Transmission Techniques: Wire and Cable 43714.27.1 Damping FactorThe damping factor of an amplifier is the ratio of the
load impedance (loudspeaker plus wire resistance) to the
amplifier internal output impedance. The damping factor
of the amplifier acts as a short circuit to the loudspeaker,
controlling the overshoot of the loudspeaker. Present day
amplifiers have an output impedance of less than 0.05:
which translates to a damping factor over 150 at 10 kHz,
for instance, so they effectively dampen the loudspeaker
as long as the loudspeaker is connected directly to the
amplifier. Damping factor is an important consideration
when installing home systems, studios, or any system
where high-quality sound, especially at the low frequen-
cies, is desired. As soon as wire resistance is added to
the circuit, the damping factor reduces dramatically,
reducing its affect on the loudspeaker. For instance, if a
#16 AWG 50 ft loudspeaker cable (100 ft round trip) is
used, the wire resistance would be 0.4: making the
damping factor only 18, considerably less than
anticipated.
It is not too important to worry about the effect the
damping factor of the amplifier has on the loudspeakers
in a 70 V system as the 70 V loudspeaker transformers
wipe out the effects of the wire resistance.
Consider the line as a lump sum, Fig. 14-21. The
impedance of the line varies with wire size and type.
Table 14-33 gives typical values of R, C, and L for 33 ft
(10 m) long cables. Note, the impedance at 20 kHz is
low for all but the smallest wire and the 3 dB upper
frequency is well above the audio range. The worst
condition is with a capacitive load. For instance, with a
4 μF load, resonance occurs around 35 kHz.
The results of the above are as follows:
- Make the amplifier to loudspeaker runs as short as
possible. - Use a wire gage that represents less than 5% of the
loudspeaker impedance at any frequency. - Use twisted pairs on balanced 70 or 100 V distrib-
uted systems to reduce crosstalk (amplifier output
is often fed back into the amplifier as negative
feedback). - Use good connectors to reduce resistance.
Table 14-34 gives the length of cable run you can
have for various loudspeaker impedances.14.27.2 CrosstalkWhen a plurality of lines, carrying different programs or
signals, are run together in the same conduit, or wheremultiple pairs or multiple coax cables are bundled, they
tend to induce crosstalk currents into each other. Cross-
talk is induced by two methods:- Electromagnetically through unbalanced coupling
between one circuit and others. - Electrostatically through unbalanced capacitance to
other circuits, or to the conduit if it carries current.
This develops a voltage difference between one
circuit and the others, or to its own or other shields
carrying current.
If the line is less than a quarter-wavelength at the
frequency of operation, then the cable does not have to
have a specific impedance, or be terminated in a
specific impedance. The terminating impedance could
then be small compared to the open line characteristic
impedance. The net coupling with unshielded pairs
would then be predominantly magnetic. If the termi-
nating impedance is much larger than the characteristic
impedance of the wires, the net coupling will be
predominantly electric.
Two wires of a pair must be twisted; this insures
close spacing and aids in canceling pickup by transposi-
tion. In the measurements in Fig. 14-22, all pickup wasFigure 14-21. Amplifier, cable, loudspeaker circuit using
lumped circuit elements to represent the properties of the
cableTable 14-33. Lumped Element Values for 33 ft (10 m)
Lengths of Cable
Cable Type L–HC–pF
Rdc–:Z–:@20 kHzNo. 18 zip cord 5.2 580 0.42 0.44
No. 16 zip cord 6.0 510 0.26 0.30
No. 14 speaker cable 4.3 570 0.16 0.21
No. 12 speaker cable 3.9 760 0.10 0.15
No. 12 zip cord 6.2 490 0.10 0.15
Welding cable 3.2 880 0.01 0.04
Braided cable 1.0 16,300 0.26 0.26
Coaxial dual cylindrical 0.5 58,000 0.10 0.10
Coaxial RG-8 0.8 300 0.13 0.13Amplifier Loudspeaker
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