In Admiration of Music

(and the Dali motto)

 

 

 

Index

  

 

Tradeoffs in Stereo Systems

 

From an engineering perspective, choosing the parts of a stereo system is an unusually interesting problem.  Like camera equipment or mountain bike suspensions, there are a wide range of designs for different purposes.  Unlike say, optics, there are not well defined and objective performance criteria for assessing how well stereos perform.  A remarkable amount of dubious information is therefore sloshing around and things are further complicated by the human ear's tremendous powers of discrimination.  Effects which are negligible in other areas of analog engineering are quite audible and therefore important in audio design.  Even if you're an electrical engineer who's used to designing high performance analog RF components, audio engineering requires a change in mental gears.  Things which are negligible almost everywhere else matter in audio.  Unfortunately, it also turns out a lot of things which don't matter are claimed to be significant.

 

This page has one simple purpose, which is developing some rules of thumb with regards to setting up a stereo.  A good system costs a few thousand dollars, so doing some thinking about how best to spend one's money and set up what you buy is well advised.  Exacting precision in analysis is not the goal here—first order approximations are good enough for rules of thumb—but the emphasis is very much on the pursuit of the highest fidelity possible within a given budget.  In practical terms, what distinguishes hi fi systems is the precision with which they render music and much of the audiophile experience is one of seeking out and enjoying details within music.  Any $100 sound system allows one to push a button and have sound come out.  What makes hi fi systems hi fi is clarity, accuracy, transparency, and control of transients in sound.  Ideally, listening to a stereo is no different from listening to a concert in a well designed concert hall or chamber music in a nice room.

 

In engineering terms, the most important parts of a stereo are the speakers and power amps.  Even very good speakers are miserable at turning electricity into sound.  In a speaker with a 92dB sensitivity, 99% of the power the amp delivers to the speaker is dissipated as heat.  Most speakers fall in the range of 90 to 88dB sensitivity, which means more like 99.5% goes to heat.  Additionally, speakers are some of the most ill conditioned loads around, meaning power amps have to contend with significant changes in load phase and magnitude and back EMFs as well as the speakers' miserably low load impedance.  This means the power amp matters.  Specifically, it is easy to build a powerful amp and it is easy to build a precise amp.  Building an amp which is both powerful and precise in the face of an ill tempered and snarly load like a speaker is not so easy.  And, not surprisingly since they connect the power amp and the speakers, speaker cables matter.  In comparison, driving the inputs of a pre or power amp is trivial.  The load impedance is high and has much less phase and relative magnitude variation than a speaker.  This is not to say sources and preamplifiers don't matter, just that they matter less than how the speakers and power amps are wired up.  Similarly, interconnects between source, pre amp, and power amp have much less effect on the overall sound than speaker cables.

 

The first rule of thumb in choosing a stereo is therefore simply to focus the majority one's shopping, research, analysis, and money on speakers and power amps.  My own personal experience is if one is in pursuit of hi fi, most speakers leave a lot to be desired and most power amps are adequate but unexceptional.  There's amazing variability in price performance.  Some US $5000 speakers are much worse than US $1250 speakers and a well chosen US $850 power amp can sound indistinguishable from a US $6000 power amp.  Some discriminating auditioning is therefore well advised.  Audio stores' practice of wiring a bunch of sources, amps, and speakers up to a switch is great for doing quick comparisons.  But it also puts a lot of wire and componentry in the signal path between the power amp and the speakers.  This does the neither the amp or the speakers any good, particularly as stores which demonstrate speakers in well set up biwired or biamped topologies are few and far between.  A fair listening test therefore means getting the power amp off the shelf and wired directly to the speakers with cables hopefully not longer than 1.5 meters.  This in turn requires a store which is willing to rearrange things for you, but the variety of sound qualities in speakers and amps is large enough making good choices without such full on listening tests is quite difficult.  It also, of course, helps if you know what you want.  In its simplest form, hi fi comes down to having a sense the stereo is actively playing music the way musicians do, rather than following along with what the CD player sends out.  A good system leaves one with the feeling the speakers and amps are right where they should be right when they should be.

 

Two observations stand out to me in my listening experience.  One is a surprisingly large fraction of speakers only sound their best with particular types of music, at particular volumes, and within a relatively small sweet spot of listening positions.  This is fine if you have narrowly defined tastes which match the speaker, but good equipment plays everything well.  The second observation is that as components become better, the tolerance for bad components actually increases.  For example, a poor cable can kill an adequate speaker and an OK amp, but can be acceptable on the same speakers with a good amp.  A corollary to this is biwiring and biamping make less of a difference on higher end components than they do for less expensive equipment.  This results in situations where relatively inexpensive biamps outperform considerably more expensive biwires.  In particular, my experience is throwing money into a high end biwire makes little sense because the system's performance is limited by the speaker cables and not the components.  Passive biamping removes a noticeable amount of the cable limitation by letting you put the amps next to the speakers.  Active biamping goes a step further by removing the passive crossovers within the speakers.

 

A goodly fraction of what's written here is therefore devoted to getting as much performance as possible out of a biamp and getting rough estimates of how well various circuit topologies can perform.  This choice is not accidental.  While one can build one's own speakers and amplifiers and have complete control over the whole system, it's vastly less work to buy speakers and amps and wire them up in an optimal fashion.  Particularly if some judicious choices result in a stereo which sounds better than systems US $10,000 more expensive.

 

 

Biwiring and Simple Passive Horizontal or Vertical Biamping

 

Assuming you have two way speakers, the five most interesting wiring topologies are

The primary reason sound quality changes with wiring topology is back EMF from the woofers.  In a typical speaker, the low frequency section consists of a bass woofer and a midrange woofer.  The high frequency section is usually a single tweeter.  The design of the passive crossover network in the speaker varies from speaker to speaker based on the cabinet design, the drivers used, the speakers' load impedance, and other factors.  With some crossovers, back EMF from the woofers can pass through the crossover and enter the high frequency stage.  Other crossovers prevent back EMF from entering the high frequency stage.  Others attenuate the back EMF but allow some to reach the tweeter, where it turns into unwanted sound.  Whether or not this is a problem depends on how large the back EMF is, the amount of attenuation provided, and the power spectral density of the music played.

 

Biwiring reduces back EMF effects by interposing the impedance of two runs of speaker cable between the stages.  Since a solid state power amp's output impedance is typically well under 0.1 mΩ, this change is usually a significant rebalancing of the network.  Instead of the inputs of the speaker's trebel section seeing the full back EMF voltage, most of the back EMF is absorbed by the amplifier before it gets to the trebel section's terminals.  Exactly how much attenuation this provides depends on the speaker, amplifier, cabling, and frequency of interest, but it's usually around 30 dB or so.  Tube amps, with output impedances of 1 Ω or more, have considerably less to offer in a biwire.  Biamping eliminates back EMF coupling, since there are separate amplifier channels handling the speaker channels.  If back EMF is significant, the result of biwiring or biaming is greater openness and clarity in the middle and high frequencies.  If the back EMF is not significant, then biwiring or biamping is unlikely to result in any great improvement.

 

Unfortunately, information about a particular speaker's crossover design and its back EMF handling is seldom available, so the only reliable way to find out if biwiring or biamping will improve the speaker's sound by reducing back EMF effects is to try it and see how much improvement results.  Your mileage will vary.  If you're lucky, your speaker manual might have a hint in it like Dali's low key statement that "bi-wiring or bi-amping is recommended".

 

Back EMF aside, a dual monoblock or vertical biamp is still worth pursuing for its reduction in speaker cable length.   As the next two sections discuss, using longer interconnects and shorter speaker cables is preferable to short interconnects and long speaker cables.  Rebalancing cable lengths is a significant but not huge change—an amplifier upgrade can sometimes make as much of a difference—but using a wiring topology which permits short speaker cable runs is a logical optimization to make if one is already looking for a new power amp.  Dual monoblock or passive vertical biamps require an identical pair of amplifiers in order to maintain phase coherency between the two speakers.  Different amplifiers have slightly different response times and slightly different responses.  Ears are discriminating enough to hear the resulting differences between the left and right channels if different amps are used on different speakers.  In my experience, the result is usually mushy sound that is worse than just picking one of the amps and running a monowire.  Passive horizontal biamping doesn't have this problem because the same amplifier drives the same section of both speakers.  As a result, the left and right high frequency stages are consistent, as are the low frequency stages.  In a horizontal biamp there can be problems with matching of the two stages if the amplifiers are not reasonably similar, but these are smaller problems than the loss of phase coherency from a mismatched vertical biamp.  Horizontal biamps can have problems with the low frequency sections leading or lagging the high frequency sections; I personally find lagging sounds better but gets a little silly when the bass seems to be coming from the next block over.  Also, differences in amp response around the speakers' crossover frequency can cause burrs or other artifacts in the sound.  So getting the most out of a horizontal biamp means using identical amps, at which point one might as well run a vertical biamp and shorten the speaker cables.

 

The passive in passive horizontal and passive vertical biamping comes from the use of the passive crossover in the speakers.  Rod Elliott discusses the inefficiencies and problems of passive biamping and the advantages of using an active crossover upstream of the power amps.  From an engineering perspective, biamping with an active crossover is a far more elegant solution than passive biamping, but unfortunately commercially available speakers which come with a matched active crossover are extremely rare in the hi fi market—the only ones I'm aware of are the US $30,000 Dali Megalines.  Which, seeing as biamped active speakers with integrated active crossovers are available in the professional audio market starting around US $300, is a dramatic testimony to how overpriced the hi fi market can be.  My personal path to audio was by way of the hi fi market, so my experience is one of working through incremental upgrades as I learned more; I started with a biwire, then a passive horizontal biamp, then a passive vertical biamp, and finally did surgery on my hi fi speakers to convert to an active vertical biamp.  The result is this page is backed by a fair bit of personal experience with different options, but if I were doing it all over again I'd take a hard look at active speakers and studio monitors for use as home audio main speakers.  My first set of speakers was a US $300 pair of powered ones which I found surprisingly hard to beat.  Hence I would bet moving a bit higher end in that space would have better price performance than following the hi fi route I took.  It would certainly be less hassle; I don't know how many hours I've spent soldering up incremental upgrades of speaker cables or taking apart my speakers and figuring out what to do next.  In comparison, all you have to do with active speakers is plug in an XLR cable.

 

 

Why Interconnects Don't Matter Much

 

Audio cable marketing is full of much voodo, and an equally large amount of discussion has been devoting to debunking it.  Some of the more thorough sources are Audioholics, Douglas Self, and Rod Elliott and it's not my intent to repeat their writings, but it's with no small amusement I've looked hard for audio cable manufacturers which actually specify RLC parameters for their cables and ended up reading volumes of marketing fluff instead.  On inspection, most US $100, $500, or $1000 cables turn out to be 2 x 20 or 2 x 24 AWG stranded wire with some US $2 connectors.  Yes, really.  They may look cool, but the electrons don't care and, from an electrical engineering perspective, these cables have miserable price performance since you can build up the same thing yourself with less than US $10 in parts.

 

Very simply, audio systems consist of a chain of amplifiers driving loads through cables.  The output amp of the source drives the preamp inputs.  The output amp of the preamp drives the power amp inputs.  And the output power amp drives the speakers.  In each of these stages, the load the output amp sees is the sum of the cable impedance and the load impedance.  In the case of speakers, the load impedance is nominally 2 Ω, 4 Ω, or 8 Ω.  In the case of source out or preouts, the load of the pre in or power in is someplace above 20 kΩ.  Cheap interconnects typically use 28AWG wire, which has a resistance of about 200 mΩ per meter.  In comparison, heavy speaker cables are usually around 9 AWG, which has a resistance of 2.6 mΩ per meter.  

 

Trivial application of Kirchoff's circuit laws shows the voltage drop across the cabling relative to the voltage at the output amp is Zcable / (Zcable + Zload).  When driving pre or power amp inputs, Zload is large, so Zcable can be large without causing significant loss.  To use some math instead of marketing, the figures below show the signal loss on an amp with a 33 kΩ input impedance due to 1 and 2 m long interconnect cables of a variety of types (see termination impedance for discussion of ZT).  An amp with a 33 kΩ input impedance is roughly a worst case; most amps are above this figure, in which case the cable loss figures are a few dB lower.  The interconnects in the graphs are

To put these figures in perspective, the signal to noise ratio of a good CD player and power amps is usually a bit above 110 dB and line level inputs on pre amps are usually around 95 dB.  What this means is the performance of the system is limited by the noise floor of the preamplifier and not by interconnect impedance (more so for vinyl; phono stages are typically something like 75 dB SNR).  The practical dynamic range of a 16 bit standard audio CD for most genres is around 70 dB (the theoretical max is 96 dB but differences in music loudness prevent all of the range from being used all the time—most classical CDs are probably below the 70 dB figure because of the large loudness range in the music; 24 bit SACDs definitely make sense in such situations).  The range between the quietest audible sound and sound loud enough to permanent hearing loss is about 90 dB.  Comfortable listening levels are usually 60 or 70 dB above the quietest audible sound, which means ones' ears are operating in a range that's 20 or 30 dB smaller than what the electronics can do and is about the same as what a standard CD is capable of.  The inexpensive 2 x 28 AWG pair of interconnects which come with a CD player are indeed worse than a US $80 pair audiophile interconnects, but their reduction in performance is negligible since the signal lost in the interconnect is about an order of magnitude smaller than what your ears can detect.  Besides, as amp inputs are well conditioned loads, interconnect losses can mostly be compensated for by increasing the volume a tiny bit.  If they were audible in the first place, which they aren't.  Unlike speaker cables, inductive increases in interconnect impedance are not significant either, assuming halfway decent construction.  Typical interconnects have 200 nH or less of inductance per meter, which results in about a 50 mΩ impedance increase above the DC resistance at 20 kHz.  This is negligible compared to a >33 kΩ input impedance.

 

Much ado has been made about the need for shielded interconnects.  Like most things said about interconnects, there is no strong case for shielding.  Not only is it difficult to get anything to efficiently radiate in the electromagnetic spectrum at audio frequencies (even something the size of Jupiter has a hard time) but even if there is significant incident electromagnetic radiation below 20 kHz a twisted pair cable will cancel the interference.  Skin depths are large at audio frequencies (roughly 5 mm in copper at 200 Hz), so shielding has to be quite thick to result in significant attenuation; canceling the field via twisted pair is more practical than dealing with massive amounts of shielding.  Where shielding might conceivably make a difference is with AM radio interference, since noise picked up at the upper end of the amplifier's frequency could be coupled down into the audible range through intermodulation products.  Such coupled noise is typically in the microvolt range and is attenuated by >40 dB in intermodulation, putting it something like 10 or 20 dB below the noise floor of a good power amp or CD player.  Even if you live in the near field of an AM radio station the incident field will be quasistatic over the twist length of a twisted pair interconnect and is therefore easily cancelled without a shield.

 

There is, however, one noise source external to the interconnect, and it can potentially be devastating.  Nearly all audio components short chassis ground, circuit ground, and white and green wire wall wiring grounds together.  As a result, connecting two components with an interconnect cable puts the interconnect cable and one component's power cord in parallel with the other components power cord, forming a ground loop.  Kirchoff's laws say any current which a component pulls off its power supply and doesn't fully return through the supply will return through both parts of the ground loop.  Happily, these leakage currents are usually small.  But they will induce some voltage in the ground conductor of the interconnect which is not part of the audio signal.  This injects common mode noise, most commonly in the form of 60 or 120 Hz hum.

 

There are several ways of dealing with this.  One of the simplest is using amps which have ground lift switches.  These switches disconnect circuit ground from chassis/white/green wire ground and prevent the ground loop from forming.  Another is switching from a single ended (unbalanced) to a differential (balanced) signal, usually by way of XLR connectors and cabling, and rely on the differential receiver's common mode rejection ratio (CMRR) to block the common mode noise from the ground loop.  Since CMRR is typically 60 dB or more this approach is quite effective.

 

A more involved but more elegant solution is a power amp with an attenuating input.  One of the strange quirks of audio design is preamplifiers usually act as attenuators and not as amplifiers.  In order to hit their maximum output power, power amps usually have a gain of around 30 dB.  At a typical listening level of 1 W with a 4 Ω speaker, this means the pre outs are running around 60 mV, versus the 2 V line level between the source and pre ins.  Matching the -100 dB or better noise floor of a typical amp therefore requires an interconnect noise voltage below 600 nV RMS, which is difficult to achieve.  As discussed above a -100 dB floor is usually overkill, but if the preamp is running at unity gain instead of attenuating the -100 dB floor lifts to a more realistic 20 µV.

 

A final alternative is to throw copper at the ground wiring in the interconnect in order to reduce its resistance (having a shield is, ironically, one way of doing this, and may be why some people find shielded interconnects sound better).  This works because the voltage the ground loop develops over the interconnect is proportional to the interconnect's impedance.  The noise voltage does not, however, decrease linearly since decreasing the interconnect impedance causes more current to flow down the interconnect's branch of the loop.  The slope is steepest when the interconnect impedance is less than the power cord and chassis impedance so, while using speaker cable in an interconnect may seem overkill, it is actually a logical optimization.  At least assuming you haven't done something silly and upgraded the AWG 16 power cords plugged into the components to a heavier gauge.  One can buy a few RCA plugs, some speaker wire, plus a soldering iron and assemble some 2 x 12 AWG interconnects for about US $20.  A cost around a quarter the price of off the shelf interconnects in the 2 x 17 AWG range.
 

As an aside, some interconnects are offered in copper and much more expensive silver versions.  Silver is the only metal to have higher conductivity than copper, 63.01 MS versus 56.6 MS—a 5.7% improvement—but the silver versions usually cost about six times much.  In comparison, the reduction in resistance by increasing one AWG gauge is right about 20% and the cost of doing so is around an extra 20% as well.  Buying heavier gauge copper therefore has 17 times price performance of switching to silver.  A very few interconnects come in gold versions, which is even more ridiculous than using silver.  Gold's conductivity is 45.2 MS, or 82% of copper's.  So not only do gold cables cost 100 times as much as copper interconnects at the same AWG, but electrically they are worse.

 

 

Why Speaker Cables Matter

 

Assuming something reasonable is used, the exact choice of speaker cable is not as significant as choice of speakers, amplifiers, or the amplification topology used.  It is, however, the next most significant factor in the system and changes in speaker cables have distinctly audible effects.  As with interconnects, most speaker cable manufacturers don't publish specifications (which is usually a pretty good indication of how poor the specs would be if they were published) but a handful of the better cabling companies do.  This section takes a detailed look at the differences between standard AWG 12 zip cord, based on measurements from an LCR analyzer, a selection of Cardas's cables, Kimber's 4VS, 8VS, and 8TC cables, Goertz's MI series.  I chose Cardas, Kimber, and Goertz precisely because they publish full RLC parameters for their speaker cables.  Pear haphazardly mentions RLC for certain cables, Nordost publishes L and Cs in the same range as Kimber's figures, but not R.  Cobalt publishes R and a better than average 100nH/foot for their speaker cables, but not C.  (Kimber, to their credit, publishes full RLC figures for their interconnects too—Cardas and Cobalt have R and C and Goertz R, but no other manufacturer I've come across consistently makes full RLC available.)  I don't have access to an RLC meter or samples of all of these cables, so the published figures are taken on faith even though there may be errors or smoke and mirrors involved.  In general, there's some difficulty reproducing manufacturer results and it's unclear how manufacturers are accounting for termination impedance.  Goertz's published inductances appear to be high by a factor of two, which may be the result of an incorrect measurement setup.  Cardas touts their golden section stranding patent, but if you read the patent it indicates they don't understand why golden section stranding works.  This calls into question whether there's anything real to the patent or if it's just marketing hype (I personally think it's the latter).  But the cable models and results presented here correlate well with my listening experiences so I'd say the approach is useful as a predictor of real world cable performance (as well providing a general sense of what you'd get for your money if you're cable shopping or looking at building your own cables).

 

The figure below shows the cable loss for an eight foot run of these cables as a function of frequency, eight feet being a typical cable length for monowire, biwire, and horizontal biamp topologies.  The loss calculation here is the same as described in the interconnect section above and calculations use an RLCG cable model which includes skin effect.  Published RLC cable parameters are used and I've included a worst case G so people who are interested in exploring how negligible dielectric absorption really is can play with it.  The Matlab source code for the analysis is here (the code for interconnect analysis above is basically the same, see termination impedance for discussion of ZT).  While I'm not entirely satisfied with the skin effect integrations, stranded cables are approximated as solid wire, and edge and back effects in low inductance planar structures are neglected, the numbers should be accurate within a few percent, which is probably better than the manufacturer data they're based on.  An ideal 4 W speaker is assumed.  Unlike interconnects, whose loss is subsumed by the electronics' noise floor and the limitations of your ears, speaker cable losses are well above the -110 dB noise floor of a good amp and the -70 dB or so floor of your ears and the CD.  As speakers are ill conditioned loads, differences in sound between cables are definitely noticeable; reducing the impedance between the amp and the load pays off.  I've listened to 4VS, 8VS, MI2, and doubled MI2 (essentially the same as MI3) with 2.4 meter long cables and the roughly 6 dB improvement of 8VS over 4VS is definitely worthwhile.  It's not huge, but the 8VS has noticeably cleaner sound, particularly with regard to transients.  The 4 dB low frequency improvement going from 8VS to MI3 is similar, though not as dramatic; high frequencies do open up noticeably.  Compared to 8VS, MI3 has a smoother and more natural sound which reveals more details and texture.  I found it more relaxing to listen to as well.

In a fully optimized vertical biwire or dual monoblock the amps' binding posts are placed right next to the speakers' binding posts and very short cable runs are used.  This reduces cable losses by about 25 dB, as shown in the figure below.  This is a significant improvement over nominal eight foot runs, but the change here is about the largest possible.

A more realistic minimum cable length for a well set up monowire, biwire, or horizontal biamp is six feet or so.  This offers a modest 3 dB or so improvement over eight foot runs and, again speaking from personal experience, it's an improvement worth seeking out.  In a vertical biamp or dual monoblock, putting the amps right behind the speakers is often impractical due to how the stereo is positioned in a room or because there's need to get to the amps' power switches.  Cable runs around two feet therefore tend to be a practical minimum distance.  Two feet is something like four times the minimum cable length of 0.15 meters.  So there is significantly more loss over minimum length cables, but there's still an 8 dB reduction in loss and a roughly 12 dB improvement over eight foot runs.  I've done side by side comparisons of horizontal and vertical biamp configurations using these cable lengths and the additional detail, texture, tonality, and transient control of the vertical biamp is quite distinct.  But not huge.  Perhaps the best description I can think of is it's the difference between good and great.  Certainly, if one has a pair of identical power amps, there is no reason not to run a vertical biamp or dual monoblock, save some money on speaker cabling, and get better performance, too (though if you're willing to take the risk of converting to an active biamp you're better off investing in the active crossover before spending on cables).

The reason speaker cables have noticeable loss is because speakers, unlike amplifier inputs, are low impedance loads.  As a result, getting a low loss speaker cable requires the cable be quite low impedance.  The figure below shows the impedance per meter for the cables considered here.  Two effects dominate.  One is the DC resistance of the cable.  The other is the cable's inductance.  Reducing DC resistance is just a matter of using ever more copper.  MI 1 is the equivalent of AWG 13, 4VS the equivalent AWG 12, Crosslink is AWG 10, MI2 is AWG 10, 8VS is AWG 9, 8TC is AWG 9, Neutral Reference is AWG 8.5, MI3 is AWG 7, and Golden Cross is AWG 5.5.  The MI cables are around 20 nH/m, whereas all the other cables are above 125nH/m.  This why the Goertz impedance curves are so much flatter than the round wire based cables.  Goertz is not cheap (unless you compare to what Cardas charges for most of their cables anyway); I picked up my MI3 equivalent cables for about 60% off list at Audiogon.  They're definitely worthwhile at that price, but I'd think twice and look at buying bulk cable and bare wire terminating it yourself or buying used before paying for new Goertz cables.  If you're cable shopping the price/performance standouts are zip cord, 8VS, and MI2, though if I were doing it again I'd build my own MI2 for about a tenth of list price.

Resistance increase due to skin effect has been the subject of considerable debate.  I've looked high and low and have yet to find an analytic skin effect model which exhibits fully correct behavior.  However, the numerical integrations in the code linked above verge on the trivial and exhibit convergence to DC resistance and the correct sqrt(frequency) shape across a wide frequency range.  The resulting answer is simple; skin effect adds a few milliohms over the audio band.  If the cable has significant inductance, skin effect resistance is an order of magnitude lower than the tens of milliohms added by inductance.  If the cable has low inductance, skin effect and inductance are comparable and add a few milliohms between DC and 20 kHz.

 

 

 

Contact Resistance and Termination Impedance

 

Contact resistance often comes up when speaker cables are discussed.  Usually, discussion centers on which form of termination—bare wire, bananas, spades, etc.—best makes electrical contact and therefore delivers the lowest resistance.  Actual measurements of the contact resistance of different audio terminations are hard to find, but contact resistance characterizations for various platings applied to various test fixtures are not hard to come by if you start looking in technical journals.  If you're interested in details this paper on contact resistance measurements in the AMP Journal of Technology is a good introduction, but a reasonable rule of thumb for a mechanically sound connection between ohmic metals (i.e. gold, silver, copper) is 0.5 mΩ/mm2.  Bananas and spades have significantly more than a square millimeter of contact area.  A bare wire termination which has been through several iterations of binding post tightening and cable wiggling in order to ensure a good contact can have a few square millimeters of good contact as well, though it's been my experience bare wire connections have to be retightened about once a month in order to keep the wire in good contact with the binding post (when I was using bare wire the eventual loss of detail reminded me to tighten the binding posts; a loose binding post can easily be the limiting factor in a stereo's performance).  Since the contact is ohmic regardless of how the connection is made, the resulting resistance is on the order of 0.1 mΩ per cable.  This is much less than the skin effect resistance increase or inductive impedance increase of well made cables, so cable performance is not limited by contact resistance.

 

What is probably the biggest issue in speaker cable termination is the spreading of the conductors needed to connect the cable to power amp or speaker binding posts.  Moving conductors away from each other increases inductance and decreases capacitance, so opening up the cable to attach to the binding posts will add some amount of extra inductance.  How much inductance is added depends on the construction of the cable, positioning and orientation of the binding posts, and how the cable is opened up.  This obviously varies from system to system, but the less the cable is opened up when terminating it the lower the additional inductance.  A reasonable, if rough, approximation is to treat the cable as two independent wires where it enters the binding posts.  There are closed form RLCG parameters for this structure and the result is about 1.25 μH/m at typical binding post separations.  If you approximate a typical manufacturer cable termination as a 0.20 m long taper from 150 nH/m to 1.25 μH/m the inductance added per termination is around 15 nH, which agrees well with the Audioquest cable inductance measurements cited in the previous section.  A reasonably well done DIY termination which does not spread the cable out as much is around 4 nH, though you can do better than that if you get particular about how the cable's broken out.

 

Termination therefore adds something like 0.2 mΩ and 5 to 30 nH of inductance to the cabling.  How much this matters depends on the cabling you're using.  Contact resistance is small compared to cable resistance in the AWG 10 range but may have a small effects in the AWG 6 range if your speaker cables are short.  Most good speaker cables are around 125 nH/m, so an extra 30 nH is about a 10% addition for a typical 2 m cable run.  Goertz cables are around 5 or 10 nH/m, so an extra 30 nH in termination is a few times the inductance of the cable.  The figures below show the effects of a 0.1 mΩ contact resistance, contact resistance with 4 nH of termination inductance, and contact resistance with 10 nH of termination inductance for 0.66 m cable runs.  The loss increase due to contact resistance is small even for Golden Cross (AWG 5.5) and Goertz MI3 (AWG 7) but a 30 nH termination inductance increases loss by around 5 dB.  In comparison, 4 nH of termination impedance increases loss by less than 2 dB even for Goertz MI 3 (13 nH/m).  Granted, these are approximate numbers, but the implications are clear; if you want the best performance from your speaker cables buy bulk cable and terminate it yourself so that it's opened up as little as possible.

Termination impedance is considerably less important  for interconnects.  Not only do the advantages of a high load impedance in reducing cable loss apply, but RCA and XLR connectors spread the cable out less than binding posts do.  The result is smaller termination impedances.  A ballpark analysis similar to the one for speaker cables suggests interconnect termination impedances are around 0.1 mΩ and 2 nH (the numbers used in the interconnect figures above) versus typical resistances of 50 to 200 mΩ/m and inductances around 100 nH/m.

 

 

Active Biamping and Optimized Passive Biamping

 

Even if a speaker's crossover doesn't offer improved improved sound quality from biamping's control of back EMF, an improvement in sound quality can still be had simply from a vertical biamp's ability to situate the power amps in close proximity to the speaker's binding posts.  As the sections above show, cables can be made significantly more transparent through construction and reduction in length.  However, in a typical floorstanding speaker there's around 1.25 meters of internal cabling between the binding posts and the tweeter.  The shorter the cabling outside the speaker, the greater the relative length of the cable internal to the speaker becomes and the less effective cabling optimization outside of the speaker becomes.  Further, internal speaker wiring is rarely of quality; in most cases AWG 12 zip cord would be a step up.  Short of unconventional, but obvious optimizations—such as drilling holes in the side of the speaker and sticking the power amp on a shelf right next to the drivers—the only thing which can be done about the internal wiring is to open up the speaker and recable it.  By itself, recabling is somewhat pointless, since shaving off a few hundred nH of inductance and some mΩ of resistance in internal wiring doesn't do much compared to the Ω, μH, and μF in the speaker's passive crossover.  As a result, by far the largest optimization in the signal path between the power amp and the speaker is removing the passive crossover.  This is only possible if you have a biamp and relocate the crossover between the preamp and power amps (removing the crossover and running a full spectrum signal the speakers will damage the tweeters and make the woofers sound bad).  One option, which for want of a better name I call optimized passive biamping, is to reimplement the passive crossovers with adjustment for a power amp's input impedance instead of a speaker's.  In the hi fi market, this makes for hand building some funky Y type interconnects since each full spectrum output of the preamp gets split into low and high frequency channels in the middle of the interconnect cable.  The low output of each crossover runs to one channel of the corresponding power amp and the high output to the other.  The power amp's outputs are carefully connected to the matching binding posts on the speaker to avoid blowing out the tweeters.  While perhaps short on elegance, such optimized passive biamping accomplishes the key goal of getting the passive crossover out of the power amp's way.  It also allows the crossover to be rebuilt without using power components, removing various parasitics and making it a bit easier to build accurate filters.  In the professional audio market you can find speakers with all of this done for you, such as Mackie's HR626 studio monitors.

The photo above shows Dali's 12 dB/octave LC lowpass woofer (left) and CL highpass tweeter (right) passive crossovers from my Suite 2.8s.  The holes in the boards are where the binding posts go when the crossovers are installed in a speaker and the 1.8 Ω resistor on the highpass (the larger of the two) is the holdback which compensates for the tweeter being more efficient than the woofers.  Dali hooks up the extra inductor on the lowpass crossover (located in the middle of the picture) to the upper woofer for an 18 dB/octave rolloff on that one driver.  Dali markets this as a 2.5 way configuration, though both woofers share the same ported chamber and the other woofer has a 12 dB/octave rolloff.

 

A better approach than optimized passive biamping is to situate an active crossover between the pre and power amps.  The active crossover can be implemented using DSP if the crossover's digital or using op amps if the crossover's analog.  Either implementation offers advantages over passive components located between the pre and power amps.  Power components and inductors are no longer needed, reducing component parasitics and eliminating phase reversals which occur at  LC resonances.   An active crossover can convert back and forth between balanced interconnects and unbalanced filtering, eliminating the need to have two closely matched passive filters handling the plus and minus signals of balanced interconnect.  Filter and level adjustments are more easily made since components are low power and the op amps in the active crossover automatically compensate for varying load impedance.  An active crossover's drawback is either cost or flexibility.  As of this writing, digital crossovers' extensive tunability comes with an price tag comparable to the pair of power amps needed to biamp.  Analog crossovers are a tenth or a twentieth the cost of a digital crossover but typically offer a fixed 24 dB/octave Linkwitz-Riley filter.  Which, while no slouch of a filter and usually tunable with respect to the crossover frequency, crossover level, and input and output signal levels, still has a fixed 24 dB/octave slope.  In comparison, the passive crossovers in most speakers use a 12 dB/octave slope, so swapping out the passive crossover typically makes a fundamental change in how the speaker produces sound.  Even if the crossover is set up with the same crossover frequency and its output levels matched to those of the passive crossover.  Further, an active crossover puts more things in the signal chain, either an A/D, DSP, D/A, and some op amps for a digital crossover or even more op amps in an analog crossover.  However, the artifacts of an active crossover are small compared to those of a passive crossover.  (Consider conversion from balanced to unbalanced and back happens in the preamp, active crossover, and power amp along with the speaker cable data above and you'll see significant complexity can be removed by running digital all the way to a powered speaker—ironically, such optimization is standard in $20 USB computer speakers but the hi fi industry hasn't yet caught up.)

 

Strangely, while discussion of the tradeoffs between active and passive biamping is easily found, specific active crossovers are rarely discussed.  In my case, I contemplated building an analog active crossover from time to time for several years, but never quite found it worth the hassle.  Eventually I discovered active crossovers with balanced inputs and outputs were readily available in the sound processing market for PA systems and all one needed to do to find them was look in for crossovers in the commercial sound sections of places like PartsExpress.  After some research I picked up a lightly used, analog Ashly XR-1001 off eBay for 10% of the combined price of my pre and power amps.  I first plugged it in with the passive crossovers still in place to see what it did.  The result was promising, so instead of selling on the XR-1001, I pulled the passive crossovers out of my Dali Suite 2.8 speakers.  Beforehand, I'd spent a great deal of time worrying about how the change from Dali's 12 dB/octave crossovers to the 24 dB/octave Linkwitz-Rileys in the Ashly would affect the Suites' sound.  In practice, it was a non-issue.  I spent about 15 minutes fine tuning the crossover frequency and the output level on the high channels and had a good setup.  There's a slight change in overall tonal balance which Spice simulation suggests is due to the Ashly lacking the incompletely suppressed LC resonances in Dali's passive crossovers, but it took me a week or two of listening to figure out what was going on.  A lower hassle, and likely lower cost approach, is to look into active studio monitors or active PA speakers.  These commonly use integrated 24 dB/octave Linkwitz-Rileys and I've bumped into a some at live gigs which struck me as having pretty good sound.  (However, I've not had opportunity to listen to them in more controlled environments.)

 

The improvement in sound quality wasn't as dramatic as the active crossover advocates I've come across claim, but it was certainly worth the eBay price of a used Ashly and the time to solder up a few more XLR interconnects.  Highs are cleaner, bass is tighter, and a remarkable amount of midrange tone from, I believe, the woofers was revealed as slush and removed.  The most succinct description I can come up with is the sound feels unplugged.  It's closer to what you hear while playing as a musician without amplification or listening to a symphony in a concert hall rather than a typical concert or stereo sound.  Bass drums go whump like they do when you tap the pedal, without the crunch or harshness which amplification usually adds.  Open high E strings ring out the way they do when you unfret them while the guitar's hanging off your shoulder.  Individual instruments' lines are more definite and the overall sound became noticeably more detailed.  Intricate pieces or works with a lush variety of sounds show particular gains.  Not only can you hear all the good stuff better but musicians' mistakes become more obvious and flaws in recordings are mercilessly revealed.  Sorting through my collection, most tracks laid down before the 1990s sound a bit off and some things from the 1970s which I used to enjoy have become painful to listen to.  I wouldn't say the change is for everyone; the vintage of one's collection aside, hard rock or metal in particular have less attack and a less harsh, more instrumental quality.  If you like your bass loud, heavy, and generally out of control you may find an active crossover disappointing as it doesn't yield the same amped up kind of sound.  But for most genres the active crossover strikes me as a clear improvement and I, for one, am happy to lose overemphasized drums in exchange for greater clarity in what a lead guitarist shreds out.  Perhaps the simplest measure of how much the passive crossover got in the way is the Suites' sensitivity jumped from 90 to 96 dB on the woofers and 99 dB on the tweeters.  That's a quadrupling and octupling of efficiency, respectively.

Having gotten the passive crossovers out of the way, I proceeded to upgrade the internal wiring within my Suite 2.8 speakers.  The results are less than optimal in three regards.  First, I've retained the existing cable routing through the speakers, which adds roughly 1.5 meters of avoidable cable length.  Second, I'm using the binding posts in the speakers, which doubles the number of terminations.  Third, I'm reusing existing MI2 I have lying around instead of installing optimal runs.  I'm made these choices partly to preserve the speakers' resale value, partly for the convenience of using binding posts, and partly to avoid unnecessary cost.  The moderate improvement from removing the passive crossovers indicated the power amps have pretty good control over the drivers and the remaining headroom available from improving the signal path between the power amps and drivers is limited.  The figure above compares upgraded internal wiring options against passive biamping, the wiring in my active biamp before upgrading the Suites internal wiring, and an optimal installation of Goertz MI3.  In all cases a 0.66 m run of MI3 external to the speaker is assumed.  The values for passive biamping are approximate as Dali's inductors are unlabeled and I don't have access to an inductance meter.  As you can see from the figure, changing internal wiring offers a 14 dB improvement for woofers and 20 dB or so for the tweeters.  In comparison, a continuous MI3 installation is 1 dB better than  MI2 bulked up with zip cord for tweeters and 1 dB worse for woofers.  Installing continuous MI3 equivalent cable would incur a great deal of hassle in building new cables and binding post panels and cost a couple hundred dollars in materials, which hardly seemed worthwhile for 1 dB on the tweeters.

 

I was expecting little or maybe even no noticeable improvement from changing out internal speaker wiring, but was pleased to discover differences which sometimes exceed other cable improvements I've made.  Nothing radical but still quite nice and, to my ear, more of a difference than converting from a passive to an active biamp.  There's more detail throughout the woofers' range.  Mids are cleaner and bass is tighter.  Highs off the tweeters are so clean my jaw dropped the first time.  The woofers seem to move a little more easily and the speakers are maybe 1 dB louder.  What struck me initially is bass crunch; you can hear the power amp shoving the woofer magnets around and stopping back EMF.  But what really comes through are dynamics.  Fast paced pieces simply haul, voices have rich character, and instruments are truly lifelike.  The requirements on recordings ratchet up another notch as well.  Sound on well done CDs from around 2000 or newer shows improvements but there's minimal improvement with most of the professional recordings I have from the late 80s or early 90s.  As with my comments about recording dates and converting from passive to active biamping, this is a rule of thumb and not a hard and fast statement.  For example, I've one excellent recording from 1989 which shows moderate improvement.  I had some trepidations about recabling, as Dali installs the passive crossovers in a separate compartment (only mentioned as a feature in the Euphonias, but apparently used elsewhere in their lineup) and plugs the hole the driver wiring goes through with hot glue.  Upgrading the cabling involved pulling the existing wiring, extracting the hot glue (an end mill on a right angle Dremel worked well), and greatly widening Dali's existing hole for AWG 9 of wiring to accommodate AWG 2 of MI2 and zip cord (the end mill again).  MI2 is not especially flexible and gets even less so when bulked up , so reinstalling the binding post panel on the back of the speaker means sliding the internal cables further into the speaker.  This, in turn, makes sealing up the new holes difficult as there's a blind two foot reach from the woofer openings down to the slab of particle board which blocks off the crossover compartment.  Leaving the holes open adds poorly coupled volume to the speaker cavity which, while nominally extending the speakers' bass reach, throws off the porting and risks the establishment of funky resonances.  I decided to go ahead with the project as the added volume was fairly small compared to the designed volume of the cavity and, worst case, I could always reinstall Dali's wiring and plug up the routing holes.  So far any deleterious effects are unnoticeable against the overall improvement.

 

 

A Few Concluding Remarks

 

1This page has advanced some electrical reasons why active biamping results in better sound than one is likely to get from throwing an equivalent amount of money at cabling or, especially, interconnects.  Passive crossovers constitute the dominant impedance between solid state power amps and drivers.  Cabling changes, while worthwhile, are incidental in comparison.  While the source, preamp, active crossover, and power amps all matter this is fundamentally a page about cabling since it focuses on what you can do to optimize your existing stereo without changing components (well, except for possibly buying a second, matched power amp).  The core point herein is inductance kills; splashing out on speaker cables or speaker internal wiring doesn't do any good if all that money doesn't drive the inductance down.  As of this writing small quantity list pricing on AWG 12 zip cord was US$ 0.60 per foot, Kimber 8VS was US$ 7.50 per foot, Goertz MI2 US$ 10 and MI3 US$ 25 per foot.  This means that for less money you can run 10 times more zip cord than 8VS, 15 times more than MI2, and 40 times more than MI3.  Inductances in parallel divide, so the roughly 190 nH/m inductance of zip cord can easily and cheaply be brought down by doubling, tripling, quadrupling, or even more upling zip cord so long as you connect it right.  This approach has its limitations—32 sections of zip cord have about the same inductance as MI2 but cost twice as much, are far bulkier, and considerably harder to handle—but it's the best way I know to get inductance down short of a planar geometry.  For example, Pear's AWG 12, $7.50 per foot Comice is basically tripled AWG 16 zip cord (at 7.5 times the price).  On cue, Pear's claimed 60 nH/foot inductance is right around a third of zip cord's.

Surprisingly, Cardas and Kimber don't strand their cables this way.  In particular, 8VS approximates octupled AWG 18 zip and could trivially have its color coding changed to result in such termination.  8VS's pair spacing is wider than zip so the resulting inductance is probably around 35 or 40 nH/foot, comparable to quintupled instead of octupled zip.  As the figure below shows, such rebraiding offers a dramatic improvement which moves the frequency at which MI2 outperforms 8VS from 2.4 kHz to 13 kHz.  Quadrupled AWG 12 zip has higher inductance than rebraided 8VS but beats MI2 below 14 kHz or so due to its lower resistance.  The zip's a third the price of 8VS and quarter the price of MI2 as well as being a good bit easier to terminate than MI2, so quadrupling it is an attractive proposition.  Similarly, augmenting MI2 by strapping a run or two of zip on each side produces results comparable to MI3 for under half the list price.  MI2 is not terribly hard to find used while MI3 seldom turns up (it's much easier to find MI2 biwires), so in practice MI2 plus zip cord ends up being about the quarter the price since MI3 would usually have to be bought new.

 

 

Practice What You Preach

 

My stereo is a vertical biamp with an active crossover.  Hardware details are

The left channel Suite 2.8, A23, cabling, XR-1001, P3, 640C, and T500 are shown in the picture above.  I bought the A23, P3, and MI2 used off Audiogon, the XR-1001 used from eBay, and the Suite 2.8s new from Speakerlab, while the 640C and T500 came from Spearit as closeouts and refurbs (the table was built by a local high school kid who wanted to try his hand at furniture making; I found it on Craigslist).  The cabling and interconnects are soldered up using parts ordered from PartsExpress or extra stuff I had lying around.  I first bought Kimber 8VS to biwire when I was running a mono amp and added some Kimber 4VS when I switched to a horizontal biamp.  The 4VS sounded bad so I added more 8VS and the 4VS ended up getting used between the P3, 640C, and T500 since it looks cool and its excessive inductance doesn't matter for interconnects.  I converted to vertical biamp a few months later, chopping up some of the 8VS to use in shorter speaker cable runs.  I later picked up some shotgunned Goertz MI2 and chopped up half of it up upgrade the runs between A23s and the Suites.  This left me with a spare set of 8VS and a spare set of MI2; the 8VS has been chopped up again and used to upgrade the internal woofer wiring in the Suites; the MI2 will follow along soon enough for the tweeters.  The XLR interconnects between the XR-1001, P3, and A23s all use PartsExpress' 22 AWG Dayton MSC microphone cable.  Interconnects are using either Neutrik XLRs—often marketed as high end, but available for a few bucks even in small quantities—or the equally low cost, gold plated, Dayton locking RCAs.  Speaker cabling is using Dayton 1/4" spade lugs, 3/8" ring terminals, or 3/8" rings converted to spades.  Gold plated, crimped, and soldered with as little cable breakout as possible.  Total system cost is about the same as the closeout price on a pair of Dali Helicon 400s.  And, speaking from personal experience, the sound's a sight better than the 400s on a passive vertical biamp.

 

All of the incremental upgrades have made for an interesting journey through the world of sound, starting with a mono wired mono amp and progressing through nearly every step from there up to a pretty heavily modified active vertical biamp.  There have been curious discoveries along the way, ranging from learning to tap the tips of non-locking banana plugs with a hammer every so often to keep them tight to how best to solder up two foot long pieces of disassembled MI2.  Some things are just wacky.  While I wasn't surprised to discover Dali's internal wiring was individual bits of AWG 16, I still find it remarkable the two tweeter wires were run down opposite sides of the speaker.  Building crossovers out of particle board and baling wire and not putting zip cord in a US$ 1250 speaker is one thing, but installing wiring to maximize inductance is another (one wonders if innards of a Helicon or Euphonia are any better).  On the other hand, Parasound graciously emailed schematics to a friend of mine trying to fix an A23 fried by an over watered plant.  There have been weeks of coding, thinking, cutting, stripping, crimping, soldering, checking pinouts, making connectivity measurements, and taking things apart and putting them back together again.  I've met a family in a '57 Chevy at their storage locker, salvaged boards from a friend's remodel, ended up wishing I'd moved my living room into my dining room to get better speaker placement, and caught Speakerlab red handed loaning out an amp I had money down on.  But, in the end, what it comes down to is thousands of hours admiring beautiful music.

 

 

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last modified 2008.05.11