Results 1. Survival

The damping factor of an amplifier is the ratio of the load impedance (loudspeaker plus wire resist-ance) 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 frequencies, is desired. As soon as wire resistance is added to the circuit, the damping factor reduces dramatically, reducing its effect 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, Figure 6.21. The impedance of the line varies with wire size and type. Table 6.33 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.

Amplifier Loudspeaker

L

C R

Z_L Z₀

fIGure 6.21

Amplifier, cable, loudspeaker circuit using lumped circuit elements to represent the properties of the cable.

Lumped Element Values for 33 ft (10 m) Lengths of Cable

Cable Type L–µH C–pF Rdc– Z–@20 kHz

No. 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 0.13

Table 6.33 Table 6.33

200

The results of the above are as follows:

1. Make the amplifier to loudspeaker runs as short as possible.

2. Use a wire gage that represents less than 5% of the loudspeaker impedance at any frequency.

3. Use twisted pairs on balanced 70 or 100 V distributed systems to reduce crosstalk (amplifier out-put is often fed back into the amplifier as negative feedback).

4. Use good connectors to reduce resistance.

Table 6.34 gives the length of cable run you can have for various loudspeaker impedances.

crosstalk

When a plurality of lines, carrying different programs or signals, are run together in the same conduit, or where multiple pairs or multiple coax cables are bundled, they tend to induce crosstalk currents into each other. Crosstalk is induced by two methods:

1. Electromagnetically through unbalanced coupling between one circuit and others.

2. 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.

Loudspeaker Cable Selection Guide

Power (%) 11% 21% 50%

Loss (dB) 0.5 1.0 3.0

Wire Size Maximum Cable Length-ft

4  Loudspeaker

12 AWG 140 305 1150

14 AWG 90 195 740

16 AWG 60 125 470

18 AWG 40 90 340

20 AWG 25 50 195

22 AWG 15 35 135

24 AWG 10 25 85

8  Loudspeaker

12 AWG 285 610 2285

14 AWG 185 395 1480

16 AWG 115 250 935

18 AWG 85 190 685

20 AWG 50 105 390

22 AWG 35 70 275

24 AWG 20 45 170

70 V Loudspeaker

12 AWG 6920 14,890 56,000

14 AWG 4490 9650 36,300

16 AWG 2840 6100 22,950

18 AWG 2070 4450 16,720

20 AWG 1170 2520 9500

22 AWG 820 1770 6650

(Courtesy Belden.) Table 6.34 Table 6.34

201 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 imped-ance could then be small compared to the open line characteristic impedimped-ance. The net coupling with unshielded pairs would then be predominantly magnetic. If the terminating 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 transpo-sition. In the measurements in Figure 6.22, all pickup was capacitive because the twisting of the leads effectively eliminated inductive coupling.

One application that is often ignored regarding crosstalk is speaker wiring, especially 70 V distributed loudspeaker wiring. You will note in the first drawing that the two wires are not a balanced line. One is hot, the other is ground. Therefore, that pair would radiate some of the audio into the adjoining pair, also unbalanced. Twisting the pairs in this application would do little to reduce crosstalk.

The test was made on a 250 ft twisted pair run in the same conduit with a similar twisted pair, the latter carrying signals at 70.7 V. Measurements made for half this length produced half the voltages, therefore the results at 500 ft and 1000 ft were interpolated.

The disturbing line was driven from the 70 V terminals of a 40 W amplifier and the line was loaded at the far end with 125 , thus transmitting 40 W. The crosstalk figures are for 1 kHz. The voltages at 100 Hz and 10 kHz are 1/10 and 10 times these figures, respectively.

There are two ways to effectively reduce crosstalk. One is to run signals only on balanced-line twisted pairs. Even shielding has a small added advantage compared with the noise and crosstalk rejection of a balanced line. The second way to reduce crosstalk is to move the two cables apart. The inverse-square

70 V

600Ω

Conduit Amplifier

Two twisted pairs in the same conduit

E_N

Two twisted pairs in the same conduit

70 V

Conduit Amplifier

Two twisted pairs in the same conduit

1. Amplifier common grounded 0.1 V 0.4 V 2.0 V

2. Ground removed. 70 V line floating 0.014 V 0.06 V 0.3 V

3. 70 V circuit grounded using a pair of resistors matched to 10% 0.005 V 0.02 V 0.1 V 4. Same with resistors matched to 1% 0.0006 V 0.0025 V 0.012 V

5. 70 V circuit as in 4 0.000 V 0.0016 V 0.008 V

6. Same as 5, except disturbed line is 2 conductor twisted cable 0.0002 V 0.0008 V 0.004 V tf

Effects of grounding on crosstalk. (Courtesy Altec Lansing Corp.)

202

law tells us that doubling the distance will produce four times less interference. Further, if cables cross at right angles, this is the point where the magnetic fields have minimum interaction. Of course, the latter solution is not an option in a prebundled cable, or in cable trays or installations with multiple cables run from point to point.