source. If the resistor is

perfectly matched to the characteristic impedance, at all

frequencies within the desired bandwidth, all of the

energy in the signal dissipates as heat in the termination

resistor so no signal reflects backwards down the line to

the source causing cancellations.

14.27 Loudspeaker Cable

Much has been said about wire for connecting loud-

speakers to amplifiers. Impedance, inductance, capaci-

tance, resistance, loading, matching, surface effects, etc.

are constantly discussed.

Most home and studio loudspeaker runs are short

(less than 50 ft, or 15 m) and therefore do not constitute

a transmission line. When runs are longer, it is common

to connect the loudspeakers as a 70 V, or 100 V system

to reduce line loss caused by the wire resistance so the

power lost in the line does not appreciably effect the

power delivered to the loudspeaker. For instance, if a

4 : loudspeaker is connected to an amplifier with a

cable which measures 4:resistance, 50% of the power

will be dissipated in the cable. If the loudspeaker was

connected to a 70 V system, and the loudspeaker was

taking 50 W from the amplifier, the loudspeaker/trans-

former impedance would be 100:; therefore, the 4:

line resistance would dissipate 4% of the power.

When using a 70.7 V loudspeaker system, the choice

of wire size for loudspeaker lines is determined by an

economic balance of the cost of copper against the cost

of power lost in the line. Power taken from the amplifier

is calculated from the equation

(14-19)

where,

P is the power delivered by the amplifier,

V is the voltage delivered by the amplifier,

Z is the impedance of the load.

For a 70 V system

(14-20)

If the voltage is 70.7 V and the load is 50: , the

power would be 100 W. However, if the amplifier was

connected to a 50: load with 1000 ft of #16 wire

(2000 ft round trip) or 8: of wire resistance the power

from the amplifier would be

Figure 14-20. Basic termination of transmission lines.

A. Parallel termination.

B. Series termination.

Terminator

Terminator

Line driver

or transmitter Receiver

P V

2

Z

----- -=

P^5000

Z

------------=

P^5000

50 :+ 8 :

=-------------------------

=86.2 W