Frequency-Domain and Time-Domain Full-wave
Electromagnetic simulator FAQ

This FAQ provides some answers to the most common questions about EM simulators in Frequency-Domain and Time-Domain. If you can't find the answer for your question, please send it to blueflyer@my-deja.comI will try to add the question and answer to this page.

[Q] How many different types of Full-Wave Electromagnetic simulator are there?

[A] A lot. But generally speaking, they can be cataglorized as Time-Domain (TD) and Frequency-Domain (FD) EM simulators.

[Q] So you mean under FD and TD, there are many types of full-wave methods?

[A] Yes. For example, under FD, there are Finite-Element Method (FEM), Finite-Difference Method (FDM), Integral Equation Method (IE).... And under TD, there are Finite-Difference Time-Domain Method (FD-TD), and Finite-Element Time-Domain Method (FE-TD)....

[Q] You are confusing me, could you explain the difference more clearly?

[A] No problem! Let's say this way, all the EM phenomena are governed by Maxwell's equations. Maxwell's Equations are a set of partial differential equations describing the relationship between electric field, magnetic field, material
properities... So by getting the solution of Maxwell's equations, we can predict the EM behavior of the DUT (Device Under Test). Maxwell's Equations can be written in Time-Domain or Frequency-Domain......

[Q] Wait wait wait!! You mean Maxwell's equations have many different form? I
thought the form of Maxwell's Equations is unique?

[A] If you took any course on basic electronic circuit theory (or basic signal and system), you should know that you can get the frequency-domain equation by taking the Fourier transform of a time-domain equation. So they are the same
except that the domains are different. If you want, you can take the Fourier transform of the time-domain equation solution. The result should be the same as the Frequency-Domain solution.

[Q] So what's the difference between FD and TD expression?

[A] The difference is that the tricks of solving FD and TD equations are different. For example, it is easier to get a hand-derived solution from FD expression since it assume only one frequency in FD expression.

[Q] OK, then what?

[A] Back to the original question, under FD and TD, the ways to solve the FD and TD expression are many. Different methods have their very distinctive characteristics and limitations. So next time if you see an EM simulator, you should get the info about the domain expression in which the method solves and the method that the simulator adopts!

[Q] Can you give me some real world examples?

[A] Sure! The famous EEsof HFSS adopts Finite Element Method to solve the FD Maxwell's Equations. Zeland's IE3D adopts Integral equation Method to solve FD Maxwell's Equations while Remecon's X-FDTD uses Finite-Difference Time-Domain method to solve the TD Maxwell's Equations.

[Q] Now I know why there are so many different (and confusing) EM simulators. Can you tell me the pros and cons of different methods?

[A] I should say this way. For FD expression, it gets the solution for one frequency at one time. So if you want to get the solutions for many frequencies, you have to repeat the solution process many times. This might have the difficulty for high Q circuit, it is not easy to get the resonant frequency unless you sweep the frequency carefully. But it has the advantage that it can simulates frequency-dependent properties such like metal loss while it has problem for nonlinear material!

As for TD expression, you can get the solution over a very wide band by using a gaussian pulse (which contains many frequencies) and obtain the frequency response by using FFT. Since it is in time domain, it can be applied to solve
nonlinear material and nonlinear operations. But it has problem for metal loss or very thin metal.

[Q] Which one is faster?

[A] It depends. If you only want responses for several frequencies, FD method is faster. But if you want the response over a wide band and if the circuit is high Q, then probably TD is better. Generally speaking, the execution time for both are close.

[Q] I heard people mentioned 2.5D and 3D EM simulator, what does that mean?

[A] Good question! For FD methods adopting Integral Equation method (such like IE3D, Emsemble, Strata, Momentum....), the very important part is the so called Green's Function (impulse response of a system, in some sense). It is not very easy to derive the Green's function especially for general case and complicated shape. So far the Greens function used in Integral Equation are only good for infinite substrate (width and length are infinite, but can have thickness, and many layers). There is no limitation for conductors. That's where the name 2.5-Dimension came from. Also how to solve the Green's Function (derived from FD Maxwell's Equation) numerically is another big problem. Different simulator has different way of doing that, so the limitations are also different. While there is no such limitation
for the methods such like Finite-Difference and Finite-Element based method, we call them full 3-Dimension. But TD methods also have difficulties, so it is not easy to say which one is better!

[Q] So which one should I get?

[A] This is the most common question people ask! It depends on the purpose. If you are designing circuit with infinite substrate, then either one is OK. But if you are doing anything with finite substrate (such like antenna with finite substrate and Dielectric Resonator) or with inhomogenous substrate, then you need TD EM simulators.

[Q] What is your suggestion?

[A] My suggestion is to get both if the budget allows. Since every EM simulator is good for some situations and has some limitations, it is probably good to have both and use the best one for the particular situation you encounter or even use both to double check.