Deep Dive

Cable Design and the Speed of Sound, Part Two

Issue 131

In Part One of this series (Issue 130), Galen Gareis of ICONOCLAST cables and Belden Inc. began an extensive exploration into a critical but not often discussed aspect of cable design: the velocity of propagation (Vp) of audio signals. In this installment, he looks at practical ways to change the velocity of propagation and improve signal linearity for the benefit of better cable performance, and examine other subjects.

Also, introductory material on the subject by Galen and Gautam Raja is available in Copper Issues 48, 49 and 50.

What can we do with the insights into the fundamental ability to change the Vp with frequency we examined in the last installment? Can we do something to improve the signal linearity in audio cables?

Here is an example of what might happen in a cable that is designed to have varying levels of Vp differential based on managing the capacitance of the cable. We can do this by varying the size of the insulation, or even the insulation material. For simplicity, we’ll hold DCR the same to isolate the capacitance effects on Vp.

Notice that the change is well within the audio range, and the Vp change is pretty extreme on an absolute basis. (Short cable lengths can allow us to ignore Vp non-linearity; as a first approximation they are too short to have a meaningful propagation time difference.) What if we do not want to ignore this issue, but achieve a better balance in performance by manipulating other cable parameters? If our objective is to make cable better overall, why not? Well, better cable is far more complex and expensive to make, electromagnetically, I grant you that.

In the example above we look at only capacitance. But, inductance is loop area-determined. The farther apart the wires are from one another, which is known as the loop area, the lower their capacitance. But the equations for measuring inductance say that as inductance gets higher, the farther apart the wires are moved. What to do?

A cable’s capacitance can be designed in several ways. If we want to retain a low inductance, which keeps changes in the phase of a signal and its resultant frequency-response anomalies to lower levels, we need to keep the inductive loop area small. Initial phase alignment, the time alignment of signals applied to the cable, in audio cables is small, so many feel it can be ignored, as the initial time-aligned phase isn’t getting too much worse with the Vp speed differences across frequency. This is called group delay, or how much the best to worst signals separate going down a cable after the initial time alignment applied to the cable. A cable shouldn’t make frequency time alignment worse, but it does.

If we consider a square wave, we can get a better idea what group delay and phase delay are, since in order for a square wave to maintain its integrity, its frequency components have to be kept in proper phase alignment with one another.

http://www.iowahills.com/B1GroupDelay.htmlA square wave is square only because its frequency components are in proper phase alignment with one another. If we pass a square wave through a device and expect it to remain square, then we need to ensure that the device doesn’t misalign these frequency components. A Group Delay measurement shows us how much a device causes these frequency components to become misaligned.

Keeping the signal in correct phase right from the start is imperative, but group delay, which is caused by the differential in the velocity of propagation, is how a cable makes things worse.

Our objective is to attain the best cable performance possible. How do we do that?

One way is to lower inductance and capacitance. Thicker insulation does not lower inductance; it increases loop area (the space between the wires), which as we have seen increases inductance. To keep the loop area as small as we can for low inductance, but not increase capacitance, we need to use the absolute most efficient dielectric(s) we can. Air is the best dielectric and Teflon is the best material. A low “E” or dielectric constant in an insulating material will allow two wires to be as close together as they can be and reach the lowest possible capacitance.

When E, the dielectric constant, is high, the capacitance is higher at a set RF impedance. We can use the capacitance value calculated at RF through the audio band because L and C are both fixed across frequencies. Only at RF is the Vp=1/SQRT(e). We test RF coaxial cable capacitance at 1 kHz for example.

 

The graph above shows how capacitance and the velocity of propagation are directly related to the dielectric constant for a 100-ohm RF cable type. The capacitance value can be used at audio frequencies, but not the dielectric’s RF velocity.

At RF;

Vp = (1/SQRT (dielectric constant)) or Vp = (1/SQRT (L*C))

L and C are constant from low frequencies through RF with a set dielectric material. We’ll look at this in more depth later in the article.

We certainly want to start with the lowest “E” value possible, and not just for its effect on capacitance alone. But in designing a cable, does capacitance have to be as low as possible and then we’re done? Not exactly.

The above equation for low-frequency Vp also has the variable, R (resistance). Resistance is almost always considered a “passive” element. It is thought to be responsible for attenuation only, like turning up and down a volume knob. However, it influences Vp non-linearity, too. Higher DCR flattens the Vp linearity through the audio band – but only if the DCR seen in each cable “circuit” is sufficiently isolated from other electrical paths. The data below shows what happens when resistance is varied, and we hold the capacitance to 15 pF/foot. And, do we even want zero R or C? And what happens if we ignore the Vp differential and lower the resistance as far as we can?

Vp ACROSS LOW FREQUENCY BY AWG

The chart and table above show that if we decrease the wire size, which increases resistance, we can also manage the Vp differential across the audio band. This allows us to use lower capacitance if, if, IF we can utilize higher DCR wire. Designs can use multiple smaller wires, but beware what happens to C and L when we use more aggregate wires to reach a low bulk DCR.

Physics says we can’t speed up the low frequencies, only slow down the higher frequencies. The curve flattens below 250 Hz. But to avoid too high of a capacitance in order to lower the Vp differential, we can also change just the wire DCR, which allows us to lower the capacitance. We balance the R and C.

Observations

Let’s look at a few things to better understand what is available to us in designing cable, and where these factors are working. R, resistance, isn’t stable with frequency, as a wire’s skin effect (its self-inductance, which is predominant at higher frequencies) and its proximity effect (inefficiency in passing current, which is predominant at lower frequencies) can cause attenuation that varies with the audio signal’s frequency.

The tables below on inductance and capacitance show a few cables’ response across frequency. They are close to a constant to the first approximation. Do we see this in audio cables?

Does the ICONOCLAST cable really show flat L and C, too? It does. The table below shows R, L and C measurements up to 1 MHz for an earlier design prototype. Notice that Rs (Resistance swept) increases as we go up in frequency. Why? Some of this is caused by skin effect and some is the result of closely-spaced conductor wires. Also, the proximity effect concentrates current flowing in the same directions near the wire surfaces nearest one another, and pushes the current away from the two closely-spaced wires in the that carry current in the reverse direction. Both of these factors superimpose to decrease wire efficiency (less current uniformity across the wires’ cross sections).

ICONOCLAST SPEAKER CABLE PROTOTYPE LUMP ( TOTAL VALUE)/
ADJUSTED TO FOOT ELECTRICALS

Higher frequencies, which don’t require much current, need a larger surface area, not the overall volume of wire, to propagate with low attenuation.

High-current applications need a larger wire volume for low attenuation at low frequencies.

If you have high current and high frequencies, you get a double whammy for attenuation. This kind of wire would be very inefficient.

This chart, which was shown earlier, shows that the impedance curve is non-linear and need three separate approximation equations to characterize three different regions of test performance. The low-frequency curve contains the imaginary component “j” times omega or v. Omega is equal to 2f. We saw this set of variables in the Vp equation at low frequencies too; Vp = SQRT (2v/R*C). Capacitance is directly related to; Vp = 1/ SQRT(E) at RF.

Why is increasing impedance through audio frequencies a problem? Below we see a graphic from one of Paul McGowan’s Daily Posts that shows the energy spectrum of typical music. (I have these types of graphs too, but Paul’s is better than mine!) If we want to match the power transfer of the cable to the musical spectrum we need to do it in the highest average power distribution spectrum we can within with a non-linear sweep distribution.

What cable needs to do is match the impedance where the most power is being distributed, or the power energy spectrum.  Where is this region actually? It is below 500 Hz – and smack dab in the region where the impedance curve rises. This makes a true cable-to-low-impedance load match technically impossible to do. It is great to think about, but the physics says we can’t get there. Vp drops too much and too fast as frequency drops raising the impedance when we need to really have it lowered.  At “zero” Hz Vp is by definition zero so we know we’re going to see a change with frequency.

TWEETER POWER,
AUGUST 31, 2020 by PAUL MCGOWAN

There is a near 1,000 watt peak at 60 Hz. The impedance of a cable can’t be close to 4 to 16 ohms in this region due to Vp non-linearity. It is impossible to do using low frequency open-short impedance tests. The physics says low-impedance measurements through the audio range can’t be done with reference open-short impedance measurements (except open-short is most close to how audio cables work, and need to be measured).

True, and honest impedance graphs of a speaker cable show this to be the case. Better cable can indeed decrease the low-end impedance rise, but not eliminate the physics we are working against that cause that impedance rise. The impedance and phase curves below exhibit proper open-short impedance measurements.

ICONOCLAST is a 0.08uH/foot and 45pF/foot 11.5 AWG aggregate design, all very good values for a complex design with 24 0.20” wires in each polarity, which serves to flatten the Vp curve and as we have seen, thus lower the impedance rise at low frequencies.

Below is what a typical ported-speaker impedance trace actually looks like. The solid line is impedance and the dashed line is phase. Superimpose this onto the above graph. This is the true situation we have to deal with, and illustrates how speaker cable really “matches” with a speaker. We can’t match “8-ohm” cable.

What do some other cables do at low frequencies? The chart below graphs several measured cables. If we look at good old POTS (Plain Old Telephone System)-type cable, we see that we can have cable that measures 600-ohms at 1 kHz! Yes, the dropping Vp differential low-frequency properties increase impedance to about 600 ohms. We’ve decreased that effect to just 270 ohms in ICONOCLAST speaker cable but 2-16 ohms is an impossibly low reality in a referenced open-short test. That’s because capacitive reactance, Xc=1/(2FC) keeps going up (resistance to AC electrical energy flow) as the Vp keeps going down (raising impedance even more).

In the next and final installment we’ll look at resistance, the effects of various dielectrics, wire geometry, skin effect and other considerations, and summarize our findings.

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