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Subwoofers
So I am undecided on subs....
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<blockquote data-quote="Electrodynamic" data-source="post: 7429675" data-attributes="member: 548723"><p>There is a common misconception about heavy or big woofers must be “slow” and light or small woofers must be fast. The same thing goes for BL/Mms as an indicator of woofer speed/transient response. At first you think “yeah, that sounds about right!” but all of the latter is incorrect.</p><p></p><p>Breaking it down, force equals mass times acceleration (F=ma). A loudspeaker consists of what – a coil of wire which creates an alternating magnetic field which interacts with a static magnetic field in the gap coupled to a fixed amount of mass. Pass current though the voice coil and the coil moves. And as the current changes the voice coil moves in and out. So motor force (BL) times current (i) equals the moving mass of the driver times acceleration of the driver (a).</p><p></p><p>Now we have BLi=ma. Looking at this new equation we can see that:</p><p></p><p>BL is time invariant.</p><p></p><p>i is the current into the driver (music, test tone, etc) which is an AC waveform which changes with time.</p><p></p><p>m is mass and if this changes as you operate you have a BIG problem! Mass stays the same while in operation.</p><p></p><p>a is the acceleration. This is what we are after. The rate of acceleration <em>is</em> the transient response.</p><p></p><p>If we re-write the last equation using a “C” to indicate what remains constant you get:</p><p></p><p>Ci=Ca or i:: a (the “::” symbol is for proportionality), which shows that the change in acceleration of a driver is strictly a function of the current through the driver.</p><p></p><p>Looking back on the model of a loudspeaker you have a coil of wire wound on a former that attaches to the cone. What does a voice coil look like? How about an inductor? You know those things in crossovers that look like tiny voice coils? A voice coil IS an inductor! An inductor stores energy in the magnetic field. Inductors like to hold current. The higher the inductance the longer it can/will hold current flowing it, which means that the more time elapses before it starts to respond to the amplifiers applied voltage. AKA slower transient response.</p><p></p><p>Here is an impulse graph showing modifications to a speaker and how those modifications have impacted the performance of the driver. The red line is the raw driver. The other two lines are added mass and added inductance.</p><p></p><p><img src="http://www.stereointegrity.com/images/Impulse_response.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p><p></p><p>The blue is added mass. The green is with an inductor in series.</p><p></p><p>The green has delays in the negative and the positive.</p><p></p><p>And here is a graph of the frequency response:</p><p></p><p><img src="http://www.stereointegrity.com/images/Bandwidth.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" /></p></blockquote><p></p>
[QUOTE="Electrodynamic, post: 7429675, member: 548723"] There is a common misconception about heavy or big woofers must be “slow” and light or small woofers must be fast. The same thing goes for BL/Mms as an indicator of woofer speed/transient response. At first you think “yeah, that sounds about right!” but all of the latter is incorrect. Breaking it down, force equals mass times acceleration (F=ma). A loudspeaker consists of what – a coil of wire which creates an alternating magnetic field which interacts with a static magnetic field in the gap coupled to a fixed amount of mass. Pass current though the voice coil and the coil moves. And as the current changes the voice coil moves in and out. So motor force (BL) times current (i) equals the moving mass of the driver times acceleration of the driver (a). Now we have BLi=ma. Looking at this new equation we can see that: BL is time invariant. i is the current into the driver (music, test tone, etc) which is an AC waveform which changes with time. m is mass and if this changes as you operate you have a BIG problem! Mass stays the same while in operation. a is the acceleration. This is what we are after. The rate of acceleration [I]is[/I] the transient response. If we re-write the last equation using a “C” to indicate what remains constant you get: Ci=Ca or i:: a (the “::” symbol is for proportionality), which shows that the change in acceleration of a driver is strictly a function of the current through the driver. Looking back on the model of a loudspeaker you have a coil of wire wound on a former that attaches to the cone. What does a voice coil look like? How about an inductor? You know those things in crossovers that look like tiny voice coils? A voice coil IS an inductor! An inductor stores energy in the magnetic field. Inductors like to hold current. The higher the inductance the longer it can/will hold current flowing it, which means that the more time elapses before it starts to respond to the amplifiers applied voltage. AKA slower transient response. Here is an impulse graph showing modifications to a speaker and how those modifications have impacted the performance of the driver. The red line is the raw driver. The other two lines are added mass and added inductance. [IMG]http://www.stereointegrity.com/images/Impulse_response.jpg[/IMG] The blue is added mass. The green is with an inductor in series. The green has delays in the negative and the positive. And here is a graph of the frequency response: [IMG]http://www.stereointegrity.com/images/Bandwidth.jpg[/IMG] [/QUOTE]
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