• Choosing loudspeaker cable

    The importance of cables for the connection between the amplifier and the speaker is often controversial. Hi-fi aficionados spend fortunes on cables that promise spectacular results, and our short auditory memory and subjectivity lead many to confirm these improvements in their systems.

    The truth is that there are very few serious studies on the importance of the cable in relation to the perceived sound quality. A cable has impedance (opposition to electric current as a function of frequency), capacitance (behaves to some extent like a capacitor) and inductance (behaves like a coil). However, a few years ago an AES article concluded that the differences between cables were very small in terms of capacitance and inductance, and only recognized the importance of impedance.

    Therefore I invite you to leave aside any cable with such an exaggerated price as its promises, and look only at the gauge (thickness, cross-sectional area) of the cable, as far as the electrical characteristics are concerned (then there are important practical issues in our business such as the ease with which it can be wound, particularly in cold weather, which are outside the scope of this article). Although, from an audio point of view, thicker is better, in the end it may be necessary to adopt compromise solutions if the ideal cable is impractical either because of weight, volume (in a fixed installation with a lot of wiring the space taken up by the cables is a factor that can be important) or cost (again, in fixed installations, this is a parameter that can be very significant if very long lines are used).

    1. The cable, the cook, the thief, his wife & her lover

    The damping factor of an amplifier can be defined as its ability to control the movement of a speaker's coil. A high damping factor is desirable to obtain a "tight" sound at low frequencies, which otherwise will sound "slack" and "loose".

    An ideal amplifier has an infinitely high damping factor. In practice, here on planet earth at least, amplifiers exhibit some output impedance, resulting in typical damping factors between 300 and 600 for an 8 ohm load.

    The damping factor is calculated as the ratio of the load impedance (designated by the letter Z) to the output impedance:

    Damping factor = ---------

    For example, an amplifier with an output impedance of 0.02 ohm (this is not usually specified, but can be calculated by clearing the output impedance in the formula above) connected to a load of 8 ohm results in a damping of 400. In this example the damping would be 200 for 4 ohm, 100 for 2 ohm, and, following the same logic, 800 for 16 ohm.

    So far so good. Normally a damping factor above 50 is recommended, with a minimum of 25. As mentioned above, this is particularly important for low frequencies.

    Things get complicated when we add a cable of a certain length. The impedance of the cable is directly proportional to its length. And inversely proportional to its section, that is, the thicker it is, the lower its impedance.

    To calculate the damping factor with a real cable, of a given length and thickness (gauge), between the amplifier and the load (the loudspeaker), we have to add an additional term to the above formula: the impedance of the cable.

    Damping factor = ------------------
    Zoutput + Zcable

    Example for 4 and 8 ohm loads and gauge 14 (2 mm²) cable, using an amplifier with a damping factor of 400 at 8 ohm
    Cable length Resulting system damping factor Cable impedance
    4 ohm 8 ohm
    5 40 80 0.08 ohm
    10 21 40 0.17 ohm
    15 15 30 0.25 ohm
    20 11 23 0.33 ohm

    For example, for 20 meters and 4 ohms, the damping factor is 4/(0.33+0.02), which is equal to 11.4 (which we have rounded to 11 in the table, as the rest of the table uses rounded values for simplicity). For the value of the cable impedance we have assumed that the conductor is made of copper, which will be the case in 99.9% of the cases. Impedance varies with frequency, so we could really calculate values for all frequencies, although for the day to day it is not worth getting into those complexities, so here we have limited ourselves to the calculation with the nominal impedance.

    As the cable impedance becomes larger than the output impedance of the amplifier, the initial damping factor of the amplifier becomes less important. For example, if we were to double the amplifier's damping in our example to 800 (at 8 ohm), the resulting damping factor for 8 ohms would be 89 and 23.5 for 5 and 20 meters respectively, which is very similar to the results we would obtain for the 400 factor (80 and 23, as can be seen in the table above), particularly for 20 m, since the longer the cable, the lower the importance of the amplifier's (initial) damping factor.

    We have previously commented that the damping factor affects the "tightness" of low frequencies. Thus, depending on the importance of the low frequencies for the different applications, we can make the decision of the cable thickness to be used. For example, in a discotheque it will be worth using a very thick cable for the bass boxes, while for a public address system the damping is not a factor that affects us due to the fact that only voice is reproduced, so we will choose the cable exclusively according to the power loss, as detailed below.

    2. Power loss

    Since the impedance of the cable is in series with that of the speaker, the amplifier is delivering power to both the speaker and the cable. Also, as the cable raises the total system impedance, the amplifier will deliver less power. However, since the decibels are calculated logarithmically, the cable must be very thin and very long for the power loss to be significant in auditory terms, i.e. in decibels.

    We could say that a loss of 1 dB is acceptable, and a loss of 3 dB reasonable, which is equivalent to wasting in the cable 11% and 29%, respectively, of the power coming out of the amplifier. Although the power loss is within reasonable limits, this does not mean that the damping factor is equally reasonable. In fact, from a damping factor standpoint, am SPL reduction greater than 0.3 dB is not acceptable. However, for public address/peripheral and ambient sound applications where the damping factor is not critical, we may use a criterion for cable selection based only on pressure level reduction (or power loss).

    Example for 4 and 8 ohm loads and gauge 14 (2 mm²) cable, using an amplifier with a damping factor of 400 at 8 ohm
    Cable length Energy lost in the cable Level reduction
    4 ohm 8 ohm 4 ohm 8 ohm
    5 2% 1% -0.2 dB -0.1 dB
    10 4% 2% -0.4 dB -0.2 dB
    15 6% 3% -0.6 dB -0.3 dB
    20 8% 4% -0.7 dB -0.4 dB

    The above calculations assume speaker cable without connectors, as is often the case in fixed installations. The connectors will also add their own impedance which is low but not negligible, so from the point of view of keeping the impedance as low as possible it is preferable to use a single cable than to chain several cables together.

    3. Transformer lines

    Transformer lines, which use voltages such as 50, 70 or 100V, allow the use of thinner cable than in direct connection installations (without transformer). We refer to these line systems as "high impedance", while our 2, 4, 8 or 16 ohms are "low impedance". The input impedance of a loudspeaker equipped with an input transformer typically ranges from several hundred to several thousand ohms, which means that the cable impedance is now small compared to the impedance of the speakers. In practice this means that we can either use a thinner (and cheaper) cable, or long cable runs.

    In these installations the only criterion when selecting the cable has to be the power loss, forgetting the damping factor (since the transformer prevents tight bass anyway). Sometimes in an installation it is decided to use speakers with transformers to avoid energy losses, when often a thicker cable with low impedance speakers will give us a more economical system with a power loss within reason.

    4. Conclusion

    Always choose the appropriate cable gauge for the application, the type of enclosure, the load impedance and the cable length.