Theory Page Discussion Page Cable Damping Factor

Absolute control over the driver diaphragm and how high should the amplifier's damping factor be?

Peter Strassacker Dr. Peter Strassacker
involved in loudspeaker design since 1977
Books on material and field research
speakers like Lagrange 98, Laplace XT, Sub 10-60

Peter Strassacker interview by
Dennis Frank (12/2004).
 

Dennis:
Peter, our customers fancy amplifiers with a high damping factor. How high should the damping factor be?

Peter:
That's a matter of controversial discussions. Our Cable and Damping Calculator gives you some information. To really understand the subject we should first think about what damping factor means. I am giving you a simple example using a subwoofer.

The following equivalent circuit will help to understand the interrelations: Ersatzschaltbild
Picture 1: Equivalent circuit: amplifier, cable and loudspeaker are separated by green lines.

The damping factor D of an amplifier indicates how strong the amplifier's output voltage is effected by load of the loudspeaker. The damping factor depends on the impedance of the loudspeaker RL; from it follows that:

D = RL / Ra, whereby Ra is the output resistance of the amplifier.     (equation 1)
It's also possible to calculate the output resistance of the amplifier:
The output resistance depends on the loop amplification Vu, the emitter output resistance remittance, the resistor Re of the emitter branch, the negative feedback resistors R1 and R2, determining the voltage amplification of the main amp:
Ra = k * (remittance + Re) * (R1 + R2) / (R1 * VU)     (equation 2)
Whereby k is a coefficient indicating 1 for a class B amp. The coefficient for a class B amplifier is 0.5, since both the negative and the positive are conducting simultaneously.

Dennis:
Well, I am now in a position to calculate the damping factor. But I can look up this value in the technical data sheet that usually comes with an amplifier; but what does it mean?

Peter:
One has to look at it as a whole; the damping factor alone doesn't mean anything; it can be calculated directly from the amplifier's output resistance Ra. For the loudspeaker, however, the total sum of resistance Rges is important, comprising the additional resistance of the cable Rk and the DC resistance of the loudspeaker's voice coil Rs (the reactance L we neglect here to simplify matters):

Rges = Ra + Rk + Rs     (equation 3)
To use an example:
--- Properties of the amplifier --- -- Properties of cable and voice coil -- Result
Damping factor
(related to 8 Ohm)
output resistance
of the amplifier
Impedance
of the cable
DC resistance
of the loudspeaker
Total resistance Rges
1000 0.008 Ohm 0.1 Ohm 5 Ohm 5.108 Ohm
200 0.04 Ohm 0.1 Ohm 4.968 Ohm 5.108 Ohm

In other words: if in both configurations (line 4 and 5 in the table) only the resistance differs (resulting in a damping factor of 1000 or 200, causing the loudspeaker's DC resistance to differ by barely 1%), then there won't be any sonic difference.

Dennis:
But we can clearly hear that an amplifier with a high damping factor somehow sounds more realistic and lively?

Peter:
That's correct; but, there is a totally different reason for this. We have to look at the bandwidth of the amplifier. The bandwidth is dependant on the loop amplification g. The loop amplification g indicates how much more the amplifier would amplify the voltage if there wasn't a negative feedback by means of resistors R1 and R2:

g = (R1 * VU) / (R1 + R2)     (equation 4)
The expression 1/g is contained in equation 2 (the green area); that means that an amplifier with low output resistance (i.e. high damping factor) possesses a high g.

Amplifiers with a high g also have a high bandwidth, since a phase stable amplifier has to be designed in such a way that up to the cut-off frequency g decreases by a factor of 10 (i.e. 20 dB) per frequency decade. (Here is a PDF file covering the somewhat difficult Theory 1, the important diagram (picture 16) is to be found in Theory 2).

In a nutshell:
By design, amplifiers with a high damping factor also have a high bandwidth. This higher bandwidth results in the generation of more harmonics (by means of noise and intermodulation distortion). This in turn is perceived by the human ear as a particularly clear and crisp sound. Many recording studios add harmonics by using an exciter (a professional device for sound enhancement). However, the added effect should be subtle, otherwise the sound is just horrible.

Dennis:
So, a high amplifier damping of more than 100 doesn't contribute that much to a clear sound as originally anticipated?

Peter:
That's right; the damping factor should be around 100, but higher values are not helpful in creating a realistic sound. Additional harmonics and noise are in fact the determining factor in creating a sound that are perceived by the listener as fresher, clearer, more realistic and believable, especially in direct comparison.

Dennis:
And how do we get to absolute control given the choice of loudspeakers?

Peter:
A loudspeaker should be chosen with a low total electrical loss Qeges. Basically, a loudspeaker with a low electrical loss Qes is appropriate:

Qeges = Qes * (Ra + Rk + Rs) / Rs     (equation 5)
whereby Ra is the output resistance of the amplifier, Rk is the DC resistance of the cable and Rs is the DC resistance of the voice coil. (Rs is also often called DC resistance of the loudspeaker Re; Ra = RL / D, this can be derived from equation 1).

Dennis:
Which parameters do I have to pay attention to and are there any loudspeakers with low Qeges?

Peter:
The Q factor of the amplifier should be 100, the cable shouldn't have much more than 0.1 Ohm DC resistance (for 8 Ohm speakers), otherwise a low Qes for midrange and bass drivers are important. A low Qes can be found:
- especially for some midranges - in large bass horns
- in specially tuned subwoofers, like Alcone Sub 10-60
 

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