Gauss 2D – Uncertainty Analysis for Controlled Impedance and Controlled Loss

Multivariate Monte Carlo Uncertainty Analysis

One thing that is often overlooked in controlled-impedance and controlled-loss design and development is the effect of manufacturing tolerances. Gauss 2D allows a user to understand the impact of these manufacturing tolerances on impedance and loss by conducting Multivariate Monte Carlo simulations based on variation in Dielectric Height, Trace Width, Trace Thickness, Gap Between Traces (for Differential lines), Effective Dk and DF of the dielectric material, and RMS Roughness (for Hammerstad) or Surface Ratio and Sphere Radius (for Huray or Causal-Huray) of the conductor. Through these simulations, Gauss 2D enables a user to build confidence intervals, to understand what kind of manufacturing tolerances to enforce in order to maintain the level of impedance control desired.

Impedance Control

In order to ensure sufficient impedance control on your PCB transmission lines, you cannot design for an impedance that simply falls within your acceptable window – you need to define a transmission line that is as close to the middle of your acceptable window as possible (i.e. the number you predict from your high fidelity simulation should be very close to the target impedance). The reason for this is that your simulated impedance (assuming your simulation is accurate) will reflect the mean value of your stochastic distribution for impedance. The combined effect of manufacturing tolerances and variations in properties can result in a substantial standard deviation with respect to that mean value. The example on the left shows a case where the range for the 95% confidence interval for impedance is nearly 8 Ω, centered on the simulation output value of 94.69 Ω.

Dealing with Loss Budgets

Just as with the case of controlled-impedance designs, when you’re working on high speed applications, where you need to control for loss, not only do you need to simulate loss accurately (Gauss 2D is the only field solver that accounts for ground plane losses), you also need to characterize the impact of manufacturing tolerances and variations, as well. As to the insertion loss, a product developer should really focus on the upper bound of that confidence interval, because, if that value is below the specified loss budget, then there is a high likelihood that the insertion loss values of the transmission lines on actual built boards will fall under the required loss budget. In the case shown on the right, looking at jus the single point value would tell you that the insertion loss is 0.688 dB/in, but there is a 95% confidence that the insertion loss would be less than 0.726 dB/in, a critical distinction if your loss budget is 0.7 dB/in.

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