Note: This simulation focuses on the words "imitation" and "true." Integrating these two concepts requires careful attention to many details. This article highlights two key points that are essential for accurate results.
Background Introduction
In high-speed digital design, the electrical path between a transmitter and a receiver is commonly referred to as the channel. Channel performance plays a critical role in signal integrity. One common approach to evaluate this performance is by using ADS (Advanced Design System) for simulation. The standard process involves using an EM simulation engine like ADS Momentum, SIPro, or EMPro to extract S-parameters of the channel. These S-parameters can then be used in time-domain simulations, where eye diagrams are one of the most frequently analyzed outputs.
However, it's crucial to pay close attention to the details when extracting S-parameters to ensure accurate results in time-domain simulations. This document discusses some of those important considerations.
Channel Time-Domain Simulation
Let’s start with a practical example. The following figure shows a circuit used for time-domain channel simulation. It includes a simple differential transmission line connected to ideal transmitter and receiver models. The signal rate is 10 Gbps, with a rise and fall time of 20 ps. The simulation was performed under these conditions:
The resulting eye diagram is shown below:
The eye diagram looks very good, with an eye width of 89.5 ps and an eye height of 426 mV. Next, we conducted an experiment to extract the S-parameters of the transmission line.
Extracting S-Parameters of the Transmission Line
We used the S-parameter solver to extract the S-parameters of the differential line over a frequency range of 0–20 GHz, with a step size of 1 GHz:
After the simulation, we used a data extraction tool to convert the results into an S-parameter file:
Next, we replaced the original transmission line with the extracted S-parameters and performed another channel simulation. The circuit setup is shown below:
The resulting eye diagram is as follows:
The eye width is now 62.5 ps and the eye height is 198 mV—clearly different from the original simulation. To investigate further, we repeated the experiment with a smaller frequency step of 0.1 GHz. The new eye diagram is shown below:
This time, the eye width increased to 93.5 ps, and the eye height reached 397 mV. The results improved significantly, getting much closer to the original simulation. We continued by reducing the step size even further to 0.01 GHz. After re-simulating, the eye diagram looked like this:
The eye width was now 89.5 ps, and the eye height was 403 mV—very close to the original results. While finer steps improve accuracy, they also reduce simulation efficiency.
Next, we tested the effect of bandwidth by keeping the step at 0.01 GHz but varying the upper frequency limit to 15 GHz, 20 GHz, and 30 GHz. The results were as follows:
Here are the eye widths and heights for each case:
| Eye Width (ps) | Eye Height (mV) | |
| Original (10GHz) | 89.5 | 426 |
| 15GHz | 93.5 | 439 |
| 20GHz | 89.5 | 103 |
| 30GHz | 90 | 425 |
From these results, it’s clear that increasing the bandwidth of the S-parameters improves accuracy. When the bandwidth reaches three times the data rate, the results become much closer to the original simulation.
Conclusion:
1. As the frequency step increases, the S-parameter model becomes more accurate compared to the original simulation.
2. Once the frequency step is determined, increasing the bandwidth of the S-parameters brings the model closer to the original performance.
3. For a 10 Gbps system, to achieve results nearly identical to the original, it’s recommended to use a frequency step of 0.01 GHz and a bandwidth of up to 30 GHz. This level of precision can be achieved through internal interpolation or adaptive algorithms during the S-parameter extraction process.
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