# How to calculate permittivity for higher frequencies?

In many books the permittivity of a material is only listed as dielectric constant for one or a couple of frequencies. 1 kHz is used often (for example in the Plastics Technology Handbook, 4th ed, ISBN-13: 978-0-8493-7039-7), but I'm looking for the permittivity for a frequency at least 2000 times higher (2-4 GHz).

How does one calculate the permittivity of a material for a higher frequency? Is the dielectric constant still useful here?

• I would strongly recommend against attempting a calculation. materials behave in funny ways at relatively high frequencies. I would look thru as many reference books (CRC, etc) as well as manufacturer data sheets to find some measured values for permittivity, or for that matter transmissivity. Dec 16 '15 at 0:46
• @CarlWitthoft Plenty to find, but nothing for the frequency range I have in mind.
– Mast
Dec 16 '15 at 0:47
• @hypfco To improve an existing design. The current material is sub-optimal.
– Mast
Mar 28 '16 at 12:11
• @hypfco I assume that when I can calculate the permittivity this will allow me to make a selection of the most promising materials. The final decision can be made experimentally. Simulation could work, but IIRC that's a lot more time consuming (therefore more expensive) than a couple of experiments.
– Mast
Mar 28 '16 at 15:53
• The design is quite simple: a module with RF antenna is packed in a closed casing. The RF needs to get out.
– Mast
Mar 28 '16 at 15:54

There are a lot of methods for determining permittivities at high frequency, but they are uniformly experimentally-based. One of the easy methods is a resonant cavity. You create a resonant cavity that has a known resonant frequency. Then insert the material inside the cavity by some holder and see how much the resonant frequency is perturbed (using a vector network analyzer or similar equipment). From this you can figure out the permittivity. This is a pretty accurate method but an open probe test can do a reasonable job with a lot less manufacturing.

From experience, there typically is good data on common dielectric materials around the heating frequency (2.45 GHz). It will not likely differ meaningfully for 1-4 GHz.

I've tested microwave cavities with dielectric materials at the 18-20 GHz range and usually published values are fairly accurate for 10 GHz even applied at 20 GHz. It is certainly still a meaningful thing to have!

If you're looking for specific data, I'd look to data sheets from manufacturers of a given material. Matweb is also a good resource - you can sign up for a free account to get full results, I believe: http://www.matweb.com/

Also - just as an aside, doing antenna + dielectric simulations may be pretty easy to test the viability of dielectric materials, depending on the complexity of your antenna geometry. I've used COMSOL and a bunch of other packages to determine applicable relative permittivity / loss tangent ranges for microwave antennas / end launches. It sure beats purchasing expensive materials & manufacturing only to find out your frequency response is poor.

• I haven't located the correct statistics in Matweb yet, but I'll keep digging. I'd considered COMSOL, I have some minor experience with the suite, but wasn't certain whether it could even be used for something specialized like this. To the best of my knowledge you have to set the permittivity yourself in simulations.
– Mast
Feb 22 '17 at 19:31
• @Mast you do, but you can set a range to simulate over. It's not going to change by an order of magnitude, so if you sweep over (say, for common plastics and ceramics) a range of 2 to 10 Er, 0.0001 to 0.001 loss tangent, you will have covered your bases. Feb 22 '17 at 19:45
• Definitely not as good as I hoped, but also definitely better than nothing.
– Mast
Feb 22 '17 at 19:52

Calculating permittivity as a function of frequency is extremely difficult at best, to the point of being considered so impractical as to be impossible. Permittivity as a function of frequency behaves in response to a many properties of the dielectricum, and does not follow a predictable curve. As you sweep across the frequency spectrum, permittivity of a given dielectricum may go up and down at seemingly random intervals.

If you need accurate data of the permittivity of a given dielectricum under given circumstances (temperature, voltage, mechanical properties etc.) measurement is the only recommended option.