# Compute Average Power Density

Analyze planar sensor results based on IEC/IEEE 63195-2.

XFdtd's algorithm for computing spatial-average power density (sPD) and peak spatial-average power density (psPD) adheres to the Committee Draft (CD) and Committee Draft for vote (CDV) of IEC/IEEE 63195-2 [1]. This standard is under development so results from XF are considered preliminary and serve as a basis for understanding a device's performance under the current specifications. The script's functionality is incorporated into the user interface upon approval of the standard.

## CD vs. CDV

The CD was released in 2018 and the CDV was released in 2019. Both drafts compute spatial-average power density

$$sPD(r)=\frac{1}{2A}\iint_{A(r)}\text{Re}\left\{E\times H^*\right\}\cdot \hat n dA$$

where $A(r)$ is the averaging area centered on a vertex of the triangulated evaluation surface.

Of the multiple algorithmic differences between the CD and CDV, the most notable is averaging area orientation, which affects runtime. Both drafts indicate that sPD is computed at each vertex of the triangulated evaluation surface, but they differ in handling the orientation of the averaging area around the evaluation surface's normal. The CD does not mention orientation, allowing each code manufacturer to define its own arbitrary orientation. The CDV corrects for this by stating that the averaging area is rotated around its center point in five degree increments until it has rotated 85 degrees from its initial position. This provides consistent results from different code manufacturers, but it also negatively impacts runtime because sPD must be computed 17 times for each vertex.

## Prerequisites

IEC/IEEE 63195-2 provides an algorithm for testing emissions from a radiating device. In addition to setting up an XF project to simulate a radiating device, an evaluation surface must be provided where power density is calculated.

Often, the evaluation surface must be a specific distance from the device at a location that does not coincide with a gridline. The user must therefore specify a planar sensor in order to define the evaluation surface, as well as a volume sensor that surrounds the planar sensor. The script then interpolates the fields of the volume sensor onto the planar evaluation surface.

• Create a Planar Sensor or Rectangular Sensor to serve as the evaluation surface.
• Collect steady-state electric fields in the associated Surface Sensor Definition.
• Create a Solid Box Sensor that is larger than the planar sensor, surrounding it by one cell edge in all directions.
• Collect steady-state electric and magnetic fields in the associated Solid Sensor Definition.
• Specify one or more steady-state frequencies when creating the FDTD simulation.
• Run the FDTD simulation to completion.

Multiple evaluation surfaces could potentially be surrounded with a single, large solid sensor.

## Workflow

After meeting the prerequisites, run the macro by following these steps:

1. Download the Compute Average Power Density.xmacro
2. Right-click on Scripts in the Project Tree and select Import Scripts.

Once the script is available, select two result sensors for analysis.

1. Open the Results browser.
2. Specify the evaluation surface by left-clicking on a planar sensor result in the lower portion of the Results browser.
3. Press Shift while left-clicking on a volume sensor result in the lower portion of the Results browser in order to specify the associated electric fields.
4. Double-click on Compute Averaged Power Density in the Scripts branch of the Project Tree to open the Scripting window.
5. Click Execute at the top of the window, then select Execute Macro to open the Average Power Density window.

Selecting the magnetic fields is unnecessary because the script accesses them based on the name of the selected solid sensor.

Specify the calculation inputs.

1. Select the desired frequency. This drop-down menu lists the steady-state frequencies specified when creating the FDTD simulation.
2. Select the desired algorithm. The CD and CDV options correspond to the drafts of the standard.
3. Leave Automatic Area checked for the script to select the averaging area size based on the frequency. The averaging area is a square that is 4 cm2 for frequencies less than or equal to 30 GHz and 1 cm2 for frequencies greater than 30 GHz.
4. If Automatic Area is unchecked, provide a custom size in Averaging Area.
5. Optionally, check Save Output to Disk to save sPD at each vertex on the evaluation plane to a Matlab *.m file.
6. If Save Output to Disk is checked, either click Browse to specify the output filename and location or enter the file in Filename.

If the CD algorithm is selected, provide the axis along which one side of the averaging square will be oriented.

1. Enter the U-Direction as x, y, z global coordinates.
2. Click OK.

The script triangulates the evaluation surface and computes sPD for each vertex using the electric and magnetic field data pulled from the solid sensor. The psPD appears in a dialog window when the script is complete and if specified, the sPD is written to an output file.

## Reference

1. International Electrotechnical Commission (IEC) and the Institute of Electrical and Electronics Engineers (IEEE), IEC/IEEE 63195-2, Assessment of Power Density of Human Exposure to Radio Frequency Fields From Wireless Devices in Close Proximity to the Head and Body, Part 2: Computation Procedure (Frequency Range of 6 GHz to 300 GHz), 2019.