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62 The PCB Design Magazine • September 2016 is obtained as the first design but with a smaller number of vias. We can take the analysis further by reducing the number of vias for this design to five. Analy- sis results shows that the thermal junction max- imum temperature is 46.6°C (+1.6°C). 0.87 W is transferred by conduction into the PCB top layer by pin4. The rest (0.13 W) is transferred outside the junction through pins 1-2-3 by con- duction or outside the encapsulant by convec- tion (Figure 12a). 0.48 W is transferred into the TIM through the five thermal vias (Figure 12b). We can conclude that using fewer vias has no benefit. Now with this information, the good layout with 10 thermal vias can be improved. Analysis results shows that the thermal junction maxi- mum temperature is 42.9°C (-2.1°C). 0.90 W is transferred by conduction into the PCB top lay- er by pin4. The rest, 0.10 W, is transferred out- side the junction through pins 1-2-3 by conduc- tion or outside the encapsulant by convection (Figure 13a). 0.71 W is transferred into the TIM through the 10 thermal vias—improved use of the thermal vias (Figure 13b). These examples illustrate the importance of using a 3D model in thermal simulation to ob- tain the best design. The top layer of the PCB has the most effect on cooling the IC; thus, the path from the heat source to the thermal vias must be free of "heat bottlenecks." Thermal vias must be placed as close as possible to the heat source (in this case, pin 4). Overall, our thermal simulation illustrates that the number of ther- mal vias is less important than the quality of placement and layout. PCBDESIGN Gabriel Ciobanu is a thermal design engineer at Continental Automotive in Romania, where he is involved in the development process of creating virtual prototypes and investigating cooling concepts and materials. Boris Marovic is the technical man- ager of FloEFD products for the Me- chanical Analysis Division at Mentor Graphics, and is based in Frankfurt, Germany. When roboticists cre- ate behaviors for teams of robots, they first build al- gorithms that focus on the intended task. But that's where the problems begin. "When you have too many robots together, they get so focused on not colliding with each other that they eventually just stop moving," said Geor- gia Tech roboticist Magnus Egerstedt, director of Georgia Tech's Institute of Robotics and Intelligent Machines. "Their safety behaviors take over and the robots freeze. It's impossible for them to go anywhere because any movement would cause their bubbles to pop." Egerstedt has created a solution. His team's new algorithms allow any number of robots to move within inches of each other, without colliding, to complete their task -- swapping locations on his lab floor. They are the first researchers to create such minimally invasive safety algorithms. In technical speak, the bots are using a set of safe states and barrier certifi- cates to ensure each stays in its own safe set throughout the entire maneuver. "In everyday speak, we've shrunk the size of each robot's bubble to make it as small as possi- ble," said Egerstedt. "Our system allows the robots to make the minimum amount of changes to their original behaviors in order to accomplish the task and not smack into each other." Egerstedt also said something similar to these algorithms could be used for the next genera- tion of air traffic control. Instead of people di- recting the flow, planes will be given the author- ity in airspaces. Team of Robots Learns to Work Together, Without Colliding THE FUNDAMENTALS OF IMPROVING PCB THERMAL DESIGN