This page provides a Java applet which should allow you to assess the basic properties of a standard “twin feeder” loudspeaker cable. You can adjust the length of the cable, the size of the conductors, and their spacing, and then see the effects upon the amplitude/time response as a function of signal frequency. The calculation includes the contribution of internal impedance (i.e. “skin effect”) upon performance. For the sake of example, the wires are assumed to be made of copper, with a dielectric whose effective dielectric constant value is 1·5. The results shown on other pages indicate that the choice of dielectric and metal can usually be expected to have little effect upon performance, so these choices seem reasonable for the purposes of this applet. The applet assumes an 8 Ohm resistive load for the loudspeaker. A lower impedance would produce larger effects – e.g. a 4 Ohm load would mean the effects would be approximately double what is shown here.
How to use the Applet
If you have not previously used the above applet, you should find the following explanations and comments worth reading. Please note that the calculation performed by the applet is quite complicated, so there may be a short delay each time you change a value before the display is redrawn. The applet should work with any Sun JVM from the 1.0.x standard onwards. The appearance may vary slightly from one JVM to another, but the results should be computed to IEEE double precision standards.
The main display provided by the applet mimics the screen of a vector analyser. The horizontal (x) scale is logarithmic in terms of signal frequency, and covers the range from 100Hz to 50kHz. There are two horizontal scales. One is for the relative (nominal) power level reaching the speaker terminals. 0dB means here that the signal level at the speaker terminals is identical to that at the output terminals of the power amplifier driving the cable and speaker. Any variations in signal level with frequency imply that the frequency response may be altered by the cable impedance. The second vertical (y) scale indicates the propagation delay caused by the cable impedance, etc. This is shown in nanoseconds.
Three graph lines are plotted. An example is shown above.
- The white line shows the relative signal power level produced by the cable-loudspeaker interaction.
- The blue line indicates the propagation delay as a function of frequency.
- The red line also shows the changes in power level as a function of frequency. However the calculations displayed by the red line assume that the “internal impedance” of the cable has been suppressed.
The difference between the white and red lines can be taken as an indicator of the influence of “skin effect”. In practical terms, the white and blue lines can be taken as indicating the results obtained using either solid cables, or conventional multistranded wires which have no individual insulation. The red line indicates the behaviour we may expect when using Litz multistranded wires with insulation on each individual strand. By comparing the white and red lines you can therefore decide if Litz construction may be an advantage for a given size of cable.
When examining the plots and values it may be worth bearing in mind that a time delay of 100 nanoseconds corresponds to a movement of the loudspeaker of approximately 3·5 microns. Hence when you see a change in delay over the audio band of this order it is roughly equivalent to the effect of moving loudspeaker units towards or away from the listener by small distances of this magnitude. Similarly, when observing changes in signal amplitude of the order of 0·1dB it is worth remembering that a typical loudspeaker has variations in response that are much greater than this. It is perhaps also worth noting that variations in the humidity, etc, of the air may well produce larger variations as the weather changes. It is not clear if changes of this small order are particularly noticable, or even audible in normal use.
In practice, most real loudspeakers have a impedance that varies with frequency in a complicated manner. The details of these variations also differ considerably from one loudspeaker to another. Since the applet here assumes a plain 8 Ohm resistive load the results are not directly applicable to any specific loudspeaker. They can, however, be used as general guide as explained below:
Many practical loudspeakers have an impedance that varies from a low value (typically around 4 Ohm) up to a much higher value (typically above 20 Ohms) from one frequency to another. When the applet shows a loss of, say, 0·1dB at a given frequency then a real loudspeaker might exhibit a loss at this frequency of 0·2dB due to the cable if its impedance was 4 Ohms. However at the same frequency, it might show almost no loss if its impedance was much higher than 8 Ohms. As a result, when a see a given level of cable-induced loss (and delay) plotted above, we can expect a real loudspeaker to exhibit a value somewhere between nearly zero up to around double the indicated value. Hence when we see a value of, say, 0·1dB at a particular frequency for an 8 Ohm load, we can expect a loss of up to around 0·2dB for a real loudspeaker at that frequency, depending upon the details of its impedance properties. In a similar manner, the delay as a function of frequency for a real loudspeaker will depend upon that speaker's impedance properties, but will typically be no more than around double the values shown by the applet.
The second part of the applet display has three sections as indicated above. On the left are the currently chosen input values for the length of the cable (in metres), the radius of each wire, r0, (in mm) and the distance, s, between the centers of the two wires (also in mm).
The central section provides a set of control buttons that can be used to adjust the input values. The yellow up-arrows can be used to increase the chosen value by one unit or a tenth of a unit. The blue down-arrows can be used to decrease the chosen values. The green rectangles act as ‘reset’ buttons and restore a suitable default value. Note that since it is physically unrealisable for s to be less than twice r0 the values are checked when altered. If r0 is too large compared to s, then the value of s is automatically changed to be 0·1mm greater than 2r0.
The right hand section shows an illustration of the relative sizes and spacings of the pair of wires. The red part indicates the nominal skin depth thickness at 20kHz. In practice, the actual current level falls exponentially as we move into the metal. Hence current will also exist in the inner region, shown in yellow. However the thickness of the red part of each wire acts as a rough indicator of the thickness of metal that carries most of the current at 20kHz. At low frequency, the current will, of course, flow through the entire body of the metal and hence will occupy both the yellow and red portions indicated in the diagram. By comparing the displayed current/wire cross-sections with the graphs of signal loss and delay it can be seen that the results of “skin effect” can often be rather smaller than you might expect provided that the wires are large, and are close together.
The last section of the applet display provides some comparison of the effective values of cable inductance, resistance, etc, at low frequency (200Hz) and high frequency (20kHz). The main point to note here is that since the signal losses are often small the gain (loss) values displayed are given in milli-bels (mB) not the more usual decibels (dB). Although engineers often forget the fact, the ‘Bel’ is the standard unit and hence although decibels (tenths of a Bel) are common, we can also use millibels, kilobels, etc, as with other SI units. Since the unit is relatively rarely used it may be worth noting that 1 dB is equivalent to 100 mB. i.e. a gain/loss of 10 mB corresponds to 0·1dB, etc.
Content and pages maintained by: Jim Lesurf (firstname.lastname@example.org)
TechWriter Pro and HTMLEdit on a StrongARM powered RISCOS machine.
University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.