Five (5) Audio Myths Dispelled
originally published on AudioXpress
In my spare time I've been known to peruse various websites, newsgroups and other online forums devoted to all things loudspeaker. Over the years I've learned quite a bit; gaining further insights into the art & science of speaker building from both luminary and amateur enthusiast alike. And if you, like me, spend any time following the variegated tracery of threads which make up these various online resources, you'll also know the noise-to-useful-information ratio can be very large indeed.
I've seen it happen often where an idea or concept, lacking little or no technical merit or validity is promulgated as truth. And those seemingly invincible items that pop up year after year, I've elevated to the rank of "myth". I've taken look at some of my favorites under the objective light of hard science and I'd like to share the outcome of my own investigation into these favorite myths of mine.
The Five Myths that will be covered in this article include:
1. Damping Factor
2. Magnetic Shielding
3. Gold is the Best Conductor
4. Bass Reflex Is More Efficient Than Totally Enclosed Box
5. The Perfect Driver
1. Damping Factor
Quite a large amount of online text has been devoted to this item in the forums I mentioned earlier. Reading the various discussions raging back and forth between contributors, the general sense I get is most folk attribute to the contribution to total system damping factor made by an amplifier - and its effect on system performance - far more than should be.
Damping Factor (DF) is defined as the ratio of the load impedance (usually taken as 8 ohms) to source impedance. It is a dimensionless figure of merit and therefore has no units ascribed to it. In practical terms, when applied to an amplifier, it indicates to what degree the amp can dissipate the energy generated by a driver's voice coil as the coil's post-impulse motion decays to zero: thus is the mechanical vibration electrically damped. But focusing solely on DF as determined by an amplifier's output resistance (Rg) is too narrow in scope as it's Rsource, the sum of Rg, cable resistance (Rcable), crossover network component resistance (Rcomponent) and Revc (voice coil resistance) that determines the true DF as seen by the driver. Focusing on Rg alone also ignores the single largest contributor to DF: the driver's voice coil.
To get a clearer picture of DF and its effect on system performance, I ran a series of simulations to determine to what degree various damping factor values as determined by Revc, Rg, Rcable and Rcomponent affect system response performance at resonance frequency.
In the first simulation set I ran I used a test model representing a closed-box system, whose initial design was based upon DF = ∞, Rsource = 0 Ω, where:
Rsource = Rg + Rcable + Rcomponent (Ω)
and a Qtc = 1/√(2), (Butterworth B2 alignment) producing a maximally-flat response, with zero peak at resonance. Although DF is typically specified at a load impedance value of 8 Ω, for my calculations I used Revc = 6.2 Ω, which was the Revc parameter value of the driver I modeled (KEF B139). If you're more comfortable thinking of DF in terms of the usual 8 Ω load, you can convert the given 6.2 Ohm-based Rg figures to 8 Ω based values by multiplying the given values by 1.2903. At any rate, in running the analysis, some interesting trends emerged from the data generated by the simulations.
Fig 1: System response at DF = 1 and DF = ∞
As mentioned earlier, the Rg or amplifier output resistance, in actual practice is only part of Rsource, all three components of Rsource, along with Revc, combine to affect DF. Of all resistance components, however, Revc is by far the largest and therefore has the greatest effect of all on DF. For now, let's focus on Rg alone.
Rsource affects system response by affecting Qec, which in turn affects system Qtc. Rewriting the well-known formula for calculating Qtc from Qec and Qmc, but taking into account Rg, Revc, Rcable and Rcomponent gives:
Qec' = System Q at resonance (fc), due to electrical losses, including Rsource, dimensionless
fc = System resonance of Totally enclosed box (TEB), Hz
Bl = Force factor, Magnetic flux density in voice coil gap * coil winding length, TM
Rsource = Rcable + Rcomponent + Rg (Ohms)
Plugging Qec' (which represents Qec modified to take into account Rsource) into the well-known equation
used to calculate Qtc
Qtc' = Total system Q at resonance (fc) due to both mechanical and electrical losses, taking in to account Rsource, dimensionless
Qmc = System Q at resonance (fc), due to mechanical losses, dimensionless
A cursory examination of these formulae shows that as Rg increases, so too does Qtc and with the increase in Qtc comes an increasing response peak at resonance. And, of course, adding the other two components that make up Rsource, Rcable and Rcomponent, combine to produce even larger changes in Qec, Qtc and system response at resonance.
The question is, at what point does the affect of declining DF becomes audible? Looking at the first dataset, which I generated considering Rsource, it would appear that only in the very worst of cases do these changes enter the realm of possibly audible. And setting the upper value limit of Rsource = Revc is certainly an extreme case!
Fig 2: DF, Rsource and resulting variations in Electrical attenuation, Resonance Peak and Qtc'
DF Elec. Attn. (dB) Rsource (Ω) Resonance Peak (dB) Qtc'
∞ -20 * Log (∞) 0.0000 0.00000 0.7071
1000.0 -60.000 0.0062 0.00000 0.7075
500.0 -53.970 0.0124 0.00000 0.7079
100.0 -40.000 0.0620 0.00060 0.7116
50.0 -33.979 0.1240 0.00270 0.7161
20.0 -26.020 0.3100 0.01580 0.7295
15.0 -23.520 0.4133 0.02717 0.7368
10.0 -20.000 0.6200 0.05676 0.7512
5.0 -13.979 1.2400 0.18422 0.7925
2.0 -6.020 3.1000 0.69477 0.9013
1.0 0.000 6.2000 1.50960 1.0447
Fig 3: Attenuation (dB) vs. Damping Factor
Attenuation = -2.5286e-005 - 8.6851 * ln (DF)
Res. Peak = (0.4094 + 0.3988 * DF) ^ (-1/0.5171)
Fig 5: Qtc vs. Rg (Ohms)
Qtc = (0.7070 * 17.4457 + 1.9938 * Rsource ^ 1.0005)
Qtc = 1.3499 - 0.6422 * exp (-0.7349 * DF ^ - 1.0303)/ (17.4457 + x ^ 1.0005)
Looking where in the Qec' equation that Rsource is positioned tells us that keeping it as low as possible is helpful, but only modestly so given that Revc, under typical circumstances, is much, much larger.
This is key to understanding the true nature of DF is it's the total resistance seen by the driver's motor coil that counts and that Revc is, by far, the largest, single most important contributor to the total resistance value of the amp/cable/component/voice coil circuit. Because the value of Rsource tends to be < < Revc, Rsource doesn't change all that much the degree of damping the driver experiences at resonance owing to its own Revc. Why?
Damping is energy dissipation; here in the form of direct conversion of electrical power into heat, with the end result said energy is no longer stored in the system. Typically, 95%+ of the power supplied by the amplifier winds up as heat generated by the voice coil.
To get a clearer picture where and to what degree dissipation occurs within the amp/cable/component/voice coil circuit, I ran a simulation of a driver based on a circuit, the schematic of which some of you may recognize as one I presented in an earlier Speaker Builder article.
In that article, I demonstrated how to create an accurate model (with both temperature and frequency dependent components) of a raw driver using PSPICE. I've added Rg, Rcable and Rcomponent values, retaining the original model Revc value of 4.15 Ohms, found in that earlier article. I then probed for power dissipation at each of the 4 components to see how and where power was being dissipated.
For those who'd like to experiment with the model using their own circuit editor/analyzer, I've included the netlist generated by PSPICE.
Fig 7: SPICE Net list For Test Circuit
Fig 8: Test Circuit
Once the simulations were run it was easy to see from the generated output graphs that, indeed, the majority of dissipation - and therefore damping - was taking place in the Revc component of the circuit, i.e., the driver's voice coil. In the graph, the topmost trace is that of Revc, which clearly indicates Revc is that point in the circuit is where the most power is being dissipated.
Fig 9: Power dissipation amongst the Rsource components
By this point in the analysis it should be clear, where it comes to DF that real control lays with the driver's voice coil Revc and not with Rsource. However, there is another reason for keeping Rsource as low as possible. That's found in looking at its effect on something entirely separate from DF: dB SPL loss, where:
Here, Zevc represents the frequency-dependent impedance of the driver's voice coil, in Ohms. This equation illustrates that increasing Rsource results in greater dB SPL losses. Given this fact, best practices dictate keeping Rsource as low as possible.
From my preceding investigation I think it fair to draw the conclusion that amplifier DF has very, very little effect on the total circuit DF and what little effect it does have occurs only in the very worst of cases.
For more related reading material on Damping Factor, check out: Damping Factor: Effects on System Response
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