The simulation of complex devices is a bit easier, thanks to analysis software that simultaneously handles several physical disciplines. An example of these new capabilities comes from sensor developer TransTech Systems Inc. in Schenectady, N.Y. To gauge the density of such construction materials as asphalt and soil, its devices measure electromagnetic properties that include conductivity and permittivity. The design of these sensors employs FEA software called Comsol Multiphysics 3.4 from Comsol Inc., Burlington, Mass.

“The FEA software lets us combine a material model, a CAD model of the sensor, and a Spice model of the external circuitry,” says Trans Tech R&D Director Ron Gamache. “In the past, we’ve attempted to model sensors as simple fixed electrical circuits. But high-frequency sensors are more complicated than such models suggest. For example, some behavior is influenced by how the device interacts with the constituents of the material being measured such as water, stone, and bitumen. Also, the external electronics strongly influence the sensor response. You can’t solve for the response of many such sensor/electronics combinations analytically in closed form, so it’s necessary to use FEA,” he says.

Gamache once calculated many multidisciplinary sensor parameters by hand. “I was trying to solve for just the material properties independent of contributions from the sensor and electronics. But the sensor model was simplistic and results didn’t match predictions, so the devices could not be calibrated in a straightforward way,” he says.

Now, the procedure is to import a CAD model of a proposed sensor into the FEA software followed by a Spice model of the electronic circuitry. “In Comsol, the Spice circuit is added as a set of differential equations and global variables such as node voltages and loop currents. The predicted response closely duplicates that of the actual sensor,” he says.

Materials such as soil, which contain many constituents, exhibit electromagnetic responses that are a function of all the constituents. This effect, called “dielectric mixing,” prevents the separation of individual contributions at any single frequency, explains Gamache. But A phenomenon called the Maxwell-Wagner Effect provides a way to take them apart. Materials that contain water have a strong permanent dipole that rotates to line up with any electric field applied to them. Injecting an electromagnetic signal into the material, starting with a low-frequency sine wave, makes the pole flip back and forth in time to the excitation. As the frequency rises, at some point the thermal inertia and the tendency to randomness of the molecules will overcome the ability to align to the field. This is called a “relaxation.”

A typical response below the relaxation point shows higher than expected permittivity. “But when relaxation happens, the permittivity drops to the value predicted by dielectric-mixing theory,” Gamache says. “It turns out that permittivity changes in a unique way for each material. So with the right signature analysis on raw spectral data, it’s possible to get enough detail to separate the contribution of each constituent.”

Gamache says FEA models are proving quite accurate. “Over time, I’ve gained enough confidence in the software to reduce or eliminate time-consuming physical testing,” he says. “I know sensors will perform as FE models predict.”

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Solving the sensor model in Comsol shows voltage and electric field streamlines.

For computational efficiency, TransTech models sensors in 2D. This view from Comsol Multiphysics software uses blue for asphalt, green for the sensor, and light blue for air. Paving contractors typically use these sensors to measure the density of asphalt.