By Julian Hirsch
DAMPING FACTOR, L-PADS, AND SPEAKER RESPONSE: Although much is made of damping factor (DF) in amplifier specifications, it is one of the least significant of the properties that differentiate one amplifier from another.
Damping factor indicates the internal source impedance of the amplifier relative to the load impedance. An amplifier with a DF of 10 (based on an 8-ohm load) has a source impedance of 0.8 ohm. Since the speaker voice coil, cross over network, and connecting wiring are certain to have several times that resistance, any "improvement" of the amplifier DF to a higher number could not possibly affect the speaker's response.
But, aside from damping factor, what are the effects of "real-world" circuit resistances, including the above-mentioned factors, on the speaker's performance? A standard method of reducing the volume of speakers remote from the amplifier is to insert an "L-pad" in the speaker line. An L-pad consists of two variable resistors operated by a single shaft. One resistance element is in series with the speaker, the other in shunt (parallel) with it. When properly terminated, an L-pad presents a fairly constant load to the amplifier, while the voltage de livered to the speaker can be varied over a wide range and the speaker always "sees" a reasonably low-impedance source. This is preferable to simply put ting a variable resistance in series with the speaker to reduce its output, for this would present both speaker and amplifier with large variations in source and load impedance.
To understand why an appreciable source impedance can affect the frequency response of a speaker, refer to Figure 1, which represents an amplifier and speaker circuit with source impedance R1 and load R2. Impedance R1 is actually the sum of the amplifier's internal resistance and the resistance of the connecting speaker-lead wiring. (Since we are concerned at the moment only with the effect on the voltage appearing at the speaker's terminals, the resistance of the speaker's voice coils and crossover will be ignored.) The amplifier delivers a voltage, part of which is dissipated across series resistance R1. If the impedance of speaker load R2 were constant with frequency (this is true in very few speakers), the only effect would then be a fixed loss, with no change in sound quality. However, the impedance of a real speaker usually varies widely with frequency.
Figure 2 presents the impedance curve of a typical small bookshelf speaker system. Most speakers show at least this much impedance variation with frequency, and many show tar more. One would therefore expect the voltage delivered to the speaker terminals to vary in much the same way as the impedance curve, since R1 and R2 in effect form a voltage divider, and the increased impedance of R2 at some frequencies permits a larger fraction of the amplifier's output to reach the speaker. It can easily be seen that, quite apart from whatever its actual frequency response may be, the speaker is not being driven with the constant voltage signal which is the basis for frequency-response specifications.
Although R1 is usually much less than R2, there is still a possibility that frequency-dependent changes in R2 could cause a response variation at the output terminals of the amplifier because of the voltage drop across its internal impedance. In the past this possibility has been advanced as a partial explanation of why some amplifiers sound "better" than others with certain speakers.
Even though these effects are quite predictable, we made some measurements to establish their actual magnitudes with typical amplifiers and speakers. The speaker whose impedance curve is shown in Figure 2 was driven by several different amplifiers and the voltage-vs.-frequency response was measured at the speaker's terminals and at the amplifier's output terminals, with different values of resistance added in series with the short, heavy-gauge connecting wires.
There was no significant difference in frequency response at the speaker terminals with any of the amplifiers, which included a 200-watt-per-channel basic amplifier, a high-quality 30-watt-per-channel integrated amplifier, and a venerable vacuum-tube amplifier (Dynaco Mk IV). Figure 3 shows the voltage at the speaker terminals with the transistorized power amplifier, using resistors of 1, 2, 3, 4, and 8 ohms in the speaker line. With no added resistance (the actual circuit resistance, of course, was not "zero") the response varied only ±0.25 dB from 20 to 20,000 Hz. As series resistance was added (simulating the use of longer speaker leads or smaller-gauge wire) the response began to assume the shape of the impedance curve of Figure 2. Even I ohm was sufficient to give a ±0.5-dB response variation, and 8 ohms (equivalent to a DF of 1) produced a ±2.5-dB variation.
These curves, it must be emphasized, are not the speaker's acoustic-output responses. They show rather the change in that response caused by increasing the resistance of the source feeding the speaker circuit-which may or may not be detrimental. In all probability, with the specific speaker used, there would be some bass coloration at the resonance frequency, and perhaps a trace of "forwardness" from the elevated response in the 1,000- to 3,000-Hz region. On the other hand, the speaker might be inherently deficient in these areas, or it might have an emphasized upper bass, in which case the response change could improve its sound quality. The effect of a series resistance therefore varies with the speaker's quality and impedance.
All of which leads us to the question of L-pads- are they good or bad? We repeated the tests with an L-pad replacing the simple series resistor. As expected, the general effect is similar to that from a resistor, although the variation is less pronounced. Unless the pad is operated at its maximum (no attenuation) setting, the net response change should closely resemble the 3-ohm curve of Figure 3.
An advantage of the L-pad, as com pared to a series resistor, is the limited range of source impedance it presents to the speaker. For our tests, we used the Russound MP-2, a versatile speaker/ amplifier switcher-control unit which can select up to four sets of stereo speakers with L-pads and connect them to either of two amplifiers. To prevent the amplifier load from dropping below 4 ohms, each channel has a fixed 2-ohm series resistor. The load seen by the amplifier is a constant 10 ohms at all set tings, while the source impedance seen by the speaker is about 2.5 ohms at maximum output, increases to about 3.5 ohms as the control is turned down, and then decreases to near zero at very low settings.
The subjective importance of these effects will be heavily dependent on the actual frequency response and specific impedance characteristics of the speakers, the room acoustics, and the listener's critical perception. When we measured the actual amplifier output as it was influenced by the speaker's changing load impedance, the basic transistor amplifier proved to be unaffected by the speaker load--or, at least, any variations were considerably less than the 0.25-dB resolution of our test instruments. The vacuum-tube amplifier, which presumably has a much lower internal DF, did show a slight variation in response when we connected the speaker directly to its 8-ohm output terminals, but the difference between that curve and the response with an essentially constant load was less than 0.5 dB at all frequencies.
There is reason to believe that very critical listeners can hear even such minute effects, and that such effects are therefore at least in part responsible for the presumed difference in sound be tween transistors and tubes (in general, transistor amplifiers have a much lower internal resistance than tube types). I am not at all convinced of the importance of this factor, but it certainly cannot be ruled out.
No audio purist would dream of using L-pads to control speaker levels, but keep in mind that fairly long speaker-connecting cables (say, 20 feet or more) may well have a resistance of 0.5 ohm or so, resulting in an effective DF of less than 16 -- even if the inherent damping factor of the amplifier is rated at 1,000 or more.
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Fig. 1 (below) shows the impedances seen by the amplifier and speaker. Fig. 2 (upper right) is the impedance curve of a typical bookshelf speaker. The six different curves in Fig. 3 show the effects in decibels of five different series resistances on the audio signal delivered to the speaker terminals.
TESTED THIS MONTH
Sony ST-4950 AM/FM Tuner
Dynaco PAT-5 Stereo Preamplifier
Sherwood S-7010 AM/FM Receiver
Philips 209S Record Player
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