# Power and impedance integration

With the option pull-down box set to POWER INTEGRATION, the modal analysis tab displays the settings used to spatially integrate the power distribution of the calculated modes. It allows users to drag and draw a region for integration or define the region by the vertices using the GUI.

The power integration parameters are as follows:

- INTEGRATION SHAPE: Options include circular, rectangular and solid. The Solid option refers to any top-level geometry object (for example, a structure group, but not an object within a structure group) existing in the simulation. For overlapping geometries the mesh order is respected, otherwise they are resolved by tree order the same as in standard meshing.
- INTEGRATE: Options include power, electric field intensity, or current (which returns the characteristic impedance). In the far field, only power integration is allowed so that the normalization to the near field mode is physically meaningful. Note that in the far field, the power is proportional the electric field intensity.
- X1, X2, Y1, Y2 (or Z1, Z2) (valid for rectangular integration): defines the vertices of a rectangle over which the quantity of interest is integrated
- CENTER X, CENTER Y (or CENTER Z), RADIUS (valid for circular integration): defines the center and radius of a circle over which the quantity of interest is integrated
- NORMALIZE TO (valid for far field only): Two options exist:
- NEAR FIELD MODE: Allows the user to normalize to the near field, or
- PROJECTION SURFACE: Allows the user to normalize to the total far-field quantity

- ANGLE (valid for far-field angular integration): defines angular cone over which the quantity of interest is integrated
- FRACTION INTEGRATED: The result of the integration procedure for power or electric field intensity integration options. This quantity updates itself as variations in the above parameters are made
- CHARACTERISTIC IMPEDANCE: The result of the integration procedure for the current integration option. This quantity updates itself as variations in the above parameters are made. The characteristic impedance is calculated using

$$ Z0 = \frac {P}{I^2} $$

Where P is calculated from the Poynting vector integrated over the 2D surface of the integration region:

$$ P = \int _S P \cdot dS $$

And I is the current calculated by integrating the H field around the outer edges of the integration region:

$$ I=\oint_{c} H \cdot d l $$

- GRAPH CONTROL:
- DEFINE INTEGRATION REGION: In this state, the mouse is used to graphically define the region over which the integration will be performed
- ZOOM: In this state, the mouse controls the zoom of the current figure in the visualization window