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Damping Factor

Previously, you read about the output impedance of an amplifier. The damping factor is closely related to the output impedance. Amplifiers with low output impedance tend to have a high damping factor.

The damping factor indicates the ability of an amplifier to resist a change in it's output signal. If an amplifier has a very low damping factor, the speaker load (or any load - like a resistive dummy load) can cause the output to differ (possibly audibly) from what it's intended to be. For virtually every amplifier made, the damping factor is easily high enough to prevent audible changes in the output signal. Some people say a damping factor of 200 is the minimum acceptable damping factor. Others say it's 100. there are even those that say a damping factor of 50 is OK. I've tried inserting a series resistor with speakers and could hear no audible difference at a damping factor of 50. Around a damping factor of ~25, I started to hear a difference with 'some' speakers. At around a damping factor of 10, the difference was significant enough to be heard with virtually every speaker. You may think it always sounded worse with a low damping factor. Well, not always. Some speakers (mostly high frequency speakers) actually started to sound a little better (probably from a change in the frequency response which was due to its impedance curve). Of course, some speakers sounded worse with the low damping factor. In virtually all cases, the change in sound quality was a 'softer' sound. For very low damping factors, the punchy bass was significantly reduced but the bass sounded smoother (which may or may not be a good thing - depending on your taste in music). Now, I'm not saying that the 'smoother' or 'softer' sound was better (because the change in sound IS a type of distortion). I'm just trying to let you know how the sound changed with the low (extremely low) damping factor.

Two different ways that the damping factor can be observed:

Method 1:
As was mentioned above, the damping factor describes how well the amplifier maintains the desired output voltage under varying loads. An amp with a HIGH damping factor will maintain virtually the same output voltage whether it's driving a 4 ohm load or has no load connected to its output terminals. An amp with a LOWER damping factor will have a GREATER voltage drop when switched from no load to a 4 ohm load. Keep in mind that we are only talking about a few millivolts difference between the output voltage when loaded or not. Nothing to worry about with either amp. This type of change in output voltage would generally be observed on the test bench with a test tone. Keep in mind that a low damping factor for a 'real world' amplifier would be around 50. Nothing nearly as low as what I used in my testing (mentioned earlier).

Drag your mouse over the picture below. You'll see how the voltage drops slightly when the speaker is connected to the amplifier.This amplifier would have a relatively high damping factor. You may have to leave your mouse over the diagram until it finishes loading. Clicking on the picture will optimize it's position.

Method 2:
Since speakers are reactive (especially subwoofers), the amplifier has to be able to absorb the out of phase voltage from the speakers to prevent the signal at the amplifier's output terminals from being distorted. If you were driving a set of speakers that used passive crossovers to split the signal between the high and low frequency drivers (speakers), all of the speakers would get their signal from the same place (the input terminals of the crossover). If the amplifier had a very low damping factor, the out of phase voltage would cause the signal at the amplifier to change slightly. Since the high frequency and low frequency speakers are driven from the same point, the high frequency drivers would receive a slightly distorted signal. If the amplifier had a high damping factor, the woofers would have less of an effect on the signal which would reduce the distortion at the amplifier's outputs (and also at the input of the crossover). This means that all of the other drivers would get a 'cleaner' signal. Now you should keep in mind that the amplifier's feedback circuit, which for the most part determines the amplifier's damping factor (in solid state class A and class A/B amplifiers), is using the signal at the amplifier's output terminals to determine the level of error correction needed. This means that as soon as you start to add anything between the amplifier and the speakers, the amplifier can not compensate for the added components. This means that the damping factor starts to fall as soon as you connect a length of speaker wire between the amplifier and the speakers. Longer runs of speaker wire will cause the damping factor to fall more than short runs. If you have a long run of speaker wire, you can compensate somewhat by using a larger gauge of wire. In the calculator at the bottom of this page, you can see how much the damping factor is effected by the speaker wire. Again, keep in mind that as long as the damping factor remains above a certain value, the change in damping factor won't generally cause any audible changes.


Damping Factor Tests

Standards:
If you are going to test more than one amplifier, you should adopt some standards. You should pick a single frequency or a defined set of frequencies. You should also pick a load with a commonly used impedance (such as 2 or 4 ohms). For this example let's say that the test frequency is 50 hertz and the test load's impedance is 4 ohms.

Testing:
For this test, you want to drive the amplifier to a sufficiently high level to produce large numbers. Since your test equipment has a limited number of decimal places, the larger numbers will help increase the accuracy of the tests. You will drive the amplifier to a level which will be below clipping when loaded with the test load. You must be absolutely sure that the level of the input signal is not changed throughout the test procedure. Measure and make note of the output voltage of the amplifier with no load. Connect the 4 ohm load to the amplifier's output terminals and measure the output voltage again. Make note of it. Please note that the voltage measurements should be taken as close to the amplifier as possible. OK, enough of that.

Example:
For this example, we will use the numbers from the 'output impedance' page. If we know the output impedance of an amplifier and the load that it is going to be driving, we can find the damping factor by dividing the load impedance by the output impedance of the amplifier. By using the output impedance of 0.01 ohms (that we calculated on the output impedance page) and a 4 ohm load, we get 4/0.01 which gives us a damping factor of 400. If we were going to drive a 2 ohm load, you can see that the damping factor would fall to 200.

Since the manufacturer usually doesn't usually include the amplifier's output impedance and may not supply the damping factor, you can find it with minimal test equipment.

We will use the formula: damping factor = Eno load/(Eno load-Eloaded)

DF = Eno load/(Eno load-Eloaded)
If Eno load = 20 volts
and
Eloaded =19.95 volts

DF=20/.05
DF=400

The Damping Factor at 50 hertz is 400 when driving a 4 ohm load. The same damping factor as when we used the output impedance and a 4ohm load.

Speaker Wire and Damping Factor:
Amplifiers with a HIGH damping factor have a LOW output impedance. As soon as you start adding speaker wire between the amp and the speakers, the damping factor at the speakers starts to fall. An amplifier with a damping factor of 400 into a 4 ohm load, has an output impedance of .01 ohms. If you use 5ft of 14g speaker wire, the total resistance of the wire is .016 ohms. If you add this to the output impedance of the amplifier, you have a total output impedance of .026 ohms. This reduces the effective damping factor to 154. Longer runs of speaker wire will reduce the effective damping factor even more.

NOTE:
Many people test the damping factor at 50 hertz into a 4 ohm load. You can make the test at any frequency that you like and with any load. When comparing the damping factor of one amplifier to another, you must know the frequency at which the test was performed and the test load's impedance. Otherwise, you may be comparing apples to oranges.

Transistors vs Tubes:
In general, 'solid state' amplifiers (transistor amplifiers) tend to have a higher damping factor than tube amplifiers. Transistor amplifiers drive the speakers directly and may have a damping factor greater than 200. Most tube amplifiers drive the speakers through a large transformer which tends to lower the damping factor of the amplifier. The damping factor of top notch tube amplifiers may be as low as 20. Please understand that the lower damping factor is NOT an indication of the quality of the amplifier or the sound quality that you will get from it. Low damping factor amplifiers can sound really good, easily as good as amps with higher damping factors.

External Servo Feedback Compensation:
There are a few amplifiers which claim VERY high damping factors (over 2000). These usually employ a second pair of wires which connect to the actual speaker terminals. These feedback terminals are not the speaker output terminals. These are the servo feedback wires. Virtually all transistor amplifiers use lots of feedback. The large amounts of feedback are responsible for the high damping factors. As I said before, the speaker wire causes the damping factor to diminish. The extra pair of wires going out to the speaker allows the amplifier to 'see' and correct for any loss in the speaker wires. This causes the damping factor to be maintained. As to the amplifiers that claim a damping factor in the thousands, well... I'm skeptical to say the least but I do believe that it is possible to maintain a high damping factor at the speaker (even through long runs of speaker wire) when using the external feedback circuit. If you missed the 'servo' page, go back and read more on compensation circuits.

Switching Amplifiers:
Some switching amplifiers like Class D amplifiers have a lower damping factor than their Class A/B counterparts because the output of the amplifier has to pass through an inductor. Since the inductor is wound with copper wire which has resistance (albeit a very low resistance), the damping factor is reduced. Generally the lower damping factor is completely inaudible. Switching amplifiers with higher damping factors typically take the feedback signal from the speaker terminal side of the output filter inductor instead of the output transistors side of the output filter inductor. This gives the feedback servo circuit a greater ability to maintain the correct output, increasing the damping factor.


This program will show the effect that the speaker wire has on the effective damping factor.
Input Section
Amplifier Power Output? = Watts
Length Of Speaker Wire? = Feet
Speaker Load? = Ohms
Rated Damping Factor Into Above Load? =  
Speaker Wire Gauge? =  
Output Section
Resistance In Wire per Foot = Ohms
Resistance In Wire = Ohms
Amplifier Output Voltage = Volts
Current Flow Through Wire = Amps
Voltage Loss In Wire = Volts
Voltage Reaching Speaker = Volts
Power Reaching Speaker = Watts
Amplifier Output Impedance = Ohms
Output Impedance With Speaker Wire = Ohms
New Damping Factor Due To Speaker Wire =  


 

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