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Practical tests on damping factor and impedance matching

Exploring impedance transformer taps
&
their effect on damping factor?

[Italian version here]

Parameter: Damping Factor & Bass Alignment & System Frequency Response
Interface: Amplifier with Loudspeaker with room
Price: PRaT & Boom & now Tizz too
Author: Mark Wheeler - TNT UK
Published: October, 2023

“How on earth can an amplifier affect the sense of pace, rhythm or timing of music?” ask sceptical Plebs, stage left, “Surely an amplifier just makes signals bigger? The PRaT are surely artefacts of the source?”, continue Plebs, “And how the Zarking Almighty Bob can any of this have anything to do with amplifier impedances and negative feedback?”

Your Very Young Scribe was as equally perplexed as the Plebs' Chorus. In Part I your Old Scribe noticed that there were greatly different quoted amplifier damping factors across the same brand ranges. There appeared to be no apparent correlation to price or other parameter. Loudspeakers appeared to have impedance varying with frequency, so where did this damping factor number come from? This was before the invention of the internet, so your Old Scribe asked anyone who might know what it was and why it mattered.

It will not surprise readers that there were as many opinions as respondents. Many seemed unaware that it merely represents a ratio of loudspeaker nominal impedance divided by amplifier output impedance. Some of the older ones explained its importance in terms of valve amplifier to speaker matching, especially those with PA or guitar amp experience.

Damping Factor Theory

Luckily, while contemplating a first teenage hi-fi, your Old Scribe had acquired an extensive collection of back numbers of various wordy audio related journals. This collection dated back to the 1960s and therefore covered the transition from thermionic tubes (valves) to silicon and germanium transistors! These included some copies of Wireless World and a couple of Practical Electronics and Everyday Electronics magazines with audio features. There was also an almost complete run of HiFi News & Record Review dating back to the mid 1960s. Your Old Scribe read all the design and theory articles and any equipment reviews that looked informative.

“Was this time that should have been spent on school work?” Ask plebs rhetorically, stage left

Eventually the explanation was forthcoming that damping factor is the relationship between amplifier output impedance and loudspeaker input impedance. However, your Old Scribe had been even more eagerly reading about loudspeakers and observed that reviews included graphs of Impedance curves, whose very name implied that no such relationship could be fixed at one figure. Surely, a Young Scribe reasoned, the damping factor would be a curve similar to the loudspeaker impedance curve. If the amplifier output impedance also varied with frequency (and until a circuit design handbook was obtained from the public library this remained a guess), Damping factor would be all over the place. It would be better to know that such a damping factor curve never dropped below some mythical goodness defining figure as yet undivulged by the sacred texts.

A similar concept of damping also applies to the bass performance and impedance curve of loudspeakers too. Authors wrote about loudspeaker driver Q and loudspeaker system Q which is also indicated by that impedance curve. The similarity of term that applied to the electrical Q (Q_ES) and mechanical Q (Q_MS) of loudspeaker drive units and of loudspeaker systems also added the system Q to considerations of “damping”. Bewildering.

Loudspeaker Impedance Curves

Loudspeakers only have a “nominal impedance” and the actual impedance is a complex frequency dependant combination of inductance, capacitance and resistance. And we all know that “Resistance is futile”.

No explanation from the sages of hifi shops or electrical spares shops satisfactorily dealt with the thorny matter of loudspeaker impedance variation with frequency. Did this affect the relevance of damping factor? Looking at the impedance curves published in the hundreds of loudspeaker tests in that collection of magazines, no loudspeaker exhibited a constant impedance of 4Ω, 8Ω or 16 Ω. The published impedance graph, usually far below the frequency response line often dipped below 4Ω even when the loudspeakers were described as 8Ω;.

Therefore the theoretical explanation that sound quality might be affected in some way by the ratio of loudspeaker equivalent resistance to amplifier output stage resistance at some unspecified frequency seems somewhat vague. Too vague to be useful even if we had the faintest idea of how this might affect sound quality.

Practical Damping Factor

In the absence of published experimental outcomes, the only recourse is to experiment oneself. A pair of Quad II was being used at the time as power amplifiers which had 3 impedance matching output settings: 4Ω, 8Ω & 16Ω. Which one should be chosen if the nominally 8Ω loudspeaker impedance curve wanders from 5.5Ω to 15Ω? The first test loudspeakers showed 5.5Ω in the lower midrange and over 15Ω at the bass resonance and the crossover point.

So what is a Young Scribe to do?

Conduct experiments is what. A selection of loudspeakers, all nominally 8Ω were tried on both the 8Ω and 4Ω transformer secondary winding taps. These are seen (along with the feedback tap at Q) as the output transformer secondary winding taps at P, Q, R, S & T on the circuit diagram (schematic) above. The loudspeakers included:

• 2-way series crossover 200mm sealed bass driver small stand bookshelf
• 4-way complex parallel crossover stand mount with 300mm reflex bass driver (Quasar QS1)
• 2-way simple parallel crossover reflex bass driver stand mount (Jensen)
• Large 3-way parallel crossover 325x225mm bass driver driver sealed stand mount (EMI LE4 or B&W DM1?)

In every case the Quad II performed better using the 4Ω output transformer tap in every parameter except maximum volume.

• Frequency response from the amplifier-loudspeaker combination was flatter on the 4Ω tap than the 8Ω tap
• Bass was better defined and less prone to boom on the 4Ω tap than the 8Ω tap
• Rhythm seemed more coherent or better preserved on the 4Ω tap than the 8Ω tap
• Overall system coherence improved from lf to hf on the 4Ω tap than the 8Ω tap, resulting in more stable

Just in case the situation is unique to the particular case of the ultralinear configured Quad II with global feedback from the output transformer, this experiment has subsequently been conducted with other push-pull tetrode and pentode configurations. Indeed, the same experiment has been conducted by your Old Scribe with most available valve (tube) amplifiers since then.

Later your Old Scribe decided to conduct the experiment again with single ended triode amplifiers, with and without global feedback. Read about these experiments soon.

Conclusion

Matching valve (tube) amplifiers to loudspeaker impedance is not as simple as matching nominal impedance to the amplifier designated output transformer secondary nominal impedance match. When in doubt, unless the loudspeaker has a very flat impedance trace, with no deep dips below the 8Ω nominal impedance, the system choosing the 4Ω setting may bring sound quality benefits, at the expense of maximum volume.

The obvious benefit is a bass response closer to that intended by the loudspeaker designer.

A secondary benefit is a frequency response closer to that intended by the loudspeaker designer.

The obvious conclusion is that whenever a loudspeaker has anything other than a mainly resistive load above the nominal impedance, it is better to choose the lower Z secondary transformer winding on the output transformer.

Damping factor appears to affect bass response accuracy and frequency response. Despite rumours to the contrary, oft repeated where audiophiles gather together, Pace Rhythm and Timing are also affected by the relationship between amplifier output impedance and loudspeaker input impedance.

© 2023 TNT-Audio Mark Wheeler - mark@tnt-audio.com - www.tnt-audio.com

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