Speaker cables: do they make a difference?
(Myths and pseudo-scientific theories about speaker cables from a scientific viewpoint)
"Ignorance is a virus. Once it starts spreading, it can only be cured by reason."
- Neil deGrasse Tyson
- Myths and pseudo-scientific theories about speaker cables.
- Testability and characteristics of human hearing.
- TINA simulation of an amplifier-cable-speaker system.
Last updated: July 14, 2018
(some additional info about cable capacitance)
I have a feeling that the No. 1 of myths in audio technology is connected to speaker cables. The core of the misconception is that expensive and exotic audiophile cables transmit the audio signal in a different way and have a better sound than conventional zip-cord cables.
Speaker cable confusion - Much ado about nothing?
Exotic audiophile speaker cable companies do everything to deceive people. And the lack of electronic and acoustical knowledge of most customers gives straight way to these pseudoscientific misconceptions. Some are really ridiculous, but the game is not for fun, because who wouldn't want to get the most benefit with minimal work? For this, the speaker cable business seems a good opportunity. This kind of business is very far from any kind of accountability and responsibility.
In addition to this, myths are kept alive by some "smart" audiophile journalists with "huge" background knowledge. Looking for properties in a cable like "dynamics", or a "tone character" shows very strong ignorance in this field. Audiophile cable tests over the net are mostly nothing but disguised advertisements.
Of course, cables do make a difference, but the reason for the difference is not their exotic structure or the choice of an exotic material. The only difference what people can hear is caused by the resistance of the cable. And don't forget that the speaker's voice coil contains several meters long conventional copper wire. Not to mention the transformer wire in the amplifier...
Essence of hi-end speaker cable business
Here is a short list of the most important myths connected with cables:
- Wire material.
Oxygen-free copper and/or copper with silver plating, or copper with monocrystal structure is better for audio than plain copper.
- Wire structure
The skin effect has an audible impact on the wire resistance in the audio range, so we need Litz wire or similar in order to reduce skin effect.
Flat wire or other orthodox wiring method is required in order to reduce cable capacitance (or inductance).
There are some very crazy ideas: cable "break in", copper wire demagnetization, directional speaker cables...
And here are the claims from the scientific side:
- Wire material is not important. What is important is the resistance of wire, which has to be below a limit. This limit depends on the speaker's impedance.
- Skin effect is not important in the audio range.
- Cable capacitance is not important. On the other hand cable inductance can be a problem with long cables and low impedance speakers.
Fortunately, from loads of experiments in the last century, we know quite a lot about the human hearing. These experiments and theories can be found in books about psychoacoustics. There is a wide spectrum of test signals in a psychoacoustics research, from simple to complex: sinusoidal, white and pink noise, complex periodic signals, pulse, and of course short pieces of music. Most of the subjects are between 20 and 40 years old and have good hearing (usually university students are recruited for these studies). Skills, such as the least noticeable difference in sound level for simple or complex signals (Just-Noticeable Level Differences), the least noticeable difference in frequency (Just-Noticeable Frequency Differences), time and frequency domain masking rules are well-known.
Psychoacoustic experiments are based on blind tests and special test signals developed according to the objective of the actual research. The most common method is the ABX test: in this case the subject has to decide whether signal X is A or B ('Is X A or B?'). The other variant of the ABX test is the AXY, where the subjects have to choose from X or Y ('Is X or Y A?'). Another type of blind test is the two-alternative forced-choice test. This type of test is used for determining audible threshold levels.
Blind tests alone don't guarantee the success of an experiment or the validity of the results. There are two types of errors associated with these tests: false positive or false negative errors. Although that's beyond the scope of this paper it's always possible to construct false positive tests for marketing purposes.
Some notes on the validity of conventional (non-blind) tests. First of all, our musical memory is short and inaccurate: we can easily recall big differences, but not subtle ones. So any tests are only relevant if the participants compare up to 5 seconds of piece of music with fast switching. Most non-blind audio cable tests are flawed due to the imperfection of musical memory. "An hour ago this album was different..." - is a meaningless statement because the next 59 minutes overrode the musical memory...
For humans with good hearing the Just-Noticeable Level Difference can be as small as 0.3 dB for a pure sine wave. For other types of signals the threshold is higher. In addition, the human ear is extremely insensitive to amplitude changes at very low and high frequencies. If we accept, that the maximum amplitude error caused by the cable can be 0.3 dB, then the cable will be totally inaudible.
Amplifier, speaker cable and speaker cabinet equivalent circuit
In order to understand how the cable affects the signal coming from the amplifier, we have to analyze the electric model of the speaker cable (equivalent circuit, RLC model). In the model, Z represents the frequency-dependent impedance of the speaker cabinet, which will play a big role later. Lcable is the total inductance of the cable, Ccable is the cable capacitance, Rcable is the DC resistance of the cable (back and forth). As the impedance of the speaker can be measured, the cable parameters can be measured (or computed from catalog data), the amplifier-cable-speaker can be modeled even in a circuit simulation program.
What is missing from the model is the skin effect. Fortunately, in loudspeaker cables the skin effect is negligible in the audio frequency range. For example, the resistance at 20 kHz of a wire with 1.5 mm2 cross-section will be 12% higher than the DC resistance due to the skin effect. The skin effect also has an interesting side effect: the self-induction of the cable is reduced. (For very long cables, inductance causes greater high frequency loss than the skin effect).
There is a widespread myth that cables can be characterized by their frequency response, but cables have no such property as frequency response. The frequency response of any cable depends on the output resistance of the voltage source and on the resistance or impedance of the load. Solid state amps have low output impedance, so its not a variable factor, but the response may change due to a different speaker.
The capacitance, inductance and resistance of the cable is directly proportional to the length of the cable. By increasing the cross-section, the resistance drops proportionally, the capacitance slightly increases and the inductance slightly decreases.
The least important parameter of the loudspeaker cables is the capacitance. We can summarize the effect of cable capacitance in a few words:
- The cable capacitance has no effect on the response of the output stages in the audio range if the cable is less than 100 meters (C = 200 pF/m). In other words, a 10 meter long conventional zip-chord speaker cable does not have enough capacitance to influence the response of any kind of power amp below 200 kHz!
- Because the cable capacitance has no effect on the frequency response in the audio range (and basically the entire range of the audio signal), therefore the linearity of the insulation material does not matter. (In terms of linearity, it doesn't matter whether the insulation is PVC, rubber, teflon etc...)
- Capacitive loading of any speaker cable is negligible.
- Traditional PVC insulated speaker cables have a specific or distributed capacitance of 70 pF/m to 170 pF/m. The distributed capacitance of some specially woven audiophile speaker cables is usually much higher than this.
The inductance of the cable forms a low pass filter with the speaker. The higher the inductance or the lower the load impedance, the lower the cut-off frequency of this low pass filter. Fortunately, up to 15 or 20 meters the inductance does not cause significant (larger than 0.5 dB) loss. Speakers rated at 4 Ohm impedance are more sensitive to inductance than 8 Ohm systems.
And now here comes the most important parameter of loudspeaker cables: DC resistance . The resistance of the wire and the varying impedance of the speaker together form a frequency-dependent attenuator (voltage divider). The attenuation has a fixed (DC) component and a frequency-dependent part. In a badly designed system (using really thin and long wires), the first can be heard as a volume decrease, the latter can be heard as a change in the tone (apparent bass and middle boost in a two-way loudspeaker).
The main rule of speaker cables is very simple: the lower the speaker impedance (load impedance), the smaller the cable resistance has to be. If we allow a maximum of 0.3 dB attenuation, the resistance of the cable can be up to 4% of the speaker's minimum impedance. If we allow a maximum of 0.5 dB attenuation by the cable, the resistance of the cable can be up to 6% of the speaker's minimum impedance. And for a maximum attenuation of 1 dB, the resistance of the cable can be up to 12% of the speaker's minimum impedance.
"There is nothing magical or mystical about audio cables. They can be measured, modelled. Understanding audio cables requires basic electronic knowledge and nothing else."
After clarifying the effects of the electrical parameters and the relationship between the electrical parameters and the length and cross-section of the cable, it is now easier to see how a cable with given length or cross-section behaves with a particular load. The following options remained:
- How the frequency response changes due to the load.
- How the frequency response changes due to the length.
- How the frequency response changes due to the cross-section.
These examinations (measurements, simulations) can be performed with both ideal (or resistive) loads or real loads. I present the first case with an ideal load, the third case with a real speaker.
Frequency response of a 10 meter (3.28 feet) long standard 1,5mm2 zip-cord speaker cable with 4, 8 and 16 Ohms load resistances
In the above figure, frequency response of a 10 meter (3.28 feet) long 1.5mm 2 2-wire speaker cable with 4, 8 and 16 Ohms load resistances are plotted. The inductance of the cable is 0.7 uHenry/meter. The 4 Ohm resistor is not only attenuated more, but its high frequency response falls even faster. With the same specific wire parameters, the 4 Ohm response can be achieved with an 8 Ohm resistor with 20 meters cable or 16 Ohm resistor with 40 meters cable! The lower the load resistance (the lower the impedance of the speaker), the more sensitive to cable resistance and inductance - and the larger, the more insensitive. Otherwise: For a given wire cross section, an 8 Ohm speaker has twice the maximum cable length than a 4 Ohm system.
Since the impedance ('AC resistance') of the speaker cabinets varies according to the frequency, the attenuation of the cable will also be frequency-dependent. (The change of the AC resistance can be represented by the impedance curve of the speaker). Where the impedance of the loudspeaker is significantly higher than the nominal value (e.g. at resonant frequency, crossover frequencies), the attenuation will be much smaller than in those ranges where the impedance of the speaker cabinet approaches to the DC resistance. The greater the resistance of the speaker cable, the more 'bumpy' impedance of the speaker in the frequency response is reflected. For long and thin cables this can be perceived as a change in the tone. If the speaker's impedance were flat, then the cable would cause volume decrease only.
Frequency responses of a 10 meters (3.28 feet) long conventional 2-wire cable with a 2-way vented box (wire cross-sectional area: 1.5mm2 (green) and 0.75mm2 (blue))
In the figure above, frequency response of a 10 meter (3.28 feet) long 2-wire speaker cable with 1.5mm2 and 0.75mm2 cross-section connected to a two-way vented box is plotted. The nominal impedance of the speaker is 8 Ohms, but in reality the impedance changes between 6.6 Ohm and 30 Ohms, depending on the frequency. The maximum error generated by the impedance curve is approximately 0.25 dB for the 1.5 mm2 cable and 0.4dB for the 0.75mm2 cable - that is not an audible category.
Because the resistance of a wire is proportional to its length and inversely proportional to the cross-section, the longer the wire, the greater the cross section has to be. For each length and nominal impedance there is a minimum wire cross-section. At the same time, a wire with cross section that is much larger than the minimum is unnecessary. (There is another minimum wire cross-section requirement due to power handling, but this only affects cables shorter than 2 meters or where the amplifier power is larger than 1000 Watt.)
Fortunately noise is not a real problem with speaker cables. Self noise of speaker cables is well below the audible threshold. Most of the noise comes from the amplifiers and not from the cables.
The loudspeaker cable is the simplest, most primitive circuit element: its function is to transmit the current from amplifier to loudspeakers with no audible distortion and loss. There are no complicated multi-stage signal conversions (amplification, filtering, energy transformation, modulation) as in the active elements (amplifier) or in the loudspeaker (electromechanical and acoustical transformation). Speaker cables are really boring devices.
All in all: speaker cables, wires act as a low-pass filter due to inductance and skin effect. Fortunately, these effects are well above the audible frequency band. What is important however, is that the resistance of the wire and the impedance of the speaker together form a frequency-dependent attenuator (voltage divider). With conventional copper cables that have a large enough cross-section it is possible to restrict this frequency-dependent attenuation to be sufficiently low in the audio range. The attenuation of the cable is not audible if the speaker cable resistance does not reach the 4% of speaker impedance minimum (0.3 dB criteria).
Using high-quality speaker connectors are more important than using exotic and expensive loudspeaker cables . Expensive, exotic loudspeaker cables do not improve or fix an error in an audio system, unless the cables and connectors have a very poor quality. Audiophile loudspeaker cables are optically 'turbocharged' conventional loudspeaker cables, and although their assembly quality is indisputable, the so many hiccups in their marketing are false.