Design at the speed of 6 Gb/s: loss tangent and skin effect can degrade rise and fall times, blow noise and timing budgets, or worse. Good analysis is the only cost-effective solution.

Over the past few years many designers and engineers have become aware of the need to control schematic-level circuit design as well as PCB design to maintain functionality of digital circuits that host high-speed signals. High-speed signals have very fast rising and falling edges during transition from a logical 0 to a logical 1 or from a 1 to 0. Circuits with high clock rates must have fast rise and fall time signals to prevent timing violations but fast rise and fall time signals aren't always clocked at high rates. Since most new ICs have rise and fall times faster than 2 nsec, many designers today are stuck with high-speed concerns even though their circuits are clocked in the lower MHz range.

These realities have forced many of us to learn how to control issues like reflections (ringing), crosstalk, switching noise from power delivery and ground/Vcc bounce. At frequencies up to 500 MHz or so we can generally control most signal integrity problems by having a grasp of signal propagation delay and these four noise issues. The majority of a digital circuit's noise budget is consumed by these four concerns at frequencies under 500 MHz. At frequencies pushing 1 GHz other effects start to come into play. At such higher frequencies these other effects cannot be ignored.

Above 500 MHz, especially into the GHz range, the issues of signal loss into the board's base material (loss tangent) and voltage drop across the copper of signal lines, caused by increased resistance (skin effect), become a significant part of the circuit's noise budget. Even though these issues begin to appear in the KHz frequencies, their effects in digital circuits don't become significant until the high MHz or the low GHz range, depending on the length of the traces, or more correctly, the length of the transmission lines. For this reason transmission lines in digital circuits are thought of as lossless below 500 MHz and generally considered to be lossy at frequencies above that, especially at GHz frequencies. (As every analog designer is keenly aware, these effects show up at much lower frequencies in the small noise budget domain of analog circuits.)

Herein is a basic look at how to solve problems of loss tangent and skin effect in gigabit signaling. This article assumes the reader already has a grasp of the other issues mentioned. If not, events such as the PCB Design Conferences provide an excellent source of information on high-speed design and analysis. There are also some very good classes and books available from Lee Ritchey, Eric Bogatin, Howard Johnson, Doug Brooks and many others.

Skin Effect

Voltage drop along a PCB trace due to resistance is a fact of life. From DC through frequencies up to a few MHz, the current in a trace moves through the entire cross-sectional area of the trace. At these frequencies resistance is extremely low, hence resistive losses are extremely small. A 0.006" trace at low frequencies, made of 1 oz. copper (0.0014"), has an approximate resistance of 0.08 [ohm] per inch.

EQ. 1 R = [rho] L/A

where

R = Trace resistance, in [ohm]

[rho] = Bulk resistivity of copper (6.787 x [10.sup.-7] [ohm]-in)

L = Trace length, in inches

A = Cross-sectional area of the trace, [in.sup.2]

In a typical trace at these frequencies the resistive drop would be extremely small, on the order of a few millivolts.

As frequency increases, the energy moving in the trace is forced to the outer perimeter by the large magnetic fields present in higher frequency signals. This is known as skin effect. Skin effect reduces the amount of copper in which current flows, effectively reducing trace cross-sectional area. As can be seen in Eq. 1, as trace area is reduced, resistance will increase.

Because of skin effect, the resistance of that same 0.006" trace at 10 GHz will be 1.75 [ohm] per inch in stripline and over 3 [ohm] per inch in microstrip. A resistance this high in a long line will cause a significant voltage drop (loss of signal energy), and must be considered as another item consuming the system noise budget.

Remember that trace resistance increases by the square root of frequency increase.

Loss Tangent

Loss tangent (tan ([delta])) is a measure of how much of the signal pulse (electromagnetic wave) propagating down the transmission line will be lost in the dielectric region (insulating material between copper layers) of the PCB

All dielectrics contain polarized molecules that move when exposed to an electromagnetic field. As the molecules move within the dielectric, they create heat, which is simply the conversion of signal energy. Higher frequency EM fields move the molecules faster, with a greater conversion of signal energy to heat.

The loss tangent of any given material is expressed as a relative number. FR-4, whose loss tangent is approximately 0.02, will create as much signal loss at 1 GHz as a material with a loss tangent of 0.002 will create at 10 GHz. Ideally, PCB materials with a very low loss tangent are used. Unfortunately, that can carry a heavy cost penalty, which is why we need to analyze critical signals and look at all possible solutions.

Remember that loss tangent losses increase proportionally with increases in frequency.

Let's first understand the effect a digital signal has on frequency. Digital signals are square waves, consisting of a series of embedded sine waves called harmonics. These harmonics are multiples of the clock frequency and generally have strong amplitude up to a frequency referred to as the upper bandwidth frequency, also known as the maximum pulse frequency of the signal. This means that digital signals have multiple frequencies at any point in time that are affected by skin effect and loss tangent, not just a single frequency as would he the case with an analog signal.

At 6 Gb/s, a new bit of data is delivered from transmitter to receiver every 166 psec. Since Gh serial data is generally clocked on both edges of the clock pulse, a complete cycle time is 333 psec, with an operating frequency of 3 GHz. This requires signal rise and fall times under 35 psec, with embedded harmonic frequencies of concern that push as high as 15 GHz. This 6 Gb digital waveform, clocked at 3 GHz, will contain harmonics in 3 GHz steps to the upper-end bandwidth of 15 GHz.

Even a 1 Gb/s signal delivers a bit of data every 1.0 nsec, with a clock frequency of 500 MHz, rise and fall times under 200 psec and harmonics of concern up to 2 to 3 GHz. At 10 Gb/s the numbers are 10 times that, with rise and fall times under 20 psec.

As stated, skin effect resistance, hence loss, increases as the square root of frequency but dielectric losses increase proportionally with increases in frequency. At frequencies above 800 MHz or so in FR-4, dielectric losses begin to dominate. At several GHz, dielectric losses become a much greater cause of signal attenuation than skin effect. FIGURE 1 plots an example of skin effect and loss tangent relative to one another. Even though dielectric losses are greater at GHz frequencies than skin effect losses, look at both since the effect on signal attenuation is the accumulation of both.

[FIGURE 1 OMITTED]

All this adds up to the fact that at Gb data rates, when a digital signal propagates a transmission line, each of the sine wave harmonics of the signal loses amplitude due to skin effect and loss tangent, with the highest frequency harmonics suffering the highest losses. The loss of amplitude of the harmonics is first manifested as a degradation of rise and fall time of the signal. As losses become severe enough the signal will begin to lose amplitude as well. The effect of this is discussed next.

Analysis Techniques

Clearly, an analysis of gigabit data rate signals is essential to determine if any special considerations are necessary to prevent circuit malfunction due to losses from the four factors of the noise budget mentioned earlier, plus skin effect and loss tangent.

With the right skills, the noise and loss elements of a signal can be analyzed manually. At frequencies where skin effect and loss tangent have little effect it is fairly easy to analyze how severely a circuit's noise budget is impacted by reflections, crosstalk, switching noise and ground bounce, using purely manual techniques. From such an analysis, enough insight can be gained to provide a very good idea how a particular circuit will behave.

At frequencies in the GHz range, where loss tangent and skin effect become severe, a fair idea of signal behavior is about as much as can be expected from manual analysis. Gaining a good understanding of signal behavior at these frequencies almost always requires a signal integrity software tool capable of analyzing all of these elements at GHz frequencies. The reasons for this will be explained.

If you understand this issue and simply want an estimate of the energy losses in a signal based on skin effect and loss tangent, try two things. First, read Howard Johnson's article "Skin Effect Calculations (1) to calculate the losses due to resistance. Johnson does a great job of walking through the calculation of skin depth and resistance at high frequencies. His calculation assumes electrodeposited (ED) copper. Materials intended for high-speed digital boards, to date, use ED copper. Next, calculate loss tangent. Eq. 2 will net very good results at any given frequency.

EQ. 2

[alpha] = 2.3f * tan([delta]) * [square root of [epsilon]eff]

where [alpha] = Attenuation in dB/in

f = Frequency in GHz

tan([delta]) = Loss tangent of material

[epsilon]eff = Effective relative Er of material

In general, when calculated losses to the first harmonic--from the combination of all losses--exceed 3 dB across the total length of the transmission line, it can be assumed that circuit performance will be severely affected. That is to say in a 10" line, the amount of loss per inch shouldn't be allowed to exceed 0.3 dB. Again, this is a rule of thumb and is far from the best approach to determine circuit performance, but can certainly reveal whether you're in harm's way.

A slightly improved approach is to determine the noise budget (in millivolts or dB) for the logic family in question and make certain that all noise and losses do not exceed the available headroom.

One problem with either approach to manual analysis of skin effect and loss tangent is that they only consider the absolute values of power attenuation, the square root of which is amplitude of signal. At any given frequency this approach does not consider the fact that attenuation to the high order harmonics will change signal rise time.

In lower frequency circuits where the bit period is long, changing rise and fall time will not have much effect, if any, on performance. But then, at lower frequencies we aren't too concerned about the effects of loss tangent and skin effect. At GHz frequencies where the bit period of the signal is in the order of hundreds of picoseconds, stretching out rise and fall time can make them as long as one bit period and can so severely change wave shape as to cause circuit malfunction. This problem is not seen through manual analysis.

The other problem with manual analysis at GHz frequencies is that it does not consider signal jitter. Real world ICs, as opposed to theoretically perfect drivers, vary in the times at which output signals are delivered relative to one another. This coupled with slight variations in IC output voltage causes signal jitter, which will also affect the noise and timing budgets.

Combining all the effects of reflections, crosstalk, switching noise, ground bounce, rise and fall time degradation and jitter, it's easy to see how a signal's amplitude and bit period can be severely affected. To make matters worse the history of a bit stream can effect both timing and average voltage level on a long transmission line. As an example a long sequence of Is can push the voltage level of a line higher than the overall average, just as a long sequence of 0s can pull the voltage lower than average. All of these effects taken together are called intersymbol interference (ISI).

The best approach to see the combined effects of ISI is to view the signal as an eye diagram. An eye diagram is a view of all bit sequences and bit periods of a signal superimposed onto one another. This is like taking a snapshot of the first bit period of a signal, then laying it over the second bit period, then laying those over the third and so on until the entire sequence is overlaid and visible one to the other. Simulators capable of analyzing signals at GHz frequencies typically have the ability to view a signal as an eye diagram. A typical eye diagram of a very clean signal (low ISI) is shown in FIGURE 2.

[FIGURE 2 OMITTED]

An eye diagram might look like the one in Figure 2 only in a circuit with fairly short lines and/or at moderate frequencies. The measure of goodness in this particular scenario is seen by the fact that the eye is wide open. In other words, the effects of noise and loss haven't taken a toll on any hit period in the sequence and all the signals look clean, one to the next, causing the effective eye to be open.

As lines become long and particularly as frequency reaches into the GHz range, the effects of noise and loss begin to take a heavy toll on signal quality. Au eye diagram from an 18" long transmission line, in FR 4, at 6 Gb/s might look something like that of FIGURE 3.

[FIGURE 3 OMITTED]

Obviously the eye in Figure 3 is almost closed, a sign that ISI is very high. This is probably the result of minor impedance discontinuities on the line coupled with jitter, maybe some crosstalk, etc. Most of all, the eye is almost closed as a result of losses caused by loss tangent and skin resistance, It's highly likely that the correct bit sequence will not make it to the receiver on the line and this circuit will likely malfunction.

Solving the Problem

Rise time degradation, signal loss and jitter due to loss tangent and skin effect can be improved in three ways. Any of these will help; performing all three has a cumulative effect but it's seldom necessary to do so. Whichever is selected, it's important to simulate the results.

The first solution is to lower the trace losses by lowering skin effect resistance. This can be accomplished by making traces wider. This isn't always simple. First, there's the matter of layer count. Wider traces tend to increase layer count. Just as problematic, wider traces will lower impedance, which forces use of a thicker dielectric to maintain the target impedance. In the case of differential lines it may be possible to offset the wider trace by pushing the traces further apart. Wider traces will force something to change and that will likely have a distinct effect on cost.

The second solution is to select a board material with a lower loss tangent characteristic. For example, a material such as Nelco 4000-13, with a loss tangent half that of FR-4, will lower tan ([delta]) losses at any given frequency by a factor of 2:1. A material such as Rogers 4003 or Arlon 25 will lower tan ([delta]) losses by a factor of 10:1 verses FR-4. Needless to say these materials cost more than FR-4. (Note: these materials are simply examples of what's available.) Changing material to that of a lower tan ([delta]) will have an impact on product cost. However, the use of Rogers or Arlon, for example, will make the eye diagram in Figure 3 look more like the eye in Figure 2, a big difference.

As an aside, certain base materials come with rolled, annealed copper. Rolled copper has approximately a 10-12% lower loss factor due to skin effect than ED copper. Unfortunately, to date, all materials designed for digital applications are available only with ED copper. The materials that come with rolled copper are intended for very-high-frequency analog circuit applications. Of course, it is possible to use such a material for a digital circuit, but the cost increase will likely be extreme. Since skin losses and tan ([delta]) losses accumulate, it's a far better choice to use a material intended for digital circuits that has a much lower loss tangent than one with rolled copper.

The two previous solutions each handle one aspect of loss--the first attacks skin losses, the second tan ([delta]) losses. The solution known as equalization will account for all losses simultaneously. The concept behind equalization is to boost the signal level of the waveform at the driver before the signal is launched into the transmission line, to compensate for losses before they occur.

The real beauty of equalization is that it boosts the higher frequency harmonics of the signal by a greater percentage than it boosts the lower frequencies in the signal. Since the higher harmonics suffer higher dB losses as the signal traverses the transmission line, the signal arriving at the end will look as though it has only traveled a short distance. This is sometimes accomplished by attenuating the lower harmonics before boosting the signal, but the end result is that the higher harmonics are boosted a greater percentage at the output than the lower frequencies of the signal. There are both active and passive methods of equalization available. The cost to implement is lower for passive equalization, but the results aren't as good.

Equalization at minimum can improve the eye in Figure 3 to look something like that of FIGURE 4. At its best equalization can improve this eye to look as good as the eye in Figure 2, effectively making the signal look as though it has only traveled a short distance or was traveling in a very low-loss material.

Equalization makes the signal at the driver look almost like it has severe overshoot and undershoot, but of course it's what arrives at the load(s) that really matters. Using this technique can have a profound impact on circuit performance. Not all high speed serial data ICs are available with equalization, and when available they carry a higher price tag.

None of these solutions is free. Wider traces can he "almost free," provided room is available. But remember also that wider traces only lower the losses due to skin effect and at GHz frequencies in conventional materials like FR-4, loss tangent accounts for a much higher percentage of signal attenuation. Reducing skin effect losses should generally be viewed as a technique to help lower attenuation, not to solve it entirely. Getting a solid handle on the problem likely involves the use of either a low-loss base material or some form of signal equalization at the driver. See the bibliography for articles on low-loss materials.

It's critical to analyze signal performance at GHz frequencies to make certain things will behave as expected. Manual analysis can be of help, but at GHz frequencies it's generally best to analyze circuits using computer simulation tools. Remember, too, that not all simulation tools can function in the GHz range. Look for a simulator having a lossy transmission line model, a 2D field solver and one capable of producing eye diagrams of both single-ended and differential signals.

Also of importance is the ability to simulate the effect of vias. As rise time dips under 100 psec (approximately 2 Gb/s), vias begin to affect the performance of transmission lines as well. Most designs don't feel the impact of vias. With rise times much slower than 100 psec, they're almost never an issue. However, at gigabit speeds the lumped length of a signal starts to approach that of a via, even in 0.062" thick hoards. If the via capacitance and inductance are not controlled well they can present a very noticeable discontinuity.

It's critically important to understand the impact of loss tangent and skin effect and which resolutions to their resulting attenuation are most cost-effective. There is no silver bullet. The only solution is to analyze the circuit to determine the best and most cost-effective approach.

REFERENCES

(1.) Howard Johnson, Skin Effect Calculations, sigcon.com/pubs/news/skineffect.htm.

BIBLIOGRAPHY

Steve Kaufer and Eric Bogatin, "Managing Loss in High Speed PCBs" EE Design, eedesign.com/features/exclusive/OEG20030707S0071, July 7, 2003.

Eric Bogatin and Gene Garat, What You Lose from a Lossy Line, ericbogatin.com/technicalfeaturesarticles/GTL104.pdf, March 2003.

Lee W. Ritchey, "A Survey and Tutorial of Dielectric Materials Used in the Manufacture of Printed Circuit Boards," speedingedge.com/pressarticles.htm, November 1999.

Rick Hartley, "The Impact of Material Selection," Printed Circuit Design, March 2002.

RICK HARTLEY is a senior design engineer and PCB specialist at L-3 Communication, Avionics Systems (L-3com.com). He has 39 years of experience in electronics, 29 in PCB and circuit development with an emphasis on the control of signal integrity and EMI in digital and RF boards. He is scheduled to speak at PCB West in March.