Speaker cable guide
Last edited: May 14, 2019
Speaker cables are the most over-mystified and overrated components of audio systems. Despite the claims of the high-end audio cable industry, what really matters is the careful selection of the wire gauge. Speaker wires have no magical attributes and the signal transmission through a wire is completely understood by engineers and scientists.
This guide is a mixture of well-known facts (e.g. circuit models) and a bit of my own work (experiments, circuit analysis). It's widely known that inductance loss in speaker cables is negligible up to several meters, but how much is much? I've studied the inductance loss in detail and I found that the key concept - besides cable inductance - is the impedance response of tweeters.
▶ Construction
▶ Some words on shielded and twisted speaker cables
▶ Speaker wire plugs and terminals
▶ Resistance, inductance and capacitance
▶ Speaker impedance
▶ Determination of the minimum cross-section
▶ Table with recommended cable distances
▶ Attenuation due to inductance
Construction
Speaker cables are made of two stranded copper wires surrounded with PVC insulation. The role of the insulation - apart from isolating the two wires from each other - is to prevent the copper from oxidation. There are speaker cables that cost 100$ per meter or more, but in reality these are just 'audio jewelry', they look cool, but have no sonic benefits (and some of them can be worse than an ordinary speaker cable). A speaker cable should have very low series resistance and series inductance - and that's all.
The most common copper in electrical applications is the so called Electrolytic Tough Pitch (ETP) copper with 99.9%-99.95% copper content. Oxygen-free copper (OFC) is considered better for audio, but in fact it has the same electrical and mechanical properties as plain electrolytic copper. And if somebody sells '99.9% OFC' cable, then it is just electrical copper, not OFC.
Using exotic materials (oxygen-free copper, gold, silver, Teflon) or construction (ribbon cables, Litz wire, coaxial cables, golden ratio or other geometry for matched propagation or skin effect reduction) have no benefits in audio cables. These are just raise the cost and give cables an extraordinary look and feel.
There is a major difference between speaker wires (aka zip-cords) and speaker cables. Speaker cables have an outer jacket, so they are more durable and better for heavy duty live amplification. In addition to this the outer jacket is mandatory for in-wall installation. Speaker wires (zip-cords) have no outer jacket and they are intended to be used in home audio systems (home theater, stereo).
Some cable companies offer speaker cables with twisted wires or tinned copper conductors. Tinned copper has lower oxidation rate than 'bare copper' (useful close to the sea). The twisted pair lowers the induced magnetic field around the cable and lowers the voltage induced in the cable by external magnetic fields.
Some words on shielded and twisted speaker cables (and electromagnetic interference)
Since speaker cables are connected to power amplifiers with low output impedance, they don't require protection against electric and magnetic fields in the audio frequency range. There is no need to worry about radio frequency interference (RFI) in a typical listening room as well - unless someone lives in the close field of an LF or MF radio transmitter... So shielding and even twisting single speaker cables are completely unnecessary.
The most common and almost the only form of electromagnetic interference in a speaker wire system is the crosstalk between straight and unshielded wire pairs in multiconductor cables or between bundled speaker cables. If several speaker cables are bundled together or installed in a cable conduit side by side and they are connected to different channels on the amplifier, then using twisted pair is highly recommended. For bi-amping, tri-amping twisting is not necessary and a multi conductor cable with straight wires can be used without any further problem (there may be a little crosstalk from the tweeter to the woofer, but that's not audible). Crosstalk between those speaker cables that are lying around on the floor is zero.
Since speaker cables are connected to low impedance loads and amplifiers with low output impedance (voltage sources), the currents are high and the generated magnetic field around a speaker cable is much 'stronger' than the electric field. Inductive coupling between speaker wire pairs is higher than capacitive coupling, and any 'crosstalk reduction method' should lower the magnetic field around the cable. Methods for reducing inductive coupling: twisted pair, star quad, coaxial cable (+ the 'random cabling method' used in so many home theater or stereo systems).
Speaker wire plugs and terminals
There are two basic types of amplifier and speaker terminals in home audio: binding posts and spring clips. The chart below summarizes the possible connections between speaker/amp terminals and cable terminals. Although pin plugs may fit into binding posts, they are not recommended with this type of speaker/amp terminal.
Spring clips can accept bare wire up to 14 AWG / 2 mm2. Binding posts give more freedom as they can work directly with cables up to 10 AWG / 6 mm2. But it's much better to terminate the cables with appropriate connectors, because bare wire endings can be damaged quickly.
Speaker wire connectors have some real advantages over bare wires:
- Speaker plugs are made of corrosion-resistant material (gold-plated copper, brass or sometimes bronze) that does not oxidise in air.
- Connectors are more durable than bare wire endings. Binding posts can break bare wires after a couple of uses.
- Stable connection: no loose ends, no chance of stray strands that can cause a short circuit.
Resistance, inductance and capacitance
Since speaker cables connect an amplifier with low output impedance (~100 mOhm) to a low impedance load (3...50 Ohm), the series electrical parameters of the cable (series resistance and inductance) are more important than the parallel parameters (capacitance and shunt conductance).
The resistance, inductance and capacitance of a cable are directly proportional to its length. So the longer the wire, the more resistance, inductance and capacitance it will have. A thicker wire will have less resistance at the same length as a smaller gauge. Doubling the effective cross-sectional area of a wire reduces its resistance by half.
The current flow through a wire results in a voltage drop according to Ohm's law (voltage = resistance * current). Therefore a speaker wire should have low resistance to minimize voltage drop. The inductance result in high frequency loss, which is only audible with very long cables (see at the end of this article). The capacitance only affects the frequency response of a typical solid-state class AB amplifier above 200 kHz. The real problem with high capacitance exotic cables (such as ribbon cables, interwoven cables) is that they short the amplifier in a very wide frequency range around the quarter-wave resonance frequency (between 1 MHz and 10 MHz). There is no such problem with zip cords or twisted pairs...
Cable geometry, the spacing of the conductors determine inductance and capacitance. Greater the distance between the two conductors, larger the inductance of the cable and lower its capacitance. So separating the wires over a long distance is not recommended, because it will add a lot of inductance. (For zip cords the typical inductance per meter values are between 600 nH/m - 700 nH/m.)
The often mentioned, popular skin effect doesn't exist in stranded copper wires below 50 kHz (check out these measurements at Audioholics). In solid copper wires, that are thicker than 2 mm2, there is a small increase in the resistance at the top of the audio range. However, even with solid conductors the high frequency attenuation is insignificant: due to skin effect and proximity effect the AC resistance of a 2.5 mm2 solid copper conductor cable is 50% higher at 20 kHz than its DC resistance, but the additional loss in a 10 meter long cable is only 0.1 dB at this frequency with a 8 Ohm load, which is completely insignificant. Cable inductance is more important (as the cable length increases) than the skin effect.
Speaker impedance
A speaker's impedance rating is merely a nominal figure. In fact, the speaker's impedance (~ AC resistance) is frequency-dependent: a speaker with 4 Ohm rating can drop down to 3.2 Ohms, and get very high - say 40 ohms or more - at various frequencies.
The minimum value of the speaker's impedance will determine the largest attenuation due to wire resistance and output resistance of the amplifier. Lower the minimum impedance, higher the attenuation with a given cable and amplifier. According to the IEC 268-5 standard the minimum impedance of a loudspeaker must not fall below 80% of the nominal impedance, so for an 8 Ohm speaker the minimum would be 6.4 Ohm, and for a 4 Ohm speaker this would be 3.2 Ohm.
Speakers with 4 Ohm nominal impedance rating are more 'sensitive' to wire resistance, inductance and to the output resistance of audio amplifiers than speakers with 8 Ohm nominal impedance.
Sometimes the label on the rear panel of a loudspeaker displays something like '4-8 ohms'. In this case, the speaker has drivers with different impedance ratings, e.g. a 4 Ohm woofer and an 8 Ohm tweeter. These type of speakers should be taken into account as 4 Ohm speakers when determining the cross-section. In inductance calculations the impedance of the tweeter (or tweeter section) is what matters.
Determination of the minimum cross-section
There is a minimum wire cross-sectional area or gauge (AWG) for a given speaker impedance, cable length and allowed loss (dB). Or put it differently: there is a maximum cable length for a given speaker impedance, wire cross-sectional area and allowed loss.
A more accurate calculation may include the output resistance of the amplifier and the inductance of the cable. For even greater precision the amplifier's output inductance can be used as an extra parameter.
The most important parameters are wire gauge, length AND the nominal impedance of the loudspeaker.
The output impedance of an amplifier (in the case of audio power amps this is the output resistance) can be calculated from the damping factor. Both the damping factor and the output impedance vary with frequency. Nowadays, the output resistance of branded audio amplifiers (home theater, stereo) even at 10 kHz will not exceed or just slightly over 100 mΩ. So 100 mOhm is a good approximation in loss calculations.
Datasheets with DF (or output impedance) vs. frequency graphs are rare and single DF values in spec sheets should be treated with caution. Fortunately, there is a great collection of audio amplifier measurements here.
Output inductance is between 1 uHenry and 2 uHenry. The source of this inductance is that in the vast majority of amplifiers there is a small inductor parallel with a resistor to prevent oscillation with long (and 'bad') cables. 1 uHenry is the inductance of 1.5 meter zip cord.
Table with recommended cable distances
The table below describes the recommended maximum cable distances for various speaker cable gauges (cross-sections) and speaker loads with 0.3 dB and 0.5 dB loss. The amplifier's output impedance is an adjustable parameter: it can be set to zero (ideal amp) or 100 mΩ (close to a real-world class AB amplifier).
AWG (American Wire Gauge): the higher the gauge number, the smaller the diameter, and the thinner the wire.
| Maximum length in meter | ||||
| Sq. mm | 0.3 dB loss | 0.5 dB loss | ||
| 4 Ohm | 8 Ohm | 4 Ohm | 8 Ohm | |
| 0.75 | 2.5 | 5 | 4 | 8 |
|---|---|---|---|---|
| 1.5 | 5 | 10 | 8 | 16 |
| 2.5 | 8 | 16 | 12 | 24 |
| 4 | 13 | 26 | 22 | 44 |
| 0.75 | 0.3 | 3 | 2 | 6 |
| 1.5 | 0.5 | 6 | 4 | 12 |
| 2.5 | 1 | 9 | 6 | 21 |
| 4 | 2 | 15 | 10 | 33 |
(Switching between units and amplifier output resistance require JavaScript.)
How does it work? Set the amp output resistance to 100 mΩ (preferred) and select the column with the desired loss, then select the length and the appropriate cross-section.
Notes:
- This table was calculated for pure copper wire. Cables with copper-clad aluminium wire (CCAW) should have two AWG sizes larger (e.g. 14 AWG instead of 16 AWG) or 1.5 times larger cross section to be selected.
- With 0.5 dB loss (margin of error) the attenuation of the cable will be inaudible with music. (With music one decibel is barely audible.)
- In a multi-way system the 0.5 dB limit also guarantees, that any kind of nonlinear distortion in the woofer/mid-woofer's current will not modulate the tweeter's current. In other words the tweeter always receives a clear signal from the amplifier regardless of the woofer's current and bi-wiring will not improve a properly designed system...
Selecting the right cables for 8 Ohm speakers even for 0.3 dB loss is an easy task in a domestic audio system, on the other hand it's impossible to achieve better than 0.3 dB error with real amps and 4 Ohm speakers for sure (relying only on calculations, without doing real measurements). The reason for this is simple: the greatest uncertainty in the calculation is the output resistance of the amplifiers. The amplifier used in the measurements by the speaker manufacturer probably has a different type compared to the amp that powers the speakers at home. The difference between the output resistances can be as high as 100 mOhm (e.g. 30 mOhm vs. 130 mOhm, both pretty good values). This results in 0.27 dB loss with 4 Ohm load and 0.13 dB loss with 8 Ohm load. Considering the magnitudes of the reflections in a typical room, it's really just a game with numbers, and this error won't make a good system worse, but it's still part of the system.
Loss (transfer function) calculations:
loss = 20 · log ( Rspeaker / ( Rcable+Ramp+Rspeaker ) ) [dB]
Rspeaker = 0.8 · Znominal [Ω]
Rcable = 2 · ρ · l / A [Ω]
ρ = 17 mΩ·mm2/m (resistivity of copper)
Here is a simple method for calculating the resistance of a copper wire or cable. The resistivity of copper is 17 mΩ·mm2/m, which means that one meter wire with 1 mm2 cross-sectional area has 17 mΩ resistance. The resistance of a wire is directly proportional to its length and inversely proportional to its thickness (cross-sectional area) and if we use mm2 for the area (A) and meter for the length (l), then Rcable = 2 · 17 · l / A - the result in mΩ. (for cables the resistance has to be doubled, because speaker cables have two wires)
Attenuation due to inductance
The inductance of long speaker cables may cause some loss of the highest audible frequencies. The actual high frequency roll-off depends on the inductance of the cable and the nominal impedance of the tweeter (more closely the impedance curve of the tweeter measured from the speaker terminals). The cable's inductance is function of length and cable design.
Fortunately, dome tweeters with same nominal impedance rating have similar (almost the same) impedance curve between 10 kHz and 20 kHz, so speaker wires of the same length and design will have a very similar attenuation. The difference between two 8 Ohm 25 mm (1 inch) dome tweeter is almost zero below 10 meters, and about 0.1 dB at 20 meters. The graph below shows the estimated loss for 8 Ohm and 4 Ohm tweeters and for pure resistive loads. With resistive load the attenuation would be less.
The graph is valid for conventional speaker cables and zip cords (distributed inductance of these cables: 600 nanoHenry / meter - 700 nanoHenry / meter). Not valid for coaxial, star quad, woven CAT5, ribbon, 'more wires than the colors of the rainbow' type cables.
The attenuation of the cable's resistance and inductance are additive, however the addition is not a perfect summation, the overall loss at 20 kHz is a bit less than the sum of the two losses. If we allow 0.5 dB loss for the resistance, then 0.5 dB additional loss at 20 kHz for the inductance is still acceptable.
What about the audibility of inductance loss and the length of the cable? First of all, I don't think that we can define an exact limit for the cable length. If I had to choose a limit, then I would choose 7 meters for 4 Ohm and 15 meters for 8 Ohm speakers. On the other hand, it can be stated for sure that inductance loss is not audible up to five meters for 4 Ohm tweeters and up to ten meters for 8 Ohm tweeters. It follows that there is no need for ultra low inductance speaker cables.
Sometimes there is a little overshoot in the response due to the interaction between the reactive load presented by the crossover and the cable inductance. This may happen when a cable is longer than ten meters and the cross-sectional area is large (>2.5 mm2). The magnitude of the overshoot is very small (less than 0.05 dB) and negligible.
Csaba Horváth
See also:
Audio interconnect cables explained
Audibility thresholds for SINAD/THD measurements
