Extending bandwidth into the gigabit range: package designers face gigabit signaling rates through packages that require alternatives to lumped element modeling.

Today's package designers face gigabit signaling rates running through packages that require alternatives to lumped element modeling. Unfortunately, tradeoffs between using W-element models and multisegment models are not always obvious. This article will discuss some of those tradeoffs and look at a specific example where we extend the bandwidth of an existing package model with a multisegment approach.

The Right Modeling Approach

There are three main considerations when deciding on the correct modeling approach:

1) The edge rate, which determines skin effect prominence

2) The length of the nets

3) The number of discontinuities in the structure

One key factor in determining whether W-element models are needed lies with the edge rate we are trying to push through the structure. If we are well into the skin effect region, there may be a significant difference in the resistance that the signal "sees" as it passes through the structure. In many cases signals can run at frequencies well into the gigabit range, or at edge rates well below 500 psec before W-element or root frequency-dependent resistance is required. W-element models simply follow from the familiar transmission line behavior described below:

[differential]{V(x,t)}/[differential]x = -[L] [differential]{I (x, t)}/[differential] -[R]{I (x, t)}

[differential]{I(x,t)}/[differential]x = -[C] [differential]{V (x, t)}/[differential]t -[G]{V (x, t)}

The dilemma for signal integrity designers is that in order for the model to accurately mimic reality, the nets should be of approximately the same length. When net lengths are significantly different, some sort of lumped (FIGURE 1) or distributed (multisegmented) model (FIGURE 2) is necessary. That way, distinctions in time-of-flight through the package for the different signals is maintained. The other important consideration has to do with the number of discontinuities and the bandwidth requirements on the final model.

[FIGURES 1-2 OMITTED]

Most current tools simply divide total R, L, G, and C by the number of segments to arrive at values. However, users would benefit from greater accuracy if their tools calculated RLGC values for individual layers/vias and cascaded them to arrive at the final distributed model. In this manner, discontinuities and subtle reflections associated with the separate pieces of the structure as it traverses the package layer by layer are captured. These important distinctions make a difference not only in the signal waveforms but also in the noise on the supplies, since slight variances in current over time (current signatures) required by the drivers is now evident.

A Sample Case

In this example, we are looking at eight high-speed differential pairs routed through a Xilinx package. These pairs vary in length from approximately 2-12 mm. In the following examples, eye diagrams show skew between lanes (4 bits), not just in one lane. Traces are stripline with a GND plane above and a VCC INT plane below used as a reference. GND and a plane section VCC1 are analyzed and are part of all circuit models out, so that we can investigate noise on the supplies. In actuality, other signals do use the GND and the VCC1 plane, but we are treating them here as exclusive suppliers to these signals for the purpose of this example.

FIGURE 3 shows a rough layout (top view) of the nets. The bump region is in the lower right-hand section of the plot. Most differential pairs are recognizable as such (closely coupled). Two 3.3 V five-stage drivers with complementary input waveform signatures are used to drive four of the eight differential pairs; the other four differential pairs are driven with ideal drivers that use VCCI as the reference (FIGURE 4). Each pair is also terminated differentially with 100 fl at the PCB.

[FIGURES 3-4 OMITTED]

A 1 Gb/sec signal with a 200 psec edge rate was used to excite each of the lines. This simple circuit (FIGURE 5) allows us to test the model to gain confidence and investigate various switching scenarios.

[FIGURE 5 OMITTED]

An easy way to test if a W-element approach may be more appropriate is to create two or three versions of your model at high and low frequencies and see if there is a significant difference in the waveforms (e.g., create or use models computed for @500 MHz and @2 GHz). For this example (FIGURE 6), low-frequency resistance values range from 180-553 milliohms, while high-frequency values range from 343-1080 milliohms.

[FIGURE 6 OMITTED]

Without much difference in the supplies or the signals, we can feel reasonably confident that going forward using our highest reasonable frequency of interest will lead to slightly conservative design margins. This is common since package traces are so short in comparison to PCB lengths. Remember, however, that DC values are significantly affected when using high-frequency models.

Lumped vs. Multisegment Models

In considering a multisegment modeling approach, sometimes the size of the model is a concern because of the complexity or number of drivers you are simulating. This package, while it has only six plane/routing layers, has an additional five "through" layers with cover dots; thus choosing a distributed model results in a 20-section model. While this may seem like a lot, the advantage of being able to see all of the discontinuities associated with a diff pair, especially running at gigabit rates, is important. For most packages, selecting a distributed model will result in a SPICE deck with 5-12 sections. Complex or large drivers and PCB structures tend to dominate SPICE run times, so in many cases there is not a significant penalty for using a distributed model. It is always good to run a test case with a multisegment model because of the dramatic difference in the waveforms for signals/supplies.

The following plots show signal waveforms using the lumped model, a 20-section model and a 30-section model. Notice that with the lumped model (FIGURE 7), most edges are very smooth, indicating the low pass filter (LPF) effect (model is not suitable for 200 psec edge rates on the net). Compare the lumped model with the waveform in FIGURE 8.

[FIGURES 7-8 OMITTED]

Notice the signal overshoot shape difference on the both H = >L and L = >H transitions. It is important to realize that peak noise will not always decrease when going from a lumped to a multisegment model, but low-frequency ringing quite often does. Finally, as we progress to the 30-section model (FIGURE 9) there is still a difference in the signal waveforms, and therefore going forward using the 20-section model may not be adequate. Multisection models traditionally exhibit less overshoot, undershoot and sometimes higher-frequency ringing.

[FIGURE 9 OMITTED]

So, as we can see, decisions involving whether to use W-element, lumped element, or multi-segment models involve many factors. Three of these factors are edge rates being forced through the package, net lengths and the number of discontinuities in the package.

While complexity of the model and time to simulate are also important, usually these are secondary considerations. Large complicated drivers or PCB circuitry will tend to dominate time to simulate over going to a multisection (distributed) model. We have shown that in cases where W-element models are not appropriate, we can significantly extend the utility of models by using a multisegment approach. Multisegmented models may take longer to run, but they typically improve low-frequency ringing on supplies (an artificial artifact of lumped models) and improve overshoot/undershoot of signals because the higher-bandwidth model can now support higher-frequency components.

GREG FITZGERALD is the technical marketing specialist for Optimal Corp. He can be reached at [e-mail].