[Detailed Mode] Electromagnetic Waves Directivity

Item

Notes

Graph Type

Either XY Graph and Polar Graph are available. The polar graph is available only if the angle is selected for the horizontal axis.

Efficiency

Calculates the one specified in [Efficiency type].

Save File

Saves the calculation results in a csv file.

Observation Point

Specifies by the angle from the origin.

See the figure at Coordinate system for the angles definition.

Calculation of Electromagnetic Waves Directivity

Antenna's electromagnetic field is calculated by solving the electromagnetic current source induced on the plane S which surrounds the antenna entirely.

The induced electromagnetic current source is given by the electromagnetic field generated by the antenna on the plane S.

If the observation point for the directivity calculation is far enough from the antenna, the electric field at the observation point is expressed with the integral on the pane S as below. [1]

Where and n is a normal vector in the inward direction on the plane S.

: Electric field

: Magnetic field

: Unit vector directing to the observation point

: Position vector to S

: Wavenumber

: Impedance of free space

: Distance to the observation point

: Equivalent electric current

: Equivalent magnetic current

The directivity is calculated by performing the integration on the open boundary.

Ref [1] Finite Element Method for Electromagnetics :John L.Volakis Chapter1

Display Type

The electric field in the far field is as shown above equations. Femtet actually calculates the electric field as indicated below.

Equation (1) is modified to Equation (2).

where

Note that the left-hand side of Equation (2) is the product of the electric field in the far field and the distance.

POWER, rE, rE(θ), and rE(Φ) are solved as follows. Where E0θ is a θ-component of E0 and E0Φ is a Φ-component of E0.

For the display on the directivity dialog box, when Power, rE, rE(θ), and rE(Φ) are selected, Equations (7), (4), (5), and (6) are calculated, respectively.

To acquire the radiation pattern for the specific polarization, specify the corresponding rE(θ) or rE(φ) based on the model's orientation and coordinates.

rER, rEL and Axial ratio are used to calculate the circular polarization.

rER = (rE(θ) + j rE(φ)) / √2 : Right circular polarization

rEL = (rE(θ) - j rE(φ)) / √2 : Left circular polarization

Axial ratio = (|rER| + |rEL|) / (|rER| - |rEL|)

Unit

As shown in [Display Type] above, the quantities in equations (4) through (7) are obtained. The value is represented by V.

The maximum value of V is represented by Vmax.

dB..........10Log(V/Vmax): for Power

20Log(V/Vmax): for the items other than Power

dBi..........10Log(4π*V/Pin): for Power

10Log(2π*V*V/Z0/Pin): for the items other than Power

Pin is the input power.

See also [Gain Type] below.

Linear (normalized) ... ... V/Vmax

Linear (not normalized) ... ... V

Linear (without complex normalization) ... ... E0 : refer to Equation (3)

Plane of Symmetry and Infinite Ground Plane

Magnetic wall		Electric wall
Figure 1: Electric field E and magnetic field H with the symmetric boundary in between

The magnetic wall and the electric wall can be symmetric boundary. The directions of the electric and magnetic fields at the symmetric boundary are shown in Fig.1.

Their magnitudes are considered to be equal.on both sides of the boundary. With the results of half, quarter and 1/8 models, the partial radiation patterns are obtained.

The full radiation pattern is constructed from them.

The symmetric boundary is selectable from XY plane at Z=0, YZ plane at x=0, or XZ plane at y=0.

Select either magnetic wall or electric wall considering the symmetric electromagnetic fields

to calculate the radiation pattern.

Note that the calculation time of these partial models will be similar to that of the full model, as the calculation is executed for the area where the meshes are not generated as well.

The infinite ground plane is selected if the model has a large ground plane, e.g. monopole antenna.

See Example 30 of Electromagnetic Analysis

[Setting] - [Horizontal axis]

Select one from θ, φ, or Frequency. That will be used for the horizontal axis of XY graph or the angle component of the polar graph.

When Frequency is selected, the maximum electric field at the observation point be plotted for the frequencies.

[Setting] - [Other settings]

Activates the Directivity Setting dialog box.

Directivity Setting:

Input

Select either Number of Divisions or Interval. The method to specify the observation points is selected.

Directivity Setting:

Efficiency

Select either Total or Radiation.

The equations are as follows.

Radiation efficiency: Efficiency = 100 * Radiation power / (Input power - Reflected power)

Total efficiency: Efficiency = 100 * Radiation power / Input power

where Radiation power = (Input power - Reflected power - Joule loss)

Directivity Setting:

Gain type

Select either Input power referenced or Received power referenced.

Antenna gain is calculated as follows. For G[ dBi]

G(θ,φ) = 10xlog10( P(θ,φ)/Piso)

where P(θ,φ) is the power radiated in the (θ,φ) direction per unit solid angle and

Piso is the power that the non-directional antenna radiates per unit solid angle.

If [Input power referenced] is selected: Piso = (Input Power) / 4π (8)

If [Received power referenced] is selected: Piso = (Received Power) / 4π (9)

Refer here for the input power and received power Select [Received Power Referenced] for absolute gain and select [Input Power Referenced] for actual gain.

1 [W] per port is the default setting for Pin. It is set on the harmonic analysis tab of the analysis condition.

If [Input power referenced] is selected, the comparison is made with the non-directional antenna which radiates all the input power.

If [Received power referenced] is selected, the reference is set to the non-directional antenna which radiates the input power it actually received excluding the reflection at the port.

Equations (8) and (9) are for the input power at one port. If the power is input at multiple ports, Piso is the totaled power of all ports.

Section

Polarization

Observation Point (φ, θ)

Display Type

Setting > Horizontal axis

XZ plane, YZ plane

eθ

φ(0, 90, 1), θ(-180, 180, 100)

rE(θ)

θ

XZ plane, YZ plane

eφ

φ(0, 90, 1), θ(-180, 180, 100)

rE(φ)

θ

XY plane

eθ

φ(-180, 180, 100), θ(90, 90, 0)

rE(θ)

φ

XY plane

eφ

φ(-180, 180, 100), θ(90, 90, 0)

rE(φ)

φ