The Importance of Scale

One must pay special attention to the scaling of the graph. In the audio world, we use the dB or Decibel as a measure of amount. We do this for a couple of reasons. One is that the 'bel' unit (a decibel is one-tenth of a bel) is logarithmic; a scaling that more closely fits what happens in human hearing. The other is that the definition of  "decibel" is that it is the smallest change in audio level that the average human can hear, but that brings up a problem, because participants in audio creators, engineers, listeners are not average. They have a heightened sense of hearing.  (Like any other part of the human body, exercise tends to make it better and stronger.) These people, involved in audio, have the ability to hear differences at the "cenibel" level, which is in steps of 1/100 Bel, or ten times as sensitive a rating as the decibel. To accommodate this reality, we have scaled our graphs to the cenibel index rather than the more general decibel scale.  Below are two illustrative graphs, one in dB and the other in cB.  Both graphs show exactly the same data, but the upper graph is shown in a scale that makes sense for the average population, and the lower graph better serves the audio professional and participant. For this reason, we will continue to use the cenibel scale for our graphs as we continue to examine the cables. 

Polar Graphs-At first these graphs may appear daunting but they contain a considerable amount of information. These kinds of graphs come in two types; "polar", which tells us about the relationship between the amplitude and phase of a signal over a given frequency range, and a "Smith" graph which tell us about the effects of the reactance of the signal process. 

Both graphic techniques deal with the issue of Phase. Phase is the term for the arrival time difference between the Voltage (electric force) and the Current (resulting from electron flow). Phase differentials directly impact the power of a signal, resulting in affects we can hear. The illustration below shows the electrical relationships between the Voltage and Current in an audio sine wave for null, lead, and lag phase states: 

A Polar Graph (as illustrated below) displays the lines of amplitude as circles.  The difference in the phase of the signal--that is, the difference between current flow and voltage force--is displayed as travel along the amplitude line. Here, amplitude is not compared against the frequency, but against the phase difference. 

The Smith Chart is substantially more complex.  It is a polar plot of the complex reflection coefficient (called "gamma"). When transmission line impedance does not match that of the load, part of the transmitted waveform is reflected back towards the source. This reflected wave, which varies in phase and magnitude, adds to the incident (transmitted) wave, and the sum is called a Standing Wave. If there is no reflected wave, meaning that the impedance match is perfect, the amplitude of the total waveform (incident plus reflected wave) will be constant, regardless of the point along the transmission line at which it is measured. The result is a SWR of 1, indicating maximum power transfer to the load. The SWR can be inferred by measuring the reflection coefficient for the circuit. The network analyzer is the tool that enables us to do this. 

If we know the reflection coefficient, we can determine the characteristic impedance of the load by using a Smith Chart. The Smith Chart has circles of constant resistance and arcs of constant reactance. The relationship between reflection coefficient and characteristic impedance is shown in the diagram that follows  What is most important to us about the Smith Chart is that it addresses the problems of transmission line interfacing. Having no "off center" data means that the whole traditional Transmission Line approach is not applicable. In other words, if one looks at an audio cable as a Transmission Line, and its Smith Chart is a big "0" even though you can hear that the cable is doing something to the signal, then the only conclusion can be that the Transmission Line view of an audio cable is incorrect. There is something else going on.