Speaker cables: do they make a difference?
(Myths and pseudo-scientific theories about speaker cables from a rational viewpoint)
- Myths and pseudo-scientific theories about speaker cables.
- Testability and characteristics of human hearing.
- TINA simulation of an amplifier-cable-speaker system.
Last edited: February 27, 2019
(minor changes in the list of myths and cable capacitance sections)
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.
Hi-end (audiophile) audio cable companies have expensive solutions to problems that don't exist in reality. Their business model is based on willful ignorance: ignoring the facts and proved models of modern sciences like high speed signal transmission or psychoacoustics.
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 wires in the amplifier...
Some of the most popular cable myths and marketing lies:
- Wire material has to be expensive and special
Oxygen-free copper, copper with silver plating is better for audio than plain copper.
- Nonlinear distortion, diode rectifier effects in copper wires.
- Unusual wire or cable structure for reducing skin effect or for ultra low inductance
- Waveform dispersion and time based errors due to varying velocity of propagation in the audio band
- Some really crazy...
There are some very crazy ideas: cable "break in", copper wire demagnetization, directional speaker cables...
And the facts:
- Wire material doesn't have to be expensive: copper is a cheap and good conductor. And what really matters is the resistance of the wire, which has to be below a limit and this limit depends on the speaker's impedance.
- Skin effect is not important in the audio range.
- Nonlinear distortion nonsense: Bad connectors may cause distortion and not wires. And if the monocrystal theory would be true, then switches and connectors would stop working.
- Varying velocity of propagation nonsense: cables don't alter arrival times and don't cause waveform dispersion in the audio band up to five kilometers (3 miles). At this length any cable's frequency response probably will be far from flat in the audio band. The mathematical condition for distortion-free transmission in very long cables (long is more than 5 kilometers!) is known as the Heaviside condition named after Heaviside who solved the problem of long telephone lines in 1887!
- The material of the insulation doesn't affect the sound quality, even PVC works well for audio.
- Over a certain length cable inductance begin to attenuate high frequencies. The maximum recommended length depends on speaker impedance and cable design (inductance per meter). For zip cords and 4 Ohm speakers the maximum recommended length is about 10 meters. For 8 Ohm speakers this is about 20 meters!
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. (For those who want to gain deeper insight into human hearing research I recommend books from Eberhard Zwicker and Floyd E. Toole.)
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.
In speaker cables, the propagation of the electromagnetic wave and transmission line (TL) effects are negligible in the audio range up to a few hundred meters, however, resonances due to wave reflections can negatively affect the stability of high bandwidth amplifiers even at smaller distances. For example, in a 10 meter long cable the first quarter-wave resonance (fundamental resonance) is close enough to the operating range of high-bandwidth amplifiers. Fortunately, 99% of the power amps have built-in protection and we do not have to deal with this phenomenon.
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 an issue, 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 capacitance is a secondary parameter for speaker cables. Some facts about cable capacitance:
- Conventional zip-cord speaker cables have a specific (distributed) capacitance of 70 pF/m to 170 pF/m. Interwoven, ribbon or coaxial audiophile cables have much higher capacitance and can be as high as 2000 pF/m.
- The capacitance in zip-cord cables has no effect on the amp's frequency response in the audio range up to ~100 meters. (valid for cables with 200 pF/m max.).
- Because the cable capacitance has no effect on the frequency response in the audio range (and in the ultrasonic range), therefore the linearity of the insulation material does not matter. In other words, even the possibility of the distortion can be completely excluded. There is no nonlinear distortion in speaker cables and there is no sonic difference between PVC, rubber, Teflon. The insulation is important at high frequencies (above 1 MHz) or in circuits with high voltages and high impedances.
Sometimes power amplifiers become unstable with long and high capacitance cables and overheat, which can lead to excess distortion or even amp failure, while these amps - like any well designed audio power amp - can drive very high capacitive loads (even 200 nF) without going into oscillation. This very rare oscillation at RF can be attributed to the lower velocity of propagation of high capacitance cables which results in lower quarter-wave resonant frequency.* If the resonance 'meets' some low level RF noise, e.g. residual noise of a DAC and the amplifier does not have proper RF protection, then the amp may overheat and the current protection may switch off. To avoid RF oscillation a very simple damper circuit (10 Ohm resistor parallel with a 1-2 uH coil) is added to the output of power amplifiers. The damper circuit has no effect on the frequency response in the audio frequency range and the protection is required for high-bandwidth amps if the cable is longer than about 10 meters.
* The other problem with high capacitance cables is that they become a short circuit at their quarter-wave resonance frequency, on the other hand normal zip cords or twisted cables still have some (1-2 Ohm) shunt resistance.
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.
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 meters (32.8 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 meters (32.8 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 (32.8 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 meters (32.8 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. On the other hand, 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.)
The loudspeaker cable is the simplest component in the signal chain: 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 compared to speakers or amplifiers.
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 built quality is indisputable, the so many hiccups in their marketing are false.