The Loudspeaker/Amplifier Interface (cont.)
Table 18.1 shows the resistances per unit length of stranded copper wire. The numbers are for both wires in the circuit, so just measure the length of the two-conductor wire and multiply by these numbers. If you do not see a gauge rating for a loudspeaker wire, be very suspicious. Some exotic cables use small wire for seriously mistaken reasons.
Table 18.1 Resistances per Unit Length of Two-Conductor Stranded Copper Wire
Minimizing wire resistance is easy: use large wire (low gauge numbers) or, better yet, just use less wire (see Table 18.1). If there is a risk of radio-frequency signal pickup, it is important to know that unshielded wires act as antennas. A great deal of mystique has evolved around loudspeaker wires, attempting to elevate this simple device to impossible heights of importance. Notions that they behave as transmission lines persist, but Greiner (1980) offers persuasive arguments that this is unrealistic.
There are other beliefs, some of which are impossible (e.g., directional wires), and most of which remain unproven because of the cost of running double-blind tests. At prices that can exceed $20,000 for a pair of 8-ft (2.4 m) loudspeaker wires, one expects a lot. Enough said. Wire is a good product for the industry: totally reliable, inexpensive to manufacture, highly profitable, and, if you like what you hear, an excellent investment, so long as you did not pay more than you needed to (aye, there's the rub!).
One of the universal compliments attached to audio products, including wires, is that it results in "tighter bass." In the case of loudspeaker wire, it seems as though there might be some truth to it because of its role in the loudspeaker/amplifier interface and damping. Damping unwanted motion of a loudspeaker diaphragm is undoubtedly a good thing.
In 1975, I wrote an article for AudioScene Canada called "Damping, Damping Factor, and Damn Nonsense." I still like the title because it is a succinct statement of reality. The point of the article is summarized in Figure 18.26c. The internal impedance of the power amplifier is used to calculate something called the damping factor (DF) of the amplifier (DF = 8/output impedance); the number 8 was chosen because it is the nominal load (resistive) used to measure the power output capability of amplifiers. The logical inclination is to think that larger is better. Solid state amplifiers have damping factors ranging from about 200 to 800, using the impedances quoted earlier in this section. Tube amplifiers in my survey ran from 2.4 to 11.4 because of their high output impedances.
Figure 18.26c also shows the complete circuit involved in the electrical damping of loudspeakers. It does not mysteriously stop at the loudspeaker terminals. Current must flow through components and devices inside the enclosure. The first component to be encountered is typically an inductor, part of the low-pass filter ahead of the woofer in a passive system. Then inside the woofer is the voice coil. The inductor resistance is commonly around 0.5 ohm, and the voice coil resistance can have different values but is commonly around 6 ohms. So let us examine all of the resistances in the circuit to arrive at the following progression of damping factor changes:
Amplifier internal impedance: 0.01 ohm DF = 800
Add wire resistance: 10 ft of 10-gauge
Both conductors: 0.02 ohm DF = 266
Add crossover inductor resistance:
0.5 ohm (typical) DF = 15
Add voice-coil resistance: 6 ohms (typical) DF = 1.2
Obviously, the resistances inside the loudspeaker are the dominant factors. Even eliminating the inductor and driving the woofer directly changes things only slightly. The article (Toole, 1975) shows oscilloscope photographs of tone bursts of various frequencies and durations while the damping factor of the amplifier was varied from 0.5 to 200. At damping factors above about 20 (internal impedance less than 0.4 ohms), no change was visible in any of the transient signals, and changes in frequency response were very much less than 1 dB, and then only over a narrow frequency range. On music, no change in sound quality could be discerned, including attentive listening for "tightness."
Because 0.4 ohms is at least a factor of 10 higher than internal impedances found in typical solid-state amplifiers, it means that from the perspective of damping the transient behavior of loudspeakers, the wire resistance can be allowed to creep up substantially. However, as just shown, doing so can change the frequency response of the loudspeaker, and that, we know, is audible.
In summary, with tube amplifiers, the internal impedance is already so high that damage is done to the frequency responses of loudspeakers having normal impedance variations. Added losses in wire simply make the situation worse. To hear the loudspeakers that the manufacturer made, it is necessary to seek out those with very constant impedance as a function of frequency. Damping of the loudspeaker is also marginally impaired by the high internal impedance.
With solid-state amplifiers, internal impedances are negligibly low, so wire resistance must be controlled to minimize corrupting the frequency response of loudspeakers. How low? It depends on the variations in the impedance of the loudspeakers being used and how low those impedances are; wire resistance represents a higher percentage of low impedances.
For example, a loudspeaker ranging from 3 ohms to 20 ohms (not unusual for consumer loudspeakers and a moderately demanding situation) would experience about 0.6 dB variations in a system with 0.2 ohm wire resistance. The next chapter will show that this is slightly higher than the detection threshold for low-Q spectral variations in quiet anechoic listening. Twelve-gauge wire would allow for a run of 0.2/0.0032 = 63 ft (19 m). Obviously, this is not very restrictive.
Loudspeakers having nearly constant impedance can tolerate large wire losses, sacrificing only efficiency up to the resistance at which damping is affected. If compelled to do better than this suggestion, more copper, shorter runs, or higher-impedance loudspeakers are the solutions.