**Lossy transmission line**

Lossy transmission line effects dominate signal integrity at clock frequencies above about 1 GHz and interconnect lengths above about 12 inches. An ideal lossy transmission line model is required to predict the effects of rise time degradation, ISI, collapse of the eye diagram and deterministic jitter.

As rise times have decreased and clock frequencies increased, new signal integrity problems have arisen as we’ve reached new bandwidth regimes. For many high speed serial links, we are now entering the regime where the losses from the transmission lines begin to affect signal quality. If these effects are not anticipated and the design optimized to minimize these effects, the product may not work.

With a flexible simulation tool, design and material selection decisions can be made early in the design process to optimize the balance of cost and performance in high-speed digital systems.

**The Problem with Lossy Lines**

An ideal lossless transmission line is the most commonly used model for interconnects in virtually all SPICE and behavioral based simulators. It is described by a characteristic impedance and a time delay and assumes that as the signal propagates down a transmission line, there is no energy lost. This means that if a signal with an amplitude of 1v and rise time of 1ns enters the line, the same 1v and 1ns will come out the far end.

This is a good approximation for the behavior of real interconnects when signal rise times are of the order of 1 ns and trace lengths of 10 inches. However, as rise times approach 0.1 ns and lengths approach 36 inches, as in a backplane, the lossy effects of transmission lines begin to influence the quality of the signal. Figure 1 shows the simulated received signal on a typical backplane trace ignoring and including the lossy effects.

Figure 1. 100 ps rise time, 2 GHz clock signal at the end of a 36-inch backplane trace, 4 mils wide in FR4, modeled as an ideal lossless line and as an ideal lossy line.

The dominant problem created by the losses in the transmission line is a degradation of the rise time. This becomes a serious problem when the degraded rise time is comparable to the bit period of the signal. The precise shape of the received waveform will depend on the prior bit pattern. This effect is called inter- symbol interference or ISI.

Though it is possible to roughly estimate the rise time degradation based on rules of thumb, it can never be better than only a rough estimate. The actual rise times are not even close to a Gaussian shape, which is the basis of using just the one number, “rise time”, to describe them. The only way to get a realistic prediction of the impact from losses is using a transient simulator with the capability of simulating lossy lines.

**Why is There Loss**

To describe and accurately predict the behavior of real interconnects, a new ideal circuit model must be introduced. This model must take into account the two important mechanisms that absorb energy from the signal.

The series resistance of the signal and return path conductors will increase with the square root of frequency due to skin depth effects. At higher frequencies, the series resistance will increase, and there will be more resistive heating. Figure 2 shows the simulated series resistance of a 4 mil wide 50 ohm transmission line as a function of frequency.

Figure 2. Total resistance of ½ oz copper trace, 4 mil wide, 36 inches long due to skin depth effects.

The second important loss mechanism is the shunt leakage current through the dielectric material. All insulators have some residual dipoles that can re-orient in an external electric field. As this dipole move back and forth in the AC field of a signal, they create an AC leakage current. If they can respond as fast as the field changes, the higher frequency components of the changing field will move the dipoles back and forth faster and the shunt AC leakage current through the material will increase.

The amount of leakage current, which converts the dipole motion into heating up the dielectric, depends on the number of dipoles in the material, the size of the dipoles and how far they can move in the field. This intrinsic, bulk material property is described by the “dissipation factor” of the material. The larger the dissipation factor, the more dipoles and the greater the amount of shunt leakage current.

Even with a constant dissipation factor, the amount of leakage current will increase with higher frequency. This means the shunt leakage resistance will decrease and the AC power consumption in the dielectric will increase with frequency. We usually refer to the conductance of the dielectric, which is the inverse of the resistance. The power absorbed in the dielectric, which contributes to the attenuation of the signal, is directly proportional to the conductance through the dielectric.

These two sources of loss contribute to attenuation that is frequency-dependent. The contributions from each term and the total expected attenuation are shown in Figure 3. It is clear that for a 4 mil wide trace, dielectric loss dominates at sine wave frequencies higher than about 2 GHz.

Figure 3. Total attenuation in the 36-inch-long backplane trace from conductor loss, dielectric loss, and the combination.

**Simulating Lossy Lines**

If the losses in the line were constant with frequency, every frequency would be attenuated the same amount and the spectrum of the signal going into the line would be the same as the spectrum of the signal coming out. Though the amplitude of the signal might be reduced, the rise time of the signal would be exactly the same coming out as going in.

A simulator that does not consider the frequency dependence of the losses is worthless in predicting the most important property of lossy lines; rise time degradation. An accurate transient simulator must consider the frequency dependence of the losses from these two sources.

Figure 4 shows an example of the simulated transmitted signal through a 36-inch backplane using an ideal lossy line model and an ideal lossless model, but with series resistance that is constant with frequency, corresponding to the resistance of the line at the clock frequency of 2 GHz.

Figure 4. Comparing the ideal lossless model, with a lossy model assuming a constant resistance of 80 Ohms and an ideal lossy line model. Only an ideal lossy model accounts for rise time degradation.

As a direct consequence of higher frequencies being absorbed more than low frequencies, the bandwidth of transmitted signals is decreased, and the rise time of the transmitted signal is increased. The longer the line or the higher the losses, the longer the rise time. Figure 5 shows the transmitted signal for a length of 10 inches, 20 inches and 40 inches in a typical FR4 backplane. The rise time degradation is more than 200 ps for the 40-inch backplane trace.

Figure 5. Rise time degradation for 0 inch, 10 inch, 20 inch and 40 inch long traces. The longer the line, the more the rise time degradation.

**Impact on Signal Quality from the Losses**

When the rise time of the signal is comparable with the rise time degradation, the lossy effects will distort the received signal. Initially, this rise time degradation will affect timing. As the rise time is further increased and is comparable to the bit period, the voltage waveform of the received bits will depend on the previous pattern of bits.

Using a very long sequence of bits with all possible combinations of patterns, the impact of lossy lines can be evaluated. To shorten the simulation time, a pseudo-random bit pattern is synthesized and the transmitted pattern through the lossy line is simulated.

The resulting signal degradation can be seen briefly by superimposing each successive received bit, synchronized with the generating clock as the trigger. When the voltage levels of each received bit are far enough apart to be distinguished, the resulting pattern looks like an open eye. We refer to this sort of diagram as an “eye” diagram. Increased rise time degradation will cause the eye to close.

The performance of an interconnect used in a high-speed serial link can be characterized by the opening of the eye, which must be at least as large as the noise margin of the device family, and by the width of the crossovers at the corners of the eye. This width is a measure of the deterministic jitter in the system and must be allocated in timing budgets.

At a glance, an eye diagram will show if an interconnect is acceptable. Figure 6 shows the eye diagram of a signal as it comes out of a typical high speed driver. The eye is open and there is no ISI. However, when propagating down a 40 inch long, 4 mil wide 50 Ohm trace in FR4, the losses degrade the rise time and cause ISI. This appears as a closing of the eye and increased jitter.

Figure 6. Top: Eye diagram for 2 Gbps stream at the source with no interconnect. Bottom: eye diagram of same source after 40 inches through a 4 mil wide FR4 trace, with the eye virtually completely closed due to the losses.

**Opening of Eye Diagram**

Using a tool that simulates lossy transmission lines, we can explore three important design techniques that can dramatically influence the opening of the eye. These are the line width of the trace, the dissipation factor of the dielectric and the impedance discontinuities from vias.

The line width of a trace will affect the series resistance loss, which will increase with the square root of frequency. Obviously, a wider line will have less resistive loss and help open the eye. Unfortunately, to increase the line width and maintain the same target impedance also requires an increase in the dielectric thickness. Increasing the line width would mean a thicker board.

Figure 7 shows the resulting eye diagrams for two different line width traces, both designed as 40 inches long, 50 Ohm lines in FR4. One has a line width of 4 mils, the other a line width of 8 mils. Wider lines will increase the eye-opening.

Figure 7. Eye diagram for 2 Gbps signal with 50 Ohm, 40-inch-long backplane trace in FR4 with 4 mil and 8 mil width line.

The dissipation factor of the laminate material will affect the shunt conductance loss. A lower dissipation factor material will help open the eye. In general, lower loss laminate materials also cost more.

Figure 8 shows the eye diagram for an 8 mil wide, 50 Ohm 40 inch long backplane trace in FR4 with a dissipation factor of 0.02 and the same geometry using a low loss material such as GIL Technologies GML3000, with a dissipation factor of 0.004.

Figure 8. Eye diagram for 8 mil wide 50-ohm lines with dissipation factor of 0.02 for FR4 and 0.004 for GML3000.

Anything which causes the rise time to degrade will cause the eye diagram to collapse. In addition to intrinsic losses in the transmission line, there is another, subtle factor that can strongly influence the collapse of the eye diagram, related to the vias.

As a simple rule of thumb, the loop inductance of a signal via and its return path is about 0.5 nH/mm. For a 0.5 mm via, the loop inductance a signal might see is about 0.25 nH.

It is not so much the via itself that causes a rise time degradation, it is the combination of the capacitance of the capture pads and the capacitance of the via barrel to the reference planes that causes the problem. If the capture pads and clearance holes are designed for high yields with no concern for electrical properties, the resulting capacitance might be as much as 0.25 pF per via.

The capacitance of the via will act as an RC filter, with the R coming from the characteristic impedance of the line. Each via will contribute to a rise time degradation.

Figure 9 shows the impact of just from four vias in an ideal lossless line, using 0.25 nH and 0.25 pF for the via. The eye is distorted from the delay and impedance discontinuities.

By engineering the capture pads and clearance holes to balance the capacitance of the via to the inductance of the via, for a 50 Ohm line, the impact from the vias can be dramatically reduced.

Figure 9. Eye diagram for 2 Gbps of ideal lossless lines with 4 vias as nominally manufactured and as could be optimized for minimal distortion.

**Conclusion**

The three dominant features that contribute to the collapse of the eye diagram can be efficiently explored with a simulation tool and the impact on signal quality from design choices can be evaluated before committing to hardware and options explored.

Figure 10 shows the initial performance of a backplane trace compared with what might be possible, based on a better choice of line width, material selection and via design. Though a simulation does not predict the cost of a design change, it can at least point to what might be the potential benefit.

Figure 10. Eye diagram of 4 mil wide, 50 Ohm backplane trace, before and after optimization.

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