# Radiation Patterns and Antenna Characteristics

This chapter describes how to calculate the radiation fields. It also provides general information about the antenna characteristics that can be derived based on the radiation fields.

Once the currents on the circuit are known, the electromagnetic fields can be computed. They can be expressed in the spherical coordinate system attached to your circuit as shown in Co-polarization angle. The electric and magnetic fields contain terms that vary as 1/r, 1/r 2 etc. It can be shown that the terms that vary as 1/r 2 , 1/r 3 , ... are associated with the energy storage around the circuit. They are called the reactive field or near-field components. The terms having a 1/r dependence become dominant at large distances and represent the power radiated by the circuit. Those are called the far-field components (E ff , H ff ).

 Note In the direction parallel to the substrate (theta = 90 degrees), parallel plate modes or surface wave modes, that vary as 1/sqrt(r), may be present, too. Although they will dominate in this direction, and account for a part of the power emitted by the circuit, they are not considered to be part of the far-fields.

The radiated power is a function of the angular position and the radial distance from the circuit. The variation of power density with angular position is determined by the type and design of the circuit. It can be graphically represented as a radiation pattern.

The far-fields can only be computed at those frequencies that were calculated during a simulation. The far-fields will be computed for a specific frequency and for a specific excitation state. They will be computed in all directions (theta, phi) in the open half space above and/or below the circuit. Besides the far-fields, derived radiation pattern quantities such as gain, directivity, axial ratio, etc. are computed.

Based on the radiation fields, polarization and other antenna characteristics such as gain, directivity, and radiated power can be derived.

### Polarization

The far-field can be decomposed in several ways. You can work with the basic decomposition in (, ). However, with linear polarized antennas, it is sometimes more convenient to decompose the far-fields into (E co, E cross ) which is a decomposition based on an antenna measurement set-up. For circular polarized antennas, a decomposition into left and right hand polarized field components (E lhp , E rhp ) is most appropriate. Below you can find how the different components are related to each other.

is the characteristic impedance of the open half sphere under consideration.

The fields can be normalized with respect to:

#### Circular Polarization

Below is shown how the left hand and right hand circular polarized field components are derived. From those, the circular polarization axial ratio (AR cp ) can be calculated. The axial ratio describes how well the antenna is circular polarized. If its amplitude equals one, the fields are perfectly circularly polarized. It becomes infinite when the fields are linearly polarized.

#### Linear Polarization

Below, the equations to decompose the far-fields into a co and cross polarized field are given (
is the co polarization angle). From those, a "linear polarization axial ratio" (AR lp ) can be derived. This value illustrates how well the antenna is linearly polarized. It equals to one when perfect linear polarization is observed and becomes infinite for a perfect circular polarized antenna.

 Note Eco is defined as colinear and Ecross implies a component orthogonal to Eco. For a perfect linear polarized antenna, Ecross is zero and the axial ratio AR=1. If Ecross = Eco you no longer have linear polarization but circular polarization, resulting in AR = infinity.

###### Co-polarization angle

The radiation intensity in a certain direction, in watts per steradian, is given by:

For a certain direction, the radiation intensity will be maximal and equals:

The total power radiated by the antenna, in Watts, is represented by:

### Effective Angle

This parameter is the solid angle through which all power emanating from the antenna would flow if the maximum radiation intensity is constant for all angles over the beam area. It is measured in steradians and is represented by:

### Directivity

Directivity is dimensionless and is represented by:

The maximum directivity is given by:

### Gain

The gain of the antenna is represented by:

where P inj is the real power, in watts, injected into the circuit.

The maximum gain is given by:

### Efficiency

The efficiency is given by:

### Effective Area

The effective area, in square meters, of the antenna circuit is given by:

### Planar (Vertical) Cut

For the planar cut, the angle phi ( Cut Angle ), which is relative to the x-axis, is kept constant. The angle theta, which is relative to the z-axis, is swept to create a planar cut. Theta is swept from 0 to 360 degrees. This produces a view that is perpendicular to the circuit layout plane. Planar (vertical) cut illustrates a planar cut.

###### Planar (vertical) cut
 Note In layout, there is a fixed coordinate system such that the monitor screen lies in the XYplane. The X-axis is horizontal, the Y-axis is vertical, and the Z-axis is normal to the screen. To choose which plane is probed for a radiation pattern, the cut angle must be specified. For example, if the circuit is rotated by 90 degrees, the cut angle must also be changed by 90 degrees if you wish to obtain the same radiation pattern from one orientation to the next.

### Conical Cut

For a conical cut, the angle theta, which is relative to the z-axis, is kept constant. Phi, which is relative to the x-axis, is swept to create a conical cut. Phi is swept from 0 to 360 degrees. This produces a view that is parallel to the circuit layout plane. Conical cut illustrates a conical cut.

## Viewing Results Automatically in Data Display

If you choose to view results immediately after the far-field computation is complete, enable Open display when computation completed . When Data Display is used for viewing the far-field data, a data display window containing default plot types of the data display template of your choice will be automatically opened when the computation is finished. The default template, called FarFields, bundles four groups of plots:

• Linear Polarization with E co , E cross , AR lp.
• Circular Polarization with E lhp , E rhp , AR cp.
• Absolute Fields with .
• Power with Gain, Directivity, Radiation Intensity, Efficiency.

## Exporting Far-Field Data

If 3D Visualization is selected in the Radiation Pattern dialog, the normalized electric far-field components for the complete hemisphere are saved in ASCII format in the file < project_dir>/ mom_dsn /<design_name>/ proj.fff . The data is saved in the following format:

```#Frequency <f> GHz       /\*  loop over  <f> \*/
#Excitation #<i>         /\*  loop over  <i> \*/
#Begin cut               /\*  loop over phi  \*/
<theta> <phi_0>  <real\(E_theta\)>  <imag\(E_theta\)> <real\(E_phi\)> <imag\(E_phi\)>
/\*   loop over <theta>    \*/
#End cut
#Begin cut
<theta> <phi_1>  <real\(E_theta\)>  <imag\(E_theta\)> <real\(E_phi\)> <imag\(E_phi\)>
/\*   loop over <theta>    \*/
#End cut
:
:
#Begin cut
<theta> <phi_n>  <real\(E_theta\)>  <imag\(E_theta\)> <real\(E_phi\)> <imag\(E_phi\)>
/\*   loop over <theta>    \*/
#End cut```

In the proj.fff file, E_theta and E_phi represent the theta and phi components, respectively, of the far-field values of the electric field. Note that the fields are described in the spherical co-ordinate system (r, theta, phi) and are normalized. The normalization constant for the fields can be derived from the values found in the proj.ant file and equals:

The proj.ant file, stored in the same directory, contains the antenna characteristics. The data is saved in the following format:

```Excitation <i> /\* loop over  <i> \*/
Frequency <f> GHz /\* loop over  <f> \*/
Angle of U_max  <theta> <phi> /\* both in deg \*/
E_theta_max  <mag\(E_theta_max\)> ; E_phi_max  <mag\(E_phi_max\)>
E_theta_max  <real\(E_theta_max\)>  <imag\(E_theta_max\)>
E_phi_max  <real\(E_phi_max\)>  <imag\(E_phi_max\)>
Ex_max  <real\(Ex_max\)>  <imag\(Ex_max\)>
Ey_max  <real\(Ey_max\)>  <imag\(Ey_max\)>
Ez_max  <real\(Ez_max\)>  <imag\(Ez_max\)>
Effective angle  <eff_angle_st> steradians <eff_angle_deg> degrees
Directivity  <dir> dB /\* in dB \*/
Gain  <gain> dB /\* in dB \*/```

The maximum electric field components (E_theta_max, E_phi_max, etc.) are those found at the angular position where the radiation intensity is maximal. They are all in volts.

In EMDS for ADS Visualization, you can view the following radiation data:

• Far-fields including E fields for different polarizations and axial ratio in 3D and 2D formats
• Antenna parameters such as gain, directivity, and direction of main radiation in tabular format
This section describes how to view the data. In EMDS for ADS RF mode, radiation results are not available for display. For general information about radiation patterns and antenna parameters, refer to About Radiation Patterns.

In EMDS for ADS, computing the radiation results is included as a post processing step. The Far Field menu item appears in the main menu bar only if radiation results are available. If a radiation results file is available, it is loaded automatically.

 Note The command Set Port Solution Weights (in the Current menu) has no effect on the radiation results. The excitation state for the far-fields is specified in the radiation pattern dialog box before computation.

You can also read in far-field data from other projects. First, select the project containing the far-field data that you want to view, then load the data:

1. Choose Projects > Select Project.
2. Select the name of the Momentum or Agilent EMDS project that you want to use.
3. Click Select Momentum or Select Agilent EMDS.
4. Choose Projects > Read Field Solution.
5. When the data is finished loading, it can be viewed in far-field plots and as antenna parameters.

### Displaying Far-fields in 3D

The 3D far-field plot displays far-field results in 3D.

To display a 3D far-field plot:

1. Choose Far Field > Far Field Plot.
2. Select the view in which you want to insert the plot.
3. Select the E Field format:
• E = sqrt(mag(E Theta)2 + mag(E Phi)2)
• E Theta
• E Phi
• E Left
• E Right
• Circular Axial Ratio
• E Co
• E Cross
• Linear Axial Ratio
4. If you want the data normalized to a value of one, enable Normalize. For Circular and Linear Axial Ratio choices, set the Minimum dB. Also set the Polarization Angle for E Co, E Cross, and Linear Axial Ratio.
5. By default, a linear scale is used to display the plot. If you want to use a logarithmic scale, enable Log Scale. Set the minimum magnitude that you want to display, in dB.
6. Click OK .

#### Selecting Far-field Display Options

You can change the translucency of the far-field and set a constant phi angle:

1. Click Display Options.
2. A white, dashed line appears lengthwise on the far-field. You can adjust the position of the line by setting the Constant Phi Value, in degrees, using the scroll bar.
3. Adjust the translucency of the far-field by using the scroll bar under Translucency.
4. Click Done .

### Defining a 2D Cross Section of a Far-field

You can take a 2D cross section of the far-field and display it on a polar or rectangular plot. The cut type can be either planar (phi is fixed, theta is swept) or conical (theta is fixed, phi is swept). The figure below illustrates a planar cut (or phi cut) and a conical cut (or theta cut), and the resulting 2D cross section as it would appear on a polar plot.

The procedure that follows describes how to define the 2D cross section.

To define a cross section of the 3D far-field:

1. Choose Far Field > Cut 3D Far Field.
2. If you want a conical cut, choose Theta Cut. If you want a planar cut, choose Phi Cut.
3. Set the angle of the conical cut using the Constant Theta Value scroll bar or set the angle of the planar cut using the Constant Phi Value scroll bar.
4. Click Apply to accept the setting. The cross section is added to the Cut Plots list.
5. Repeat these steps to define any other cross sections.
6. Click Done to dismiss the dialog box

### Displaying Far-fields in 2D

Once you have defined a 2D cross section of the 3D far-field plot, you can display the cross section on one of these plot types:

• On a polar plot
• On a rectangular plot, in magnitude versus angle

In the figure below, a cross section is displayed on a polar and rectangular plot.

To display a 2D far-field plot:

1. Choose Far Field > Plot Far Field Cut .
2. Select a 2D cross section from the 2D Far Field Plots list. The type of cut (phi or theta) and the angle identifies each cross section.
3. Select the view that you want to use to display the plot.
4. Select the E-field format.
5. Select the plot type, either Cartesian or Polar.
6. If you want the data normalized to a value of one, enable Normalize.
7. By default, a linear scale is used to display the plot. If you want to use a logarithmic scale, enable Log Scale. If available, set the minimum magnitude that you want to display, in dB; also, set the polarization angle.
8. Click OK.

### Displaying Antenna Parameters

Choose Far Field > Antenna Parameters to view gain, directivity, radiated power, maximum E-field, and direction of maximum radiation. The data is based on the frequency and excitation state as specified in the radiation pattern dialog. The parameters include:

• Effective angle, in degrees
• Directivity, in dB
• Gain, in dB