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Design Article

Loudspeakers: Objective evaluations - Part 6: Other measurements

Floyd Toole

4/27/2011 12:35 PM EDT

18.6.3 The Loudspeaker/Amplifier Interface: Impedance, Wire, and Damping Factor

This topic is on the borderline for the topic area of this book; these are hard electrical engineering issues, but they routinely get elevated to different planes of thought. The reason for talking a little about them here is because as a result of them, frequency responses of loudspeakers get altered.

Impedance: 8 ohms. This is the kind of specification one sees for loudspeakers. It is an invented number. For a few, very, very few loudspeakers, it is a good approximation, but for the vast majority, it is a dreadful description of reality. Figure 18.25a shows an example of an impedance that varies substantially with frequency and that crosses the rated impedance at a few places only. The variations are normally of no concern.

FIGURE 18.25 (a) An impedance curve for a loudspeaker compared to the nominal impedance rating chosen by the manufacturer for it. (b) The change in frequency response of this loudspeaker caused by driving it with a tube amplifier having a large output impedance. Note that the shape of the frequency-response error is the same as the loudspeaker impedance curve.

Most power amplifiers are designed to be constant-voltage sources, so unless an unfortunate interaction between amplifier and loudspeaker provokes limiting or protection, all is well. Sadly, there have been some notable examples of high-end loudspeakers having impedances that dipped to small fractions of an ohm. This is a problem of incompetent loudspeaker design. However, sensing a market, amplifier designers responded with monster "arc welder" devices that can drive these problem loudspeakers, and anything else, but it is overkill for most circumstances. It was amusing, at the time, to read that these incompletely designed loudspeakers "revealed" differences between power amplifiers, as if it were a virtue.

But there is a situation in which the varying impedance becomes an issue. Going straight to the problem, Figure 18.25b shows the kind of change in loudspeaker frequency response that can be caused by variable impedance; it is easily audible. The culprit? In this case, a tube power amplifier with a large output impedance. The explanation is in Figure 18.26a and (b).

FIGURE 18.26 Schematic diagrams showing (a) and (b) the electrical circuit explaining how amplifier and wire impedances cause variations in loudspeaker frequency response, and (c) how they affect loudspeaker damping.

The output impedance of the power amplifier and the resistance of the loudspeaker wire are components in a voltage divider circuit. When combined with the frequency-dependent impedance of the loudspeaker, it means that the "flat" frequency response voltage at location "A" inside the power amplifier acquires a shape following that of the impedance curve at location "B." Because this is the voltage driving the loudspeaker, the overall performance of the loudspeaker - that is, all of its frequency response curves - are modified by this amount. Different loudspeakers have different impedance curves; some are strikingly variable, others change little.

The amount of the change in frequency response depends on the total voltage drop across the combined amplifier output impedance and wire resistance, meaning that minimizing both of these is desirable. For solid-state power amplifiers, output impedances tend to be very small: typically 0.01 to 0.04 ohms. Those for tube power amplifiers are much higher: typically 0.7 to 3.3 ohms. These numbers come from a survey of Stereophile magazine amplifier reviews over several years. (My thanks to Stereophile for doing useful measurements.)

To reviewers, these are moderately discomfiting numbers because the inevitable conclusion is that tube power amplifiers, as a population, cannot allow loudspeakers to perform as they were designed. Different reviewers handle it in different ways. Some ignore it, and others have danced around the issue, concluding that it is just one more uncertainty in sound reproduction. Rarely is it acknowledged to be what it is.

The Infinity Prelude MTS, now discontinued, had an impedance of 4 ohms ±1 ohm, almost constant, as a result of deliberate design. This loudspeaker, and the few others with this property, can perform with remarkable consistency in spite of significant losses in the upstream signal path. Rarely, though, is impedance ever discussed as a virtue or a problem. One well-known high-end loudspeaker specified that it should be used with wire in which the resistance is less than 0.2 ohms. This conscientious behavior is admirable, but it was probably not interpreted as implying that if the total upstream resistance cannot exceed 0.2 ohms, the restriction is violated as soon as any tube amplifier is connected, no matter what wire is used.


4/28/2011 12:33 PM EDT

Wonderful stuff.

However, please note that this is not a collection of contributions from various authors. Dr. Toole wrote it, in its entirety.

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4/28/2011 3:48 PM EDT

Thank you for your article. Perhaps I missed it, but I haven't seen power amplifiers that attach sense wires to the loud speaker terminals for their negative feedback rather than at the output terminals of the amplifier. Power supplies do this, so I'd expect audio amplifiers would too, thus negating much concern for the types of cables.

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5/4/2011 11:38 AM EDT

That was done some number of years ago in a Kenwood amplifier, in a line they called "Audio Purist". It created a need for a composite cable with sense leads, but AFAIK the cable folks never picked up on it --- I would conjecture because it used a lot of negative feedback, which had gotten a bad name among audiophiles by then. See also Bruno Putzeys' article "The F Word", in Vol. 1 of the new bookzine Linear Audio, for some of the history of anti-negative feedback sentiment.

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