Virtuoso Meets Maxwell: Finite Element Can Add Clarity

'Virtuoso Meets Maxwell' is a blog series aimed at exploring the capabilities and potential of Virtuoso RF Solution and Virtuoso MultiTech. So, how does Virtuoso meets Maxwell? Now, the Virtuoso platform supports RF designs, and the RF designers measure the physical and radiation effects by using the Maxwell's equations. In addition to providing insights into the useful software enhancements, this series broadcasts the voices of different bloggers and experts about their knowledge and experience of various tools in the Virtuoso IC-Packaging world along with the nuances of RF, microwave, and high frequency designs. Watch out for our posts on Mondays.

Hello, Everyone! This post is a continuation of the series on electromagnetic simulation tools that can be integrated with Virtuoso RF Solution. We are going to talk about an impressive solver engine that utilizes ‘finite element method’, which is commonly referred to as FEM. The analysis based on FEM is called 'finite element analysis' (FEA). To keep things simple, I will just stick to the commonly-used term FEM. There is an ultra-powerful FEM tool from Cadence that can equip you to capture a clear picture of electromagnetic behavior of your layouts, and it is also named appropriately as ‘Clarity 3D Solver’.

This blog answers some of the initial questions you might have when you are exploring solvers to run EM simulations:

Why consider a FEM solver?

How many elements do we need in FEM? How does Clarity 3D Solver identify the number of elements required for a layout?

Why do we need boundaries or bounding boxes and why does each boundary need a condition?

Why special care is needed in FEM port setup?

Why consider a FEM solver?

The FEM-based electromagnetic extraction tools are well known in the industry for their high accuracy and relatively high capacity (they can model ICs, modules, PCBs, etc.). In the first step of FEM simulation, the structures are chopped into a finite number of small tetrahedral mesh elements (often just called ‘elements’). These tetrahedral element-based FEM solvers are often referred to as “Full 3D” electromagnetic solvers because they can take in any arbitrary and non-planar shape (e.g. wire-bond) for simulation and they are quite capable in capturing coupling between structures. The Clarity FEM solver from Cadence incorporates a breakthrough parallelization algorithm which offers an unprecedented performance while maintaining accuracy. In addition, Clarity 3D Solver has a nice integration or ‘deep-hook’ with relevant Cadence layout tools making the transfer of layout and results very streamlined.

The integration of Clarity 3D Solver with Virtuoso RF Solution makes the layout export to the solver and backannotation of results in Virtuoso a very easy task. We all spend time on preparing and setting up the electromagnetic simulation, and later getting the result back into its meaningful place. We certainly would appreciate a flow where this are handled with automation. Virtuoso RF solution, coupled with Clarity 3D Solver, just does that for us!

How many elements do we need in FEM? How does Clarity 3D Solver identify the number of elements required for a layout?

One powerful feature of FEM-based meshing is that it is adaptive. The initial meshing will slice the structures and create a certain number of mesh elements called ‘initial mesh’. Then, it will make few more mesh refinements and create matrix. The differences in matrix entries from the new mesh and the old mesh elements are checked at a specific frequency. If the difference is larger than a defined threshold, those elements are split again into smaller mesh elements. The elements that meet the threshold of difference, do not get split anymore. This process of splitting and checking keeps repeating and, in each iteration, more mesh elements are added wherever it is needed. Eventually, all the differences fall below the set threshold, structure reaches its ‘final mesh’ and it can now proceed to run a frequency sweep.

Fig 1: Mesh element comparison between initial and final mesh (white lines are the edges of the elements)

Though it is not shown in the above illustration, FEM also creates mesh elements in the dielectric, including the air inside the bounding box.

One key advantage of this approach is that it makes the mesh denser where necessary and does not create extra mesh elements at other locations. Most of the time, the threshold of difference between elements (also called as delta_S) is set to 0.02 (i.e. 2%). Once the difference is less than 0.02, the mesh refinement stops. This 0.02 number is usually sufficient to obtain the desired accuracy for most cases. However, values smaller than 0.02 can be set to get a denser mesh, if necessary.

Clarity 3D Solver has its own proprietary meshing algorithms that automatically ensure adequate meshing. You can also take control of the meshing and play with different settings.

Why do we need boundaries or bounding boxes and why does each boundary need a condition?

An interesting aspect of 3D-FEM tools is that they require a boundary or enclosure. All simulations are supposed to happen inside of this boundary. These boundaries can be like a box with six sides or may have many faces.

In 3D-FEM, the ‘blank’ space is filled with metal by default, not free space or air. No electric field will exist inside the metal. Therefore, these boundaries create a padding and ‘push away’ those metals and create a ‘bubble’ inside of which the simulation takes place. (My other favorite analogy would be to think about a human staying inside a submarine. There is water everywhere, but that submarine creates a ‘bubble’ that allows the human to walk inside freely). The spaces between the design and the boundaries are usually filled with air (vacuum can also be used), and we often will hear the term ‘airbox’ to refer to such a bounding box.

Fig 2. Simple illustration of a design inside of a bounding box filled with air. The surfaces of this box will receive the boundary conditions.

Now, we got a boundary to enclose our design. The next step would be to assign some ‘conditions’ on the boundary surfaces. Simply, it dictates how each face of this bounding box will behave. There are several of these conditions: ABC (absorbing boundary condition), PEC (perfect electric conductor), PMC (perfect magnetic conductor), etc. As it relates more closely to our interest in simulation, we would focus on ABC. Electromagnetic radiation emanating from the design is going to hit the faces of the bounding box from the inside. If the condition of the boundary surface is set to ‘absorbing’, most of the radiation that impinges on it, will be absorbed with very little reflections going back towards the design.

What is the reason for using this absorbing boundary condition? Well, by absorbing most of the radiation, the enclosure mimics the ‘open air’ environment. From the perspective of the the device under simulation, it feels like most of the radiation emitted was dispersed into free space while it is actually inside the absorbing boundary condition. This allows the simulator to work with a finite volume and data to model the design; without needing an enormously large enclosure of air inside the scope of simulation.

On the other hand, a bad boundary size and condition can make the simulation terribly inaccurate. For example, if a boundary is too close to the signal carrying lines, then the electromagnetic fields will interact with the boundary and that would interfere with the signal lines performance and produce wrong result. Also, a PEC condition will reflect the radiation back inside, more than an ABC would reflect. The condition must be selected carefully as the simulation demands.

We also need to find a delicate balance in sizing the bounding box. Too small a bounding box may lead to inaccurate results, while too big a bounding box may waste computing resources and take more time to arrive at the results. There are many thumb rules for choosing the size, also the same-sized box may or may not be okay for all values of frequencies. Generally speaking, they should be large enough to avoid any coupling to the design, and make structure being simulated ‘feel’ similar to the intended real-life operation.

In Clarity 3D Solver, it is possible to use a dialog box to set the clearance to the boundaries in all directions, or to draw a box and define its material as ‘air’. Similarly, the boundary conditions can be set in a dialog box or on the drawn surfaces of the bounding box.

Why special care is needed in FEM port setup?

Ports are placed where the excitations are launched into the structure under simulation. There are several types of ports in FEM solvers, but we would limit our discussion to lumped ports in this installment. FEM port definitions have some specific requirements and an important one is that all ports must have a local ‘Reference’. This reference is somewhat analogous to the reference in a voltage source. Unless we are simulating a radiating structure (antenna), all the charge/current, launched into the structure at one end of the port, usually comes back after travelling the whole path at the other end of the port. In comparison, for the method of moment (MoM)-based solvers, the port may or may not have an explicit reference, but FEM ports must have a clearly defined reference that is inside the scope of the simulation.

A lumped port must have a geometric shape that touches both the reference and the structure to be simulated. This shape embodies the port and without it, the port cannot exist in FEM simulation. Most of the time, the shape holding the lumped port is just a rectangular sheet.

Fig 3: The green box is the shape of the port that touches the reference and the structure to be extracted. (metals are displayed and dielectrics are hidden)

I mentioned that the current or charge launched from the port must come back (unless radiation is intended like an antenna). The charge will travel through the structures, get to the other ports (if present) and reach the return path and travel back to the base of the port shape i.e. reference of that port. The port orientation arrow guides which way the current flows.

Fig 4: Port orientation and a simplified illustration of current loop (metals are displayed and dielectrics are hidden)

Though the directions can change for charge flow with time and phase, a common direction is required for all ports so that they can be meaningfully correlated. For example, I would orient the other port (not shown in this fig. 4) in the same way the visible port is oriented. The other port should also orient upwards. Conventionally, port orientations are set in such a fashion that the arrow tips touch the traces being extracted.

When you use Clarity 3D Solver to run EM simulations, a wizard that facilitates the port generation will find references and create port for selected nets. Clarity 3D Solver can easily handle hundreds of ports in complex designs and find results within industry-leading speed.

I will stop here for today. This time we just stepped into the domain of FEM-based electromagnetic analysis and got to know a tiny bit about Clarity 3D Solver. In the next installment, I hope to get into a little bit more details on how Clarity 3D Solver can make the electromagnetic simulation a simpler task.

Related Resources

• Virtuoso RF Solution
• Clarity 3D Solver
• What’s New in Virtuoso (ICADVM18.1 Only)
• Virtuoso RF Solution Guide

For more information on Cadence circuit design products and services, visit www.cadence.com.

About Virtuoso Meets Maxwell

Virtuoso Meets Maxwell series includes posts about the next-generation die, package, and board design flow with a focus on reinventing and optimizing the design process to ensure that the designer remains a designer! Keep watching!

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Amir Asif