They say that you can never be too thin, too rich, or able to receive a signal from too long of a cable. They also say that batting .333 will get you into baseball's Hall of Fame, so I figure that if we can manage to use longer cables in our systems, reliably, we should be able to go have a nice dinner, charge it and not worry about calories or interest rates.
The key to being able to extend the length of cable is understanding what the cable does to the signals passing through it. Electrical cable generally consists of a conductor, such as copper, with an insulator surrounding it. For the purposes of this paper, our cables always have two conductors, or a conductor and a ground. Ideal cable would be made from an ideal conductor with no loss, and would have a perfect insulator coating it. In reality, the conductor is not perfect and has some resistive loss. This is usually specified on a cable datasheet in units of Ω/unit length. For Belden 1694A, a common coaxial cable used in the video industry, this is about 10 Ω/1000 feet.
The resistive loss of a cable is primarily of interest when one is sending very low frequency (or dc) signals over long distances, and, as a rule of thumb is an issue when it is of the same order of magnitude as the impedance of the load. Therefore, if our cable has a 75-Ω load and a resistive loss of 10 Ω/1,000 feet, then at lengths greater than about 75,000 feet (25,000 meters), we need to be concerned about resistive loss. By the time we get to those cable lengths, we have bigger problems to worry about. The cable manufacturer has the ability to lower the resistive loss by using a more exotic conductor (silver vs copper for example), or by using a thicker conductor, either one of which will result in a more expensive cable.
In most real world systems, the data rates are high enough so that the ac attenuation in the cable becomes an issue well before the dc attenuation. When a dc current is passing through a cable, the current flows with a constant density through the entire cross-section of the cable. When an ac current is flowing through a conductor, it tends to flow mostly on the surface of the conductor, or skin; this is known as the skin effect. Quantitatively, the skin depth δ equals
where δ is the skin depth (which is the depth into the conductor at which the field strength has decreased by a factor of e), σ is the conductivity of the conductor, ω is the frequency of the ac field and μ0 is the permeability of free space. Skin effect means that for the higher the frequency of the signal, the smaller the effective cross-section of the cable is.
Look at the numbers
Table 1 shows the conductivity of common electrical conductors,
Table 1: Conductivities of common conductors.
and Table 2 shows the frequencies of some common signals.
Table 2: Frequencies of some common signals.
Given these values, we can calculate the skin depths that we might expect for various types of signals in various materials.
Looking at Table 3,
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Table 3: Skin depths (in mm) for some common signals and materials.
we can see that for video signals, the skin depth is quite small, which means that the bulk of the material in the cable does not contribute appreciably to carry the signal. If the cable conductor is plated, then almost all of the signal will be carried by the plating.
Recovering the signal after the cable
From the standpoint of this paper, the primary way in which the skin effect will affect us is that as the frequency increases, a smaller and smaller portion of the cross section of the cable will be carrying the signal, so there will be greater signal attenuation at higher frequencies than at lower frequencies. The response curve for this loss will be proportional to the the square root of ω, which makes it difficult to compensate for with standard types of filters. This response curve can be seen in Figure 1.
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Figure 1: Attenuation of a signal going through 100 meters of Belden 1694A coaxial cable.
Although seeing the attenuation with frequency is helpful in designing the complementary filter that we will need to recover the signal, for most of us, the image that we want to see is the eye diagram-is there an opening big enough to recover the data. Figure 2 shows the eye diagrams for a 1.5-Gbit/s signal (an HD-SDI signal), after it has gone through various different lengths of cable.
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Figure 2: Scope views of a 1.5 Gbit/s signal after 20, 50, 100, and 200 meters of Belden 1694A coaxial cable.
When we go to longer and longer cables, we see increasing low-pass filtering. Simplistically, if we apply a complementary high-pass filter to the signal, then we should be able to compensate for the cable, and use longer cables with impunity.
Unfortunately, there are a few things that work against making this as easy as it sounds. The first challenge is the shape of the low-pass characteristic of the cable. Most electronic filters are made using discrete poles and zeroes, and for each pole or zero, you can shift the slope of the response by 6 dB/octave. The cable, however, has this nasty the square root of w response, which is difficult to mimic with standard filter architectures.
The second issue is that the high-pass characteristic requires more and more gain as the frequency gets higher, and circuits don't like to do that. Another issue with which we must contend is that, ideally, we would have a filter which would automatically adapt to any length of cable to which it is connected, rather than having one circuit for 20-meter cables, another for 100-meter, and yet another for 300-meter cables.
Together these three issues make for a major design headache. Fortunately, there are semiconductor design engineers who have already been inflicted with this set of headaches, and have not only come out alive, but have produced some fine, easy-to-use equalizers which cost a small fraction of the cost of the cables which they support!
In order to attempt to match the frequency response of the cable, the designer carefully places the zeroes in the filter such that the resulting response is a close approximation to the the square root of w response of the cable. Care must be taken with the design to make the setting of zero locations independent of the IC process, or the yields of the equalizer would be very low, making the device too costly.
Achieving a double 'high'
In order to deal with the fact that both high gain and high bandwidth are required at the same time, equalizer circuits are realized in exotic, high-speed processes such as the National Semiconductor 0.25-micron BiCMOS silicon-germanium (SiGe) process.
To make the equalizer adapt to various cable lengths, the gain of the high-pass filter sections in the IC can be varied via a control voltage, and a feedback loop is established to optimally set this gain. To determine the correct amount of gain, the equalizer relies on the fact that it knows what the original launch amplitude and slew rate were, and it adjusts the gain of the equalization such that the output of the filter matches the energy profile of the original signal. This does mean, however, that if the circuit that is driving the signal into the cable is not well controlled, either in its slew rate or the signal amplitude, then the equalizer is liable to improperly set its gain, resulting in suboptimal performance.
An example of one of these equalizers is the LMH0044 cable equalizer. With this part, you can recover signals at data rates of up to 1.5 Gbits/s through 200 meters of Belden 1694A cable, Figure 3.
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Figure 3: Equalized outputs from 20, 50, 100, and 200 meters of Belden 1694A cable using LMH0044 adjustable cable equalizer.
With better cable or lower bandwidths, you can even go further.
About the author
Mark Sauerwald , of National Semiconductor Corp., graduated from the University of California at San Diego in 1982, with a bachelor's in electrical engineering. Since graduation, Mark has been involved in semiconductor components for digital video-first at TRW LSI products, working on A/D converters for digital video, then with Comlinear. Mark spent a few years working for Gennum Corp. before returning to National Semiconductor, where he now works as an applications engineer with the Interface Products Group. When not working, Mark is an avid cyclist and a serious amateur photographer.
