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Inductance Low inductance speaker cables occur because of some magnetic field hocus-pocus. But in order to understand what is occuring, it will be necessary to delve into where the inductance comes from in the first place. If we look at a single wire carrying current in a space free from any other influences, we can then ascertain the origin of the wires inductance. We must first make the distinction between the flow of a steady direct current, and one that alternates it's polarity, like an audio signal. A direct current flow is a steady unchanging current flow, the magnetic field due to the current flow is steady and unchanging. There is virtually no effect on the current flow distribution due to the magnetic fields presence. However, once we start looking at the AC situation, representing music signals, now the magnetic field has an influence. In order to see why, lets examine the magnetic fields as we alternate the current. If we start from 0 current flow and then procede to the beginning of positive current flow, we go from a condition of zero magnetic field, to an expanding magnetic field. As the current flow increases, the magnetic field increases and expands, the field coming into existence within the conductor, and expanding within it, and finally creating magnetic field lines of force outside the conductor. One could imagine these magnetic lines of force as expanding from the center of the conductor, and increasing until they expand out into the space surrounding the conductor. At the peak of the AC waveform, the current flow will be at a maximum (for a resistive load, lets not get into reactance quite yet), and the magnetic field will have reached it's furthest extension from the conductor. Now, as the current flow decreases due to the AC waveform now heading toward zero level again, the magnetic field due to the current is decreasing proportionately to the decrease in current flow, that is, the magnetic field is collapsing from it's peak extension point, until as the waveform goes to zero, the current goes to zero, and the magnetic field collapses to zero. The swing of the signal into the negative region is just the smae as the above description, except the polarities are reversed, As with many things, there always seems to be a reaction to an action, much of physics revolves around this. As the magnetic field is expanding through the conductor, it will tend to generate a current flow that is the opposite of the original current flow. Any time lines of magnetic flux cut through a conductor, they generate a current flow. Fortunately for us, this current that is generated is not as strong as the original current flow itself, or there would be no output signal at all, the self-inductance of the wire would cancel out the original current. The amount of current generated by magnetic flux lines cutting through the conductor is proportional to the rate of flux change, hence the faster the currents alternate (the higher the frequency), the more of this self-induced back current is generated. Thus, as the frequency goes up, the wire tends to impede the flow of current more and more, as the induced back current gets greater and greater. This is called the self-inductance of the wire, and does not require another wire to interact at all for the self-inductance to manifest. So how do loudspeaker cable geometries affect this self-inductance, and reduce the inductance of the overall cable? Well, when you place another wire nearby carrying current in the opposite direction, it also has a magnetic field that expands into the space around the wire, only it has the reverse polarity of the wire next to it. If the two wires are very close, the effects of the self-inductance are nearly canceled out by the mutual inductance of the two wires. The closer the second wire gets to the first wire, the closer it comes to completely cancelling the self-inductance of the first wire with the reverse polarity mutual inductance between the two conductors. Of course, the reverse holds true for the second wire with respect to the first wire, it too cancels out the self-inductance of the second wire via the mutual inductance of the two wires. BTW, for the inductance aspect, it makes no difference if the wire is solid, or is stranded, the magnetic field still expands from the center of the stranded bundle, and expands outward through all the stranded wires. Individually insulated wires in a bundle, act just like a solid wire, except for any loss of cross-sectional area due to the insulation. In the real world, a bundle of insulated wires can not be easily be kept completely in the same location with respect to the whole bundle, and then it will react slightly differently, see below. So the more intimate the current carrying conductors, the lower the inductance. For a simple construction, the ultimate expression of this is two wide flat strips of conductor, with just a minute amount of insulation separating them from each other. You can also see that if you had a multiconductor ribbon cable, and alternated the hot and ground currents in the wires that constitute the ribbon, that this would cause the mutual inductance to couple from both sides, (except for the end wires), and would further reduce the self-inductance of all the individual wires. The first mentioned two wide flat conductors could become a multilayer sandwich, which would gain the same benefit that the multiple conductor ribbon cable has and further still reduce the total inductance of the speaker cable. There are other ways to address the total inductance of a speaker cable. One way is to attack the self-inductance of the wire itself, instead of depending on the mutual inductance to reduce it. By running many insulated runs of wires, the inductance of all the wires is effectively in parallel, so that the inductance can be reduced by the amount of individual wires present for each polarity. In order for this to be truly effective, the wires must not be close to one another, or the mutual inductance, being of the same polarity, will begin to add to the self-inductance, and actually make things worse. Then there is the Litz construction, which has been touted as being effective against skin-effect, which is a different beast than self inductance (I will cover that some other time), but it also helps reduce self-inductance. This is accomplished by having the individual wires take turns being on the inside and on the outside at any given point along the length of the wire. Despite the fact that the wires are in close proximity, and that they are being affected by a similar magnetic field as a solid wire, since they trade-off along the length of the conductor bundle, no single strand is always on the inside being exposed to the maximum amount of magnetic field. So even though a Litz construction is designed for the skin-effect, it will help with self-inductance some as well. Of course, you can combine these techniques and use more than one at a time. When you braid your CAT5 cable pairs, the twisted pairs achieve a fairly intimate spacing, and then, these pairs are braided together, weaving the pairs in and out, in psuedo-litz construction. You could take this mixing of techniques to extreme levels, by using the twisted pairs, then braiding them, then taking the braided bundles and twsiting them together, and then braiding the twisted pair of bundles together again, until the whole assembly was too large and stiff to do anything to, or your fingers were raw and bleeding, which ever comes first! I hope this helps your understanding of speaker cable total inductance. BTW, the single biggest improvement you could make to your homemade speaker cable is to either make another cable for the other half of the bi-wire, or seperate the two bi-wire sections. Much of the benefit of bi-wiring is lost if you interweave the two bi-wire cables, all in one jacket bi-wire cables are a convenience, and not the best way to do it. See my explanation of bi-wiring below, perhaps this will help you understand it better too: Bi-Wiring 101 In order to explain how bi-wiring works, it is necessary to explain a bit about how crossovers work. It will also be necessary to contemplate more than the usual voltage output of the crossover sections, so do not assume that if you know the basics for crossovers, that you will know what this will be all about. Let's look at a simple two-way system with a first order crossover, the simplest crossover and system we can examine. It will be relevant to other more complex systems, so once you understand this one, the others will fall into place. We will not address the issues of tweeter level padding, response EQ, etc., just the basic crossover function itself. In a simple first order crossover, there is an inductor in series with the woofer, and a capacitor in series with the tweeter. These two components comprise the crossover system. Normally, these two components are connected to the same input terminals on the speaker, in parallel. Hence this type of crossover topology is called a parallel type crossover. A full range voltage signal is sent down a speaker cable, and appears at the single pair of input terminals. A current is drawn based on the input impedance of the speaker system as a whole, which in most cases, will have a relatively flat impedance curve once we get above the bass resonance region, where the impedance will be dominated by the cabinet design resonance's. If we say that (for purposes of this discussion) the overall impedance of the speaker in the midrange and on up is relatively flat, then a consistent amount of current will flow through the single speaker cable all across the audio band. So there are several elements to the total circuit formed by the amp output terminals, the speaker cable, and the speaker system and crossover network. A signal appears at the amp terminals, represented by a voltage, the impedance of the speaker system causes it to draw an amount of current proportional to it's impedance for a given drive voltage, and this current flows through the speaker cable. Now in order to examine what happens when we bi-wire, it will be necessary to go into some of the detail as to how a crossover "crosses over". If we look at just the woofer, and it's series inductor, the inductor provides little impediment to low frequencies traveling through the inductor, and a high amount of impediment to the higher frequencies. Looked at another way, the inductor impedes the highs but not the lows. If we examine an impedance curve of just the woofer with its series inductor, we would see that the impedance was pretty much just that of the woofer in the low frequencies, and would rise with frequency as the inductor impeded more and more of the highs. For this situation with just the woofer, for a given voltage drive level, a certain amount of current would be drawn at low frequencies, and this amount would decrease as the frequency went up, due to the rising impedance. If all that was hooked up to the amp was the woofer and it's associated inductor, then the current flow in the single speaker cable would follow the impedance curve, a certain amount of current flow at low frequencies, tapering off at higher frequencies. Perhaps a glimmer of the true situation with bi-wiring is beginning to appear. Now let's just look at the tweeter, and it's associated capacitor in series. At low frequencies, a capacitor tends to impede the flow of current, and at high frequencies, it provides little impediment. Hence, when we hook up just the tweeter and it's capacitor to the amp terminals through the single speaker cable, there is little current flow at low frequencies, and an increasing amount as the frequency goes up. At some higher frequency, the current draw is determined by the impedance of the tweeter alone. Now just to make sure that it is understood, it is the current flow through a dynamic driver (one with a magnet and a voice coil) that causes it to move. A voltage applied that had no current capability would not cause any movement. This means that in order for the voltage at the amp terminals to cause a speaker to move, it must have a relatively low source impedance, so that when a given voltage appears at the amp output terminals, a given amount of current can flow into the load's impedance. That is why when the crossover components impede the current flow, they cause the output of the driver to drop off, hence the crossover function is achieved. Note that the woofer and it's associated inductor, and the tweeter and it's associated capacitor will function independently, they roll-off the frequencies out of the driver's operating band without regard to whether or not the other half of the crossover is present or not. When both sections of the crossover are present, and connected in parallel, the overall impedance curve looks relatively flat, as when the tweeter section has it's impedance going up in the low frequencies, the woofer has it's impedance going down. At the crossover point they are more or less equal, and this is the point in frequency at which the impedance's of the two sections in parallel equal approximately half that of either section alone. This is how two 8 ohm drivers can be connected together through a crossover, and not equal a total load of 4 ohms. By now, you should be getting the idea about bi-wiring. Instead of one speaker cable, or just one of the drivers and it's associated crossover component being connected to the amp's output terminals, two separate speaker cables are connected to the same amp output terminals and run to the now separated crossover sections. With different impedance's being presented across the audio band, each cable carries a different signal than a single speaker cable. The separate cable for the woofer carries mostly the LF currents, and the separate cable for the tweeter carries mostly the HF currents. This is due to the differing impedance's we discussed above. Now if all you think of is the voltage at the amp terminals, and how the two cables are carrying the same voltage to the woofer and the tweeter sections, then it still may seem that the same signal is being delivered to the drivers as through one speaker cable. IF the speaker cables were perfect, and had zero impedance, infinite mass, and no digressions from ideal LCR behavior (DA, DF, hysterisis, etc.), then it may be that this would be the case. Since the cables we have available to us are not perfect, there are losses in the cables. The $64,000,000 question is, how much does the real world speaker cable compromise the performance of a speaker compared to bi-wiring? To make this easy to figure out, we will ignore the effects of inductance and secondary effects, and focus strictly on DCR effects. Let us assume that a cable sufficiently large enough to keep speaker system impedance variations from affecting the amplitude response by more than 0.1 dB was used, meeting the Krueger criteria. In many cases, this is a very large cable, usually at least a 14 gauge, and often 12 gauge OR LARGER.
For a copy of the Krueger criteria see: http://x42.deja.com/[ST_rn=ps]/getdoc.xp?AN=450322078&CONTEXT=927059192.1901920287&hitnum=6
(I should warn that I do not agree entirely with Arny's criteria, it completely ignores inductance, which typically gets worse as a ratio of DCR to HF impedance of the cable as the gauge gets smaller, or larger zip cords) How quick do the gauge requirements add up? If you have only 10 foot cables, and a speaker with a minimum Z of 6 ohms, then a 14 gauge wire is necessary to prevent any more than a 0.1 dB amplitude variation due to the cable DCR. If the speaker Z minimum hits 3.7 ohms, you are now up to 12 gauge. Anything longer in terms of the speaker cable, or lower in terms of the Z, will require larger than 12 gauge to reduce the amplitude variations due to voltage drops to less than 0.1 dB. For a single speaker cable, lets look at a simple signal containing only two frequencies: 100 Hz, and 6 kHz. (As a point of information, let's say that the crossover point is 3 kHz, a common crossover point for a 2-way system) In the single speaker cable that meets the 0.1 dB criteria, a lot of current will be drawn at 100 Hz to feed the woofers demands. This will cause a voltage drop due to the finite amount of resistance in the cable. While the loss of 0.1 dB of woofer output may not seem to be a problem, the current draw at 100 Hz will tend to modulate the 6 kHz signal. How much distortion will this generate? To cause a 0.1 dB change, the signal is being affected at levels of approximately -40 dB down from nominal. If the 6 kHz signal is modulated by the 100 Hz signal by that amount, the IM distortion would be on the order of 1%. These are ball park numbers, not intended to be absolute. This is a distortion that would be reduced by the amount of LF current reduction in the tweeter cable, typically 26 to 36 dB lower in level. This would reduce the distortion from borderline audibility to very likely not audible. If we were to look at the simple change in DCR from merely doubling up on the cable, then distortion would only go down 6 dB, from halving the DCR and nothing more. Of course, once we start using real music, with more than just two frequencies, and real world cable situations that might have even more DCR, and the inductance differences between a single zip cord and two high performance speaker cables, the amount of distortions in a single speaker cable go up considerably, and the amount of reduction in distortion is increased for the bi-wire comparison. This means that we might be into 2% IM or more, and with multiple frequencies, which make it even worse sounding. All of the above totally ignores any potential magnetic field interactions, many of which would be time delayed and would smear out transients and large signals. The magnetic field distortion reduction would come from the separation of the LF currents and the HF currents.
The time delayed and resonance associated signature would tend to make these distortions even more noticeable than the self-IM of the cable due to voltage drop. I think it is easy to see that a multidriver system with higher order crossovers will react similarly to this very simple first order two-way system that has been analyzed. It is interesting to note that higher order crossovers tend to have a similar input impedance for each section as a first order, and it is the output signal of the various sections of the crossover that are made to roll off steeper. In essence, the reductions in current for each cable in a bi-wire pair will be at a 6 dB/octave slope almost regardless of the crossover order. AND: Bi-wiring is accomplished via separate pairs of terminals on the loudspeaker system, typically one pair for the woofer, and one pair for the tweeter or midrange and tweeter. They are completely separated electrically from one another. The normal function of a loudspeaker crossover is to guide the proper frequency's to the proper driver. Lows to the woofer, and highs to the tweeter. This is done in part for protection from the division of labor that has occured with two disparate speakers: tweeters will be damaged or destroyed if exposed to low frequency's and woofers just heat up when exposed to the higher frequency's, as they are too massive to respond at all. The other function that a crossover provides is in allowing the two speakers to blend together, to mesh with one another to become a single apparent sound source. They can also provide some passive EQ of the drive units, as long as there is excess energy to throw away. The fundamental way a loudspeaker crossover works is to vary the impedance seen by the speaker and by the power amplifier. In the case of the woofer, the crossover network for it has a very low series impedance at low frequency's that gets gradually higher and higher in impedance between the amp and the speaker at higher frequency's. For very low frequency's, there is lots of current flow to the woofer, and for higher frequency's, there is little current flow due to the much higher impedance. In the case of the tweeter, at low frequency's the series impedance is very high and very little current flows, and as the frequency goes higher, the impedance of the crossover network gets lower and lets through more current. The situation is such that when the full range musical signal is applied to the terminals of a full-range speaker system, the woofer only gets sent low frequency signals, and the tweeter only gets sent high frequency signals. Once the crossover networks have been electrically separated, they still continue to function in the same manner, having a low impedance in their passband of application. This means that if separate speaker cables are hooked up for the woofer and it's portion of the network, and the tweeter, and it's portion of the network, not only have the speakers and the frequency's directed and divided for them, but the two separate speaker cables will now also carry different signals, the woofer cable mostly the lows, and the tweeter cable mostly the highs. Once the highs and lows have been separated in this fashion, the strong current pulses and surges that a woofer demands when reproducing bass or drums will not interact with the delicate sounds of a flute or cymbal. The magnetic field of the low frequency signals cannot modulate or interfere with the highs, and to a lesser extent, the reverse is true. Now that the low and high frequency signals have been divided among not only the speaker drivers, but the speaker cables, these cables can be more specialized for their intended purpose. The woofer cable can concentrate on low DCR, and not have any big concern for extremely low inductance, the tweeter cable can be designed for very low inductance, and not as concerned about total DCR. Using one much larger unsophisticated cable to achieve the same thing as bi-wiring is just not possible, the separation of work has not occured, and the ability to optimize each separate run is not available. Additionally, as the gauge of a wire decreases (wire gets fatter) and the spacing between the pair of wires that constitute a speaker cable gets greater, the inductance tends to go up. Using one larger unsophisticated cable actually makes things worse for the tweeter, as even though the DCR has gone down and the woofer gets more energy compared to the thinner single cable, the tweeter now gets less energy in the extreme highs. The net result is a shift in the tonal balance. The current path's I describe can easily be plotted, measured and verified by any speaker or cable engineer. There is absolutely no doubt whatsoever about their existence or validity. In point of fact, properly implemented bi-wiring has benefits that can not be achieved by a single unsophisticated cable or even a single exotic cable.
------------------------------------------ Jon Risch
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