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Cables and the Amplifier/Speaker Interface

1984 © prof. R.A. Greiner met naschrift van © Ruud Janssen (2003)

R. A. Greiner is Professor of Electrical and Computer Engineering at the University of Wisconsin, Madison. He teaches and does research in electro acoustics, acoustic measurements, applications of digital signal processing, audio system design, and noise control. He holds over a dozen patents in electronic instrumentation and audio systems and was elected a Fellow of the Audio Engineering Society in 1984.

This article is adapted from a paper which I wrote and presented to the Audio Engineering Society 10 years ago, and which was later published in the Journal of the Audio Engineering Society (Vol. 28, No.5. May 1980). My original paper discussed the issue of cables used for connecting power amplifiers to loudspeakers. In the intervening years, an entire industry for the manufacture of special cables has grown up around this issue. I have therefore added comments to expand the notions presented in the original paper and to bring it more up to date. The paper has also been edited slightly to make it clearer to persons not entirely familiar with some of the electrical engineering terms used. The substance of the paper, however, is based on electromagnetic theory and no amount of advertising in the past 10 years has changed that base.


Loudspeakers seem to be connected to power amplifiers with greatly varying degrees of care. The professional generally selects wiring of appropriate size and type for the given application, while many others are quite casual about such matters. Recently, however, considerable attention has been drawn to the issue of loudspeaker cables by the appearance of numerous ‘special’ cables with properties that allegedly improve the quality of the sound delivered by the loudspeaker. While most of these claims are no more than pure fantasy, there is just enough edge of truth showing to make a hard look at loudspeaker cables seem appropriate. In this article, loudspeaker cables are investigated to determine whether or not their transmission line behaviour is significant for audio frequencies. Conclusions are reached regarding the validity of lumped equivalent representations of short transmission lines. Certain critical frequencies are calculated and measured to estimate the effect that the cable will have on the amplifier and the loudspeaker load. The problems caused by the resistance of the crossover, level pads, and any fuses in the circuit are considered briefly.

Cable Parameters

The parameters which describe the cable electrically are series resistance, series inductance, shunt conductance, and shunt capacitance. These parameters can be determined by direct measurement and/or by calculation from elementary formulas. They depend entirely on the geometry of the cable and the nature of the conductors and the insulation used. The approximate values for a variety of cables made of copper wire and rubber or plastic insulation are summarized in Table I.

Conductors of copper, silver, or similar high-conductivity materials – regardless of the method of drawing the wire – behave similarly. The electrical properties of cables are not significantly affected, at audio frequencies, by the type of insulation used. The mechanical properties of the cable, however, may be more desirable with use of certain insulators and construction techniques. Note that the larger the physical size of the wire, the smaller its gauge number, and that each change of three wire gauge sizes doubles or halves the wire's cross-sectional area. The nature of the insulation, and whether or not the wire is ‘tinned’ have little effect on the electrical parameters of the cable at audio frequencies.

The accompanying Tables, based on my 1979 investigations. cover both ‘normal’ and selected ‘special’ cables. Three of the normal cables are typical two-wire pairs, such as standard zip cord with rubber insulation. Of these, the Nr. 12 zip cord is a European extension cable made by Lucas; its wires are more widely spaced than those of U.S. extension cords, giving it a slightly higher inductance. Two of the other normal cables are standard twisted-pair types in a vinyl jacket, normally used by professionals; these are available from Alpha, Belden, Consolidated, and other manufacturers. The RG-9 is a standard coaxial cable made, in this instance, by Belden. Of the three types of special cables included, one is a large-gauge coaxial of dual-cylindrical construction by Mogami. Another is a braided cable by Cobra. The third is a plastic-jacketed pair of ‘welding size’ conductor real welding cables. I believe – from Fulton.

Present-day cables that deviate fro the techniques used to construct cables in 1979 usually use fine strands of wire which are gathered or braided in a variety of complex geometries. Some of these techniques increase and decrease the series inductance of the cable slightly. Both techniques, increasing and decreasing inductance, are claimed to improve the electrical properties of the cables. In the following discussion, it should be apparent that neither of these techniques makes much difference at audio frequencies.

A review of Table I is interesting since it shows that something quite drastic has to be done to the geometry of the cable before its inductance or capacitance per unit length changes very much. The normal cables, even including the welding-cable pair, have values of inductance and capacitance within a factor of about 2. The resistance of the thicker wires, of course, goes down greatly. Skin-depth phenomena have only a slight effect on copper wires at audio frequencies. The skin depth for copper at 20 kHz is about 0,5 mm. Thus, wires larger than Nr. 14 gauge will have a resistance, at 20 kHz, slightly higher than the d.c. value. The ratio of the 20 kHz to d.c. resistance is given in Table I.

The wire listed as Nr. 12 zip cord is a high-quality extension-cord style of construction with slightly greater than normal spacing. Thus, it has a slightly higher series inductance compared to domestic zip cord. This cable and the welding type fall just slightly outside the range of values for normal wires (one above and one below). The issue of Litz-type wire construction, using a multitude of tiny strands, could be discussed at length, but at this point, let it be said that the topic is largely irrelevant at audio frequencies. There simply is no significance to ‘skin effect’ at audio frequencies, and wires which purport to fix this effect usually do not do so in any case.

Spacing the wire pair more closely has the advantage of reducing the series inductance. Unfortunately, this tactic also increases the shunt capacitance substantially. Various braided cables seem to attain a reduction of three or four times in the series inductance, but show a rise of 10 to 20 times in the capacitance. Whether the advantages of this type of construction outweigh the disadvantages will be considered later. Some users have suggested spacing wires farther apart to give less ‘interaction’ between the wires. However, it is well known that the inductance of a cable rises as the wires are spaced farther apart. This effect is shown in Table II. Spaced wires not only interact more with each other but also show cross talk with other nearby pairs. Spacing the wires offers no advantages whatever and several serious disadvantages. This configuration should never be used and will not be considered further here. Some regular coaxial cables have attractive values of inductance and capacitance. However, only a few of the larger sizes have large enough conductors to make them useful for loudspeaker connections. Standard AG-9 has been included in Table I. One sample of a special coaxial cable consisting of two concentric cylinders of stranded wire has been included as well. This coaxial cable is of Nr. 12 gauge and is specifically designed for low-impedance transmission-line purposes.

Cables as Transmission Lines

When considering cables as transmission lines, thoughts come to mind of characteristic impedance, termination, matching, reflections, and frequency dispersion. All of these are valid concepts, but they are not usually considered for very short transmission lines. And indeed, any reasonable length loudspeaker cable is a very short line. The wavelength of a 20 kHz signal is about 10 miles (16 km). Thus, a 10-meter cable is 1/1,500 of a wavelength. Any fluctuations in the signal caused by reflections at the ends of this cable will take place at a frequency of 30 MHz. Or, to look at it another way, 1,500 iterations toward the final voltage distribution in the cable will take place every cycle at 20 kHz. One must conclude that there are absolutely no audio frequency effects related to these reflections for cables of any reasonable length.

It is fortunate that reflections in loudspeaker cables are irrelevant, since they are never matched at either the amplifier or the loudspeaker ends. In practice, both the source and the load are quite complex and frequency dependent. Nevertheless, it is interesting to take a look at the characteristic impedance of a typical loudspeaker cable, which is also quite complex.

The characteristic impedance of a transmission line is given by:

Zo = [(R + jwL)/(G + jwC)]^1/2 Formula 1

where A is the line resistance per unit length, L is the series inductance per unit length, C is the shunt capacitance per unit length, and G is the shunt conductance per unit length. Of the two constants, j is the square root of -1 and w is equal to 2p times the frequency. For all practical loudspeaker cables, G equals O. Thus, for high frequencies, where wL > > R, we have:

ZOH = (L/C)^1/2 Formula 2

This is an impedance called the characteristic impedance. It is given for selected cables in Table I. For low frequencies, where wL << A, we have:

ZOL = (R/jwC)^1/2 Formula 3

This expression is the correct one for frequencies which fall below a value fm, which can be defined as R divided by 2pL, and which is typically somewhere in the middle to upper audio band. For the physically smaller normal cables, fm is about 13 kHz; it is about 520 Hz for physically larger welding cable, 40 kHz for braided cable, 30 kHz for cylindrical coaxial cable, and about 26 kHz for regular coaxial cable.

For frequencies well above fm the cable behaves more ideally in the sense that there is no frequency dispersion in the line, and the impedance has reached a limiting value that is resistive. At lower frequencies, the impedance is complex, and the line contributes some frequency dispersion to the signal. When there is dispersion in the line, the high frequencies arrive at the end of the line ahead of the low frequencies. This happens because the line’s series inductive reactance is too small compared to its resistance. The principles of transmission-line theory require that for purely distortionless transmission:

R/L = G/C Formula 4

Since G equals 0 for typical audio cables, it is impossible to make the line perfect. However, R should be made small and C should be made small as well. When this has been done to the greatest extent possible, then L should be made larger. The telephone company does just this by inserting loading coils in long lines to reduce dispersion distortion.

It would appear that reducing series inductance, as some special cables do, does not make much sense from a transmission-line viewpoint. When cables are considered as lumped element circuits, however, there are some good reasons to decrease all of the elements as much as possible; this will be discussed below. First, it is interesting to calculate the dispersion for some typical loudspeaker cables. Since all loudspeaker cables show some amount of loss and some dispersion, a vital question to be answered is: How much?
To determine the difference in the arrival times of the high frequencies compared to the low frequencies, we need to find the group velocity of the transmitted signal. This is given by:

VP = 2pf / b Formula 5
b = (1/2)^1/2. [(ZY)^1/2 + BX – GB]^1/2 Formula 6
Z = R + jwL Formula 7
Y = G + jwC
B = wC
X = wL
For G equals 0.
b = (1/2)^1/2 { wC [(R2 + w2L2)^1/2 + wL]}^1/2 Formula 8

Dispersion characteristics for selected cables are shown in Table III for frequencies of 100 Hz and 10 kHz. From the Table, it is apparent that for a 10-meter cable, the delay differences are only a fraction of a microsecond – except for the braided construction, which is a little worse. In any case, the delay time, or frequency dispersion, is certainly not a problem for loudspeaker cables of any reasonable length.

Before going on to the lumped parameter treatment of short lines, we should make one additional general observation about transmission lines. A line will look much like a shunt capacitance when it is loaded with an impedance much higher than its characteristic impedance, and it will look like a series inductance when loaded by an impedance much lower than its characteristic impedance. Almost all loudspeaker cables are loaded according to the latter criterion. In general, playing numbers games with the high-frequency value of characteristic impedance for short cables at audio frequencies is largely useless.

Fig. l – Amplifier/cable/loudspeaker circuit using lumped circuit elements to represent the properties of the cable. Typical R. L, and C values for cables 10 meters long are given in Table IV.

Cables as Lumped Lines

It should be clear that treating loudspeaker cables as transmission lines, while interesting, is not of much direct design value. The loads are complex, the lines very short, and the frequencies too low to allow easy ideal treatment. Exact treatment is more complex than is warranted. In this section, loudspeaker cables will be treated as wire pairs that can be represented as lumped element equivalent circuits. This method will give reasonable design guidance and intuitively sensible results. A satisfactory equivalent circuit for an amplifier/cable/loudspeaker circuit is shown in Fig. 1. In order to have convenient numbers to use for examples, the values for typical cables 10 meters in length are given in Table IV. Applications using shorter or longer cables can be scaled up or down from these examples.

There are at least two major interactions to consider in the system shown in Fig. 1. One is the interaction of the amplifier with the total load, including the cable; the other is the interaction of the loudspeaker with the amplifier, including the cable. Since the system is so tightly coupled, some consideration to the nature of Zo and ZL must be given. While it is not possible to consider all possible cases, certain more common ones will be discussed. First consider the amplifier end of the high-fidelity system.

An ideal amplifier would be a voltage source with a Zo of zero. In fact, many high-quality amplifiers come very close to this ideal. At low and middle frequencies, the output resistance of an amplifier will typically be less than 0.05 ohm, with a rise to 0.2 ohm at the very highest frequencies. The output will usually be slightly inductive. Often a series inductance of 2 mH will be used to isolate the amplifier feedback loop from capacitive loads. This inductance is 0.25 ohm reactive at 20 kHz. A good amplifier should be stable for any load, including capacitive loads.

Since even the worst of the cables is only 0.2 µF for 10 meters, such a cable should not cause a good amplifier to become unstable or to ring. It would take 35 µF to resonate 2 µH at 20 kHz. Thus, amplifier/cable interaction problems in the audio band are not likely. However, it is known that some amplifiers will not tolerate even slightly capacitive loads. This is an amplifier design problem, not a cable problem, and should be dealt with at that level. It is easy to test amplifiers for load sensitivity problems, and those amps that are not satisfactory should be eliminated. We will assume that the amplifier/ cable interface question is settled by using a ‘good’ amplifier. The problem of fuse-protecting the output circuit is not trivial and will be discussed later.

With a good amplifier in place, the remaining electrical problems are related to how the loudspeaker loads the cable and interacts with it. It is possible to simplify the equivalent circuit a bit with the assumption that the amplifier can, at the very least, drive the cable capacitance. An appropriate circuit is shown in fig. 2L R

Fig. 2 – Simplified circuit for a ‘good’ amplifier driving a cable and loudspeaker load. Critical frequencies for this circuit are summarized in Table V.

Naschrift bij het artikel van prof. R.A. Greiner
Cables and the Amplifier/Speaker Interface

© Ruud Janssen, november 2003

Ik heb het verhaal van de hoogleraar gelezen en het komt er zeer voorspelbaar op neer dat geleiders gewoon maar geleiders zijn en dat het gedrag van de elektronen in die verschillende geleiders volstrekt identiek is. Alles waar de kabelneuroten iets hogers aan willen ontlenen verwijst hij terecht naar het land de fabelen. Hij zegt het wat vriendelijker maar het komt er op neer dat het gemekker over luidsprekerkabel louter een kwestie van persoonlijke onzin is.

Paverotti's tenor komt uit de snoeren niet mooier dan hij er in ging. Waarbij natuurlijk wel aangetekend dient te worden dat in de autosuggestieve belevingssfeer dat "mooier" op individuele basis het geval kan zijn. Maar zoals bekend is het placebo-effect ook bij dit soort waarnemingen onverminderd werkzaam. Als je dat overigens op die manier verklaart, weet het gros niet eens waar je het over hebt.... In dat kader herinner ik me rond het fenomeen luidsprekersnoeren en andere aanverwante gaten in de markt een bijeenkomst in een kapitaal pand in het Gooi. Alwaar de in een nčt even te vlot Versachi-pakkie gestoken eigenaar van de High End-nering wist te melden dat de zorgvuldig op het glanzende roodbeuken parket gelegde luidsprekerkabel (op de bijbehorende mystieke steuntjes) het "zwart" in de rusten van Bruckner VII zo goed laat uitkomen. De "audiopersoonlijkheid" voegde er nog aan toe dat Bruckner die rusten vanzelfsprekend zo mooi "zwart" had bedoeld.....

Tja, als het zo wordt gebracht is het voorspelbaar dat het gros van de aanwezigen dat "zwart" (wat dat ook moge zijn) dan ook echt zo waarneemt. Ik schiet er dan bij in de lach, maar wie ben ik daar?.... En dan zijn er bij dat soort bijeenkomsten al te vaak mensen opgetrommeld die van narigheid niet weten waar ze met hun poen naar toe moeten. En dan laat zo'n uitgenodigde roestbruine golfer annex patrijzenmoordenaar met in zijn kielzog de onvermijdelijke omhoog gevallen Marie-Claire - zonnebankbruin, dichtgesmeerde kraaienpoten en door Frans Molenaar aangekleed - zo'n setje van die koninklijke snoeren komen (die lieden kopen niets, die laten zoiets "kommen"....) om ze dan ter pronk op hun eigen strak in de lak gezette rustieke parket op die bevallig vormgegeven steuntjes (natuurlijk á 100 euro) te kunnen neerleggen. Je kent het soort wel, mensen die het goed bezien alleen maar vervelend vinden dat je via zo'n set van een paar ton óók nog muziek moet gaan afspelen. Ze horen geen "wit" en ze horen geen "zwart" in Bruckners rusten, want afgezien van de test na het aansluiten van de snoeren wordt de set niet door ze gebruikt. Muziek in dat huis komt louter uit de hoofdtelefoonset van de mp3-speler van de hulp in de huishouding die daar schoonmaakt als zij tannist en hij op de golfbaan met zijn vrinden ballen in de sloot staat te slaan. Het zijn zeg maar de kringen waar bijvoorbeeld Mahler het zo goed doet omdat de vormgeving en kleurstelling van cd-inlay helemaal past bij de net op de antiekveiling gekochte Jugendstil-vaas (er zijn slechtere argumenten trouwens...).

Ik bedoel er mee te zeggen: dat het dan helemaal niet meer over het gedachtegoed hifi gaat en vrijwel standaard er niet van muziek wordt gehouden laat staan genoten. Wat hierin telt is dat de kassa rinkelt. Het onnozele adept van het High End-gilde lult vanzelfsprekend maar wat voor zijn malle moers kont weg maar wat belangrijk erger is: hij vindt gehoor. En ik moet een aantal van die audio-onbenullen nageven dat ze een zekere boeren slimheid in huis hebben. Ik vind het namelijk erg knap om iemand met een netsnoertje van 500 euro ( wel even contant betalen graag...) naar huis te sturen met de plechtige belofte dat je dan nňg meer "zwart" in de rusten van Bruckner VII kunt horen. En niet goed?... Geen geld terug.... Waarbij dan trouwens al fluitend kijkend naar de antieke gipsornamenten van het plafond in de hoge vertrekken van de villa geheel geruisloos wordt overgeslagen dat vanuit het stopcontact er gewoon maar twee keer een 20-tal strekkende metertjes 2,5 mm˛ bruin en blauw installatiedraad van de plaatselijke Joris Osram (yes..., ook daar al, of zo je wilt Karel Pope; dat mag ook natuurlijk...) in standaard 5/8 pvc-buis geheel onafgeschermd en niet behoedzaam getwist naar de meterkast loopt.... Wie durft nog te beweren dat de consumenten niet belazerd willen worden?

We moeten leren inzien dat het zo goed mogelijk weergeven van muziek een heel andere hobby is. Het hele kabelcircus is louter gebaseerd op het aan de man brengen van niets dan gebakken lucht: er worden slachtoffers gezocht die dingen moeten gaan kopen die ze niet nodig hebben. En al jaren zie je met lede ogen aan dat dat nog lukt ook want laten we eerlijk zijn die bric-a-brac ziet er natuurlijk fantastisch uit. En het is maar een enkeling die het besef heeft dat dit nergens inhoudelijk over gaat en je reinste overkill is.

En dan zitten er hier liefhebbers van muziek die willen bewijzen dat snoer gewoon maar snoer is.... Ja zeker, ik kan op zuiver wetenschappelijke grondslag keihard maken dat in standaard pisbakijzer het gedrag van de elektronen identiek is aan het gedrag in geleiders uit gans het periodiek systeem. Zilver geleidt niet beter dan lood: alleen de soortelijke weerstand is anders. Ik kan bewijzen dat zilver in kwalitatieve zin niet beter geleidt dan pisbakijzer. Het is bovendien een proefje dat voor een ieder met betrekkelijk eenvoudige middelen is te herhalen maar daar gaat het helemaal niet om..... Er moet namelijk gebakken lucht worden verkocht. De mensen die pogen te weerleggen dat het kabelverhaal gerelateerd is aan betere weergavekwaliteit zijn namelijk altijd zelf slachtoffer. Zij hebben thuis immers ook geďnvesteerd in instapmodelletjes kabel van 100-den eurootjes en zien als ideaal die rare gevlochten worsten op van die potsierlijke geile steuntjes. Moet ik voor die mensen bewijzen dat het niet uitmaakt wat je voor snoer tussen versterker en luidspreker gebruikt? Ik probeer het wel maar is het ook zinnig? Ik vrees van niet: het gaat namelijk helemaal niet om betere weergave. Wat telt is de illusie en die verstoor ik zonder dat het muntje valt dat betere weergaven vanzelfsprekend niet zit in betere (lees: duurdere) snoeren. Dat besef dringt helemaal niet door. Er is nu eenmaal blind vertrouwen in de handige snelle jongens van de branche ook al kom je met zuiver objectief vast te stellen tegenwerpingen.

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