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[danlavry]

SKIN EFFECT (in cables)
By Dan Lavry
Copyright Lavry Engineering

(These are notes from my upcoming help section to be posted soon on my web. I am placing them here because they are educational.)

INTRODUCTION

The term skin effect is not new to audio.  Many speaker cable manufacturers have been “preying on the innocent” with suggestions that their cables sound better because of the skin effect.
Skin effect is real, but like most engineering issues, it begs for QUANTIFYING. The lack of quantifying opens the doors for out of place claims, such as skin effect in relation to speaker wires. On the other hand, the skin effect is an everyday term in other industries. It is an important factor where cable transmission of high frequency signals over some distance (both analog and digital).

Again, the skin effect issue begs for quantifying and the 3 major factors are:
Cable length, frequencies of operation and cable construction. I will be talking about all three in more detail later. I will start my presentation by showing what skin effect does to a digital signal, which is a part of digital audio today.

Digital signals “rise and fall quickly”, and there are many cases where the speed can be retained. There are other cases where the rise and fall degrade (slow down). The first question to ask is: do we have enough skin effect to impact the signal in a PRACTICAL SENSE? If the rise time before skin effect is 10nsec, and the skin effect is 1nsec the answer is no. If the rise time is 10nsec and the skin effect is 1000nsec it is a definitive yes.

The skin effect does much more than “just slowing the rise time”. We, in audio, have heard the back and forth argument and counter argument about speaker wire. One guy says “we have skin effect”, the other guy says “but only at high frequencies”.  Unfortunately, most arguments seem to miss the biggest point which is: cable length is the biggest contributor of them all. But I will get to that later.

The impact of the skin effect is highly non linear, because a single step (or any digital waveform) contains a wide range of frequencies, not just a single sine wave. The wide spread notion that the skin effect causes the electrons to migrate towards the outer diameter of a wire should be modified. The low frequency part of the signal utilizes the whole wire, while the high frequency      electrons concentrate on the skin.
We end up having a “voltage divider action” between the cable and the load termination, and that attenuation is higher for the higher frequency portion of the signal.

We first need to examine what a skin effect does to a digital wave form. For that, I will show the outcome due to a SINGLE STEP digital transition from low to high. The amplitude set to 1, rise time set to 0 (a theoretical driver with an instantaneous rise time).

See plot bellow:



The Red dotted line signal shows a somewhat theoretical driver signal taking 10nSec to go from 0 to 1 value. I included this signal for reference.

The Blue wave shows the effect of “very little” skin effect, when comparing to the red signal. It reaches 90% of the final value in about 1nsec, while the red signal is only at 10% of its final value.

The Black line shows more skin effect than the blue one. The skin effect impact is in the ball park of the Red signal. They both reach 80% of the final value at about 8nsec. The skin effect is going to have some effect on a 10nsec signal.

The purple line shows a lot more skin effect. It reaches its 50% value in about 46nsec. So much skin effect is a major bottle knack for signals with 10nsec rise.

There are 2 important point to realize, before I get into quantifying the signals.

A. The blue, black and purple signals are the SAME SHAPE. The difference is the time scale, but the shape is the same. (Stretching or contacting the X axis).
B. The shape is highly non linear, nor is it exponential. The physical electromagnetic behavior is expressed by the “error function” (the shape of the curve)

Let us look again at the black line. The signal rises to 50% relatively fast, and takes a lot of time to get up the rest of the way. The next post will focus on some interesting relationships in a more quantifiable way.

See next post

Dan Lavry
www.lavryengineering.com

[danlavry]

SKIN EFFECT (in cables)
By Dan Lavry
Copyright Lavry Engineering

(These are notes from my upcoming help section to be posted soon on my web. I am placing them here because they are educational.)

Contined from the previous post

The waveform:

In the introduction I showed the general waveform shape due to a cable skin effect driven by a sudden step. Let us examine it in more detail:



The plot (black line) shows that a signal reached 50% of it’s final value in 4nsec. The same signal will reached 80% at 30nsec and 90% in 126nsec! What started as a fast signal ends up slower and slower.

I already pointed in the last post that that more or less skin effect is a matter of scaling the time (the curve is the same shape). Therefore a wave that takes 8nsec to reach 50% (twice as slow as the plot above, will take 60nec to get to 80%, 252nsec to get to 90%.

In general, we can focus our attention on the time it takes a skin effect to rise to 50% of it’s final value. We call that time T0. When we know T0, we “know everything”. Reaching 80% of the final value takes about 7.5 times T0 and reaching 90% takes about 31.5 times longer than T0.

The accepted was to view rise times of digital signals is to measure the time it takes for a signal to get from 10% to 90% of its final value. That time is about 29 longer then T0. A cable with T0 = 30nsec has a rise time of 870nsec, far slower than needed for “standard digital work”. I will explain that later.

Clearly if T0 is .1nsec, reaching 90% in 3.15nsec may not be an issue in a 10nsec environment. But a skin effect that causes a 30nsc slow down to the 50% point, will take nearly a 1 usec to reach 90% of its final value. That may have a serious impact on signals in the few MHz region (such as digital audio)

Is a 30nsec T0 a realistic value? Or is T0 =  0.1nsec a better value? What are the main factors that determine T0?
1.   The most talked about factor is frequency of operation. The skin effect causes rise in resistance at higher frequency and the rise is proportional to the square root of the frequency.
2.   Another factor effecting the resistance is the diameter of both inner conductor and shield. The relationship between rise in resistance and diameter is not a linear one, but the larger the diameters the less skin effect. The diameter is is an important factor.
3.   Some limited improvement may be gained by silver plating the wire to several times the skin depth. We will talk about skin depth later.  
4.   The biggest factor in detrmining T0 is cable length. Double the length and T0 goes up by a factor of 4. A 32 foot cable has T0 about 1000 slower than a 1 foot cable (32*32=1024). A 10 foot cable is 900 times faster than a 300 foot cable!

Lets us compare some “industry standard” 50 Ohm cables. RG8 has a 16 gauge center conductor. RG58 has a smaller diameter 20 gauge center conductor, and RG174 is made out of a 26 gauge wire (small diameter).

For 100 feet of cable:

T0 for RG8 is 3.5psec, so rise time (10% to 90% ) is 0.1nsec
T0 for RG58 is 18psec, so rise time (10% to 90% ) is 0.52nsec
T0 for RG174 is 41psec, so rise time (10% to 90% ) is 1.2nsec

So far so good so let us try 300 feet length. T0 will grow by a factor of 9:

For RG8 the rise time (10% to 90% ) is 0.9nsec
For RG58 the rise time (10% to 90% ) is 4.7nsec
For RG174 the rise time (10% to 90% ) is 10.8nsec

Let us try 500 feet:

For RG8 the rise time (10% to 90% ) is 2.5nsec
For RG58 the rise time (10% to 90% ) is 13nsec
For RG174 the rise time (10% to 90% ) is 30nsec

Of course the questions are many (such as how much rise time is too much, what is a good cable for what appication and more)

To be continued...

Dan Lavry
www.lavryengineering.com