Dielectric Absorption in Cables - Calculating Metrics
This spreadsheet calculates Cp, Ls and Z0 for a parallel pair cable, for various effective dielectric constants. The real trick here is to know what to use for the effective dielectric constant, since part of the field is in air and part is in the cable dielectric. The percentage in air also varies with the conductor spacing. The greater the spacing, the larger the percentage of the field that is in air. Therefore, the effective dielectric constant decreases with increasing conductor spacing. What is often done is that the cable capacitance is measured and compared to the calculated values to determine the effective dielectric constant.
The following spreadsheet includes a more complicated exact equation for capacitance, instead of the simpler and more commonly quoted approximate equation (which requires 2r/d < < 1). Also in the inductance equation L included the internal inductance term.
While the Dielectric Constant for PVC is generally known to be about 3.18. However, it turns out our effective dielectric in this instance is more like 2.3 (based on our measured Capacitance value of 14pF/ft). As you can see in the previous data table, the Dielectric Constant has NO effect on inductance, only capacitance which in turn affects the cable characteristic impedance (not relevant at audio frequencies since transmission line effects and impedance matching between a low output impedance amplifier and variable complex load impedance of the speaker are negligible).
So What Have We Learned?
This exercise has taught us yet another marketing claim surrounding many exotic speaker cables regarding the relevancy of Dielectric Absorption and/or the role the Dielectric plays on transmission line effects at audio frequencies is yet another snake oil myth. We have proven that the shunt losses due to the dielectric are negligible at audio frequencies. The major relevancy roles of the dielectric in this application are to serve as isolation between the two conductors and control the capacitance of the cable based on the conductor spacing and dielectric constant. If an exotic cable vendor, salesman, or cable cult hobbyist claims otherwise, tell them you know better and point them to this article.
Addendum: A Note About Dielectric Absorption or Loss Tangents
There are some cable hobbyists and exotic cable vendors that often confuse or even abuse the term "Dielectric Absorption" and its role on a speaker cable compared to a non linear capacitor.
For a capacitor formed from a lossy dielectric material, the loss tangent is the ratio at any particular frequency between the real and imaginary parts of the impedance of the capacitor. A large loss tangent means you have a lot of dielectric absorption. This article demonstrated that this is not a factor with speaker cables given the frequencies and impedance characteristics for the application we are dealing with. Back to capacitors, if you construct a capacitor C from a lossy dielectric, the dielectric absorption causes the value of C to change with frequency. For a good dielectric, the value of C will very slowly deteriorate with frequency. For poor dielectrics with higher dielectric loss, the decay in capacitance with frequency will be more prominent. The rate of deterioration in capacitance is directly linked to the loss tangent. Speaker cables are partially encased in the dielectric and free space so their effective dielectric is much lower than the actual dielectric as I have shown in the cable calculator and measurements within the article. "Since both G and Ycapacitance are both functions of frequency, the tangent (or ratio of the two) is frequency independent. Thus the ratio of the two cancels the frequency dependence between them.
As shown by this equation , the shunt losses of the dielectric can be derived from the loss tangent or dielectric absorption factor. For more info on this, I suggest reading this excellent High Speed Board Design Tutorial written by Altera.