The Damping Factor Debate
What do the numbers really mean and do very high amplifier
damping factors have any noticeable effect on performance?

By GEORGE L. AUGSPURGER
James B. Lansing Sound, Inc.

OME amplifier manufacturers have introduced circuitsthat have much higher damping factors than conventional units. A high-quality "traditional" vacuumtube amplifier can be expected to have a damping factor
ranging from 10 to 20, but some of the newer transistorized units boast of damping factors greater than 100.
Moreover, advertising and promotional literature for thesemodels explains that the damping factor is a sort of figureof merit indicating the degree of control which the amplifier has over the loudspeaker. The higher the damping

factor, the more accurately the speaker is controlled andthe better the performance. Is this right?
The subject is really pretty simple, but not quite thatsimple. To get started on the right track, let's go back andlook at a few of the more basic things about audio power
amplifiers.
We can represent an amplifier as a black box with aset of input terminals on one side and a set of outputterminals on the other, as in Fig. 1. And we have indicateda loudspeaker in the same way, except that instead of output terminals there are some sound waves emanating fromthe far side of this particular box.
The Loudspeaker LoadINPUTOUTPUT

AMP

INPUT

SPKR.

Fig. 1. Amplifier and speaker represented as "black boxes".
INTERNAL IMPEDANCE V S
RDAMPING FACTOR FOR
8 A OUTPUT
GEN.
DF
en
1i
8O.I
80
Fig. 2. The amplifier aefs Wte a generator with resistance.
SRvc
3.2fi

RATED IMP.

Rvc4n6.4SPKR.

816

12.8

Fig. 3. Speaker resistanceis about

80%of rated impedance.

Fig. 4. R, and R <. are in series between the amplifier and speaker.
v

Rvc
AMP.

Reprinted from ELECTRONICS WORLDSPKR.

The next step is to connect the speaker to the output
terminals of the amplifier. As far as the speaker is concerned, when it "looks back" at the amplifier, it "sees" agenerator of audio signals which acts as though it has acertain effective internal impedance. This can be represented as a resistor connected in series with the output
terminals. Don't be misled by the fact that the resistor
is imaginary—the behavior of the amplifier is exactly thesame as if there were a resistor in plain sight on the back of
the chassis. (Of course, generator impedance includes reactive characteristics too, but for our purpose here, a simple
resistor will do nicely.)
By taking the internal impedance of the amplifier (Rs)and bringing it outside the black box, we arrive at Fig. 2.
R.< may be relatively large or it may be small. It may evenbe non-existent (zero internal impedance is not too hardto achieve in practice).
W e assume that the black box itself produces a constant
output voltage regardless of load. Nevertheless, a certain
load impedance is required for a certain output power at
minimum distortion. This is the impedance that the amplifier must "see" when it "looks" at the speaker load and is
the rated load impedance usually indicated at the amplifier
JANUARY1967

m

The Damping Factor
Rather than specify the value of R*, it has become common to translate this into a figure which is called thedamping factor (DF) of the amplifier. As we have seen,
it really has more to do with coupling than damping. One
definition of damping factor is the ratio of rated load impedance to the amplifier's own internal impedance.
For our 8-ohm black-box amplifier, an internal impedance of 8 ohms gives a damping factor of one. An internal
impedance of one ohm gives a damping factor of 8. And if
Hx is only 1/10 ohm, the damping factor is 80. These factors are shown in Fig. 2.
This being the case, common sense leads us to believe
what the proponents of high damping factors say in theirsales literature, namely, that the damping factor is anumerical indication of coupling between amplifier andloudspeaker and the higher the figure, the better off wearc.
Unfortunately, we cannot always rely entirely on common sense. For one thing, a particular loudspeaker may not
require a high damping factor to accurately follow thesignal from the amplifier. Some loudspeaker systems givesmoothest performance if the amplifier has a damping
factor somewhere between one and three.
But there is another property of dynamic loudspeakers,
all dynamic loudspeakers, that has to be appreciated toreally understand how the damping factor works. It is thisother half of the actual damping factor which so many
people seem to ignore.
A dynamic loudspeaker has a voice coil, and the voicecoil has electrical resistance. In most practical cases, thed.c. resistance of a loudspeaker is about 80% of its ratedimpedance. This is not always the case because different
manufacturers use different impedance-rating methods, butsuch variations will not affect what we are talking about.
Let us suppose, therefore, that our 8-ohm black-box speakerhas a d.c. resistance of about 6.4 ohms.
The voice-coil resistance is effectively in series with the"working'' parameters of the loudspeaker, just as is theinternal impedance of the amplifier. And this time it isn't
even an imaginary resistor; it is a real coil of wire thatmeasures 6.4 ohms with a v ).m.
Instead of the circuit of Fig. 1, what really happens
is shown in Fig. 4. The resistance that isolates the loudspeaker from the amplifier is not just R«, but rather R&plus R r. When the two are connected together, neither
the speaker nor the amplifier can distinguish between R*and Ry . The actual damping factor depends upon theSum of these two resistances, not upon one or the other.
Vr

Table 1 shows the specified damping factor of an amPRINTEDIN U S A

Amplifier R(ohms)
CO

output terminals. We will assume that the rated load impedance is 8 ohms in this case, no matter what the valueofIf we were going to use the amplifier to drive a constant-resistance load, it wouldn't matter whether the internal impedance was one ohm or 10 ohms or 10,000 ohms.
But because the amplifier is used to drive a loudspeaker,
the value of its internal impedance becomes a most important factor.
For one thing, a loudspeaker does not present a constantload to the amplifier. An 8-ohm loudspeaker may measure
6 ohms at some frequencies and 60 ohms at others. If theamplifier has a high internal impedance, the voltage at theloudspeaker terminals will go up as impedance goes up andgo down as impedance goes down.
Secondly, a loudspeaker cone has inertia. It has to be
stopped and started and moved back and forth in very
complicated patterns. If the internal impedance of the amplifier is loo high, the speaker will move the way it wants
to move instead of the way that the amplifier tells it tomove.

4
2
1
0.5
0.25
0.125
0.05
0.025
0.01250.0000

Amplifier DF

ActualOver-All DF

12
4
8
16
32
64
160
320
640
Infinity

0.57
0.80
1.0
1.14
1.23
1.28
1.30
1.32
1.33
1.33
1.33aTable ]. The actual damping factor (with loudspeaker connected)
is limited by the speaker voice-coil resistance. Figures are for
8-ohm output terminals to which speaker having nominal 8ohm impedance and 6-ohm voice-coil resistance is connected.

plifier against the actual over-all damping factor for a wide
range of generator impedance values when the amplifier isconnected to an 8-ohm speaker. The actual damping factor
values are computed by adding R and R r, then dividing
by the rated load impedance. In this instance we have usedan 8-ohm loudspeaker with a d.c. resistance of 6 ohms toprepare the chart. The exact figures are not particularly
significant—the point is that the resistance of the speakervoice coil is the limiting factor.
RFV

Note that changing the amplifier damping factor fromunity to 8 makes a substantial change in the actual damping factor, though it is not a 1:8 change but a 1:2 change.
But changing the damping factor from 8 to 16 makes very
little difference in the actual damping factor, and anything
more than 16 has very little effect indeed. If we increase
the damping factor from 16 to 160, the change is effectively less than 10%, not 10 to one.
Conclusions
It should be obvious at this point that the quoted damping factor of an amplifier is important only if the figurelies somewhere below 20 or so. Changing the damping
factor from 2 to 20 does change the performance of theloudspeaker system (for better or for worse, depending
upon the speaker). But trying to prove that a damping
factor of 200 is somehow better than one of 20 is pretty
unconvincing because the effective difference in the particular case cited is only that between 1.25 and 1.32.
But someone is bound to insist that exhaustive tests havebeen made with such and such an amplifier and that a very
high damping factor is better than one down around 10 or
15. "The bass is just a little cleaner, just a little morenatural and open," is the way the argument usually runs.
In a given situation, this may very well be true. RR is a
byproduct of negative feedback. The more such feedback
that is thrown into a power amplifier circuit, the lower thegenerator impedance and the higher the damping factor.
The point is simply that if a lot of feedback has to be used
to lick the distortion in a particular circuit, fine—use it. But
don't believe that the reason it sounds good is because ofsome astronomically high damping factor.
When I get a letter from someone who is worried aboutbuying a certain • amplifier because it has a specified damping factor of "only" 15 or 16, I can't help but remember
an old, old joke. It goes like this:A scientist is giving a public lecture. During the courseof his speech, he predicts that in 100 billion years humanlife will become extinct. A man in the audience, obviously
upset, asks the lecturer to repeat the statement.
"1 said," quotes the professor, "that in one-hundred billion years, human life will no longer exist/'"Oh, thank goodness," replies the man, much relieved.
"I thought you said one-hundred millionl"
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