Rob,
   You cannot model arbitrary functions of frequency in Verilog-A. However, after some exhaustive research on the topic (typing "Warburg element" into Google and clicking on the I Feel Lucky button) I have found that what you call a Warburg element is what I call a fracpole. You can find a papers that describe how to model fracpoles at www.designers-guide.org/Modeling, and even some programs for generating the models. Look for papers on diffusion like processes (dielectric absorption & skin effect, but not diffusion resistors), and of course on fracpoles.

Can you give me a pointer to the battery model you are using?

-Ken

Hi Rob.
Sorry, I did recognize you. I should have been more friendly, but I kind of got wrapped up into these Warburg elements.

As I dug more into this I found different versions of the Warburg element. The simplest models "semi-infinite linear diffusion" and it has an impedance of Z_W = A_W/√s. This is naturally modeled by a fracpole. By the way, I think fracpoles are now built-in to Spectre.

There also seem to be variants that employ the tanh and coth functions. It is not why these are different from the one above, but I think it may be because they model "finite linear diffusion". I don't know. Since people call all of these models Warburg elements, perhaps they approximate each other over an interesting range of frequencies. If so, you might be able to get away with a fracpole, which would be easy. Otherwise you might consider using an N-port (nport). Use matlab or some such program to evaluate the impedance over a wide range of frequencies, write the results to a file, and then reference the file with the N-port. The N-port would end up being a one-port that would work both in transient and AC analyses. Be sure to verify it, the nport can be flaky in transient, especially in the presence of widely spaced time constants.

I will be updating the fracpole documents later today. Nothing interesting. I'm just going to mention Warburg elements so that people see the connection.

-Ken