Radiation Patterns and Antenna Characteristics for Momentum
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.
 | Note In Momentum RF mode, radiation patterns and antenna characteristics are not available. |
About Radiation Patterns
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 ).
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.
| Note It is possible to calculate far-fields for some designs that have a top or bottom layer that is not defined as open space. For more information on these structures, refer to 377 Ohm Terminations and Radiation Patterns. |
About Antenna Characteristics
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.
Co-polarization angle
Radiation Intensity
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:
Radiated Power
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
Effective Area
The effective area, in square meters, of the antenna circuit is given by:
Calculating Radiation Patterns
To calculate a radiation pattern:
- Choose Momentum > Post-Processing > Radiation Pattern .
- Select the General Tab.
- Select a frequency from the Select Frequency listbox. The radiation pattern will be calculated at this frequency. These are frequencies that were calculated during the simulation.
- Select a port from the Available Ports list to apply a steering circuit (based on the Thevenin equivalent) to the port and inject energy into your circuit. You can apply a steering circuit to any port.
- In the Port Excitation fields, enter amplitude (in volts) and phase (in degrees) of the voltage of the steering circuit of that is applied to the port.
- In the Port Termination Impedance fields, enter the real and imaginary components of the impedance of the steering circuit that is applied to the port.
Note
You may want to terminate all ports so that the ports that are not used to inject energy into the circuit do not cause reflections. For these ports, set the Port Excitation voltage to zero, and set the Port Impedance to the characteristic impedance of the port. - Select the display tool that you want to use. Enable either 2D Data Display or 3D Visualization. The 3D Momentum Visualization tool requires a separate codeword. For instructions and information about using the tool, refer to Momentum Visualization.
- If you want the display tool to open and display results automatically, enable Open display when computation completed .
- If you have selected to use the 3D tool, click Compute . More information on how to use the Momentum Visualization tool are in following chapters.
If you are using the Data Display, click the 2D Settings tab and continue with these steps. - Specify a dataset name where you want to store the far-field results.
- Select the template that you want to use for formatting results, or accept the default.
- Select either the planar or conical Cut Type Definition:
- A planar cut is perpendicular to the circuit layout plane.
- A conical cut is a cone around the z-axis.
Refer to the diagram in the Radiation Pattern Control dialog box. For more information, refer to Planar (Vertical) Cut and Conical Cut.
- Enter the value of the cutting angle, in degrees, in the Cutting Angle field.
- For a planar cut, the cut angle , phi, is relative to the x-axis. Phi will be kept constant while theta will be swept from -180 to 180 degrees.
- For a conical cut, the cutting angle, theta, is relative to the z-axis. Theta will be kept constant while phi will be swept from 0 to 360 degrees.
- Enter the value of the co polarization angle in the Co Polarization Angle field. This angle will be used when decomposing the far-fields into a co and cross polar component (see Linear Polarization).
- Enter the threshold for displaying data in the Lower Clipping Boundary field. Select units of dB or mag. Computed radiation pattern data that is below this value will be displayed as zero (when units are mag) or the lower clipping boundary (when units are dB).
- Click Compute to compute the radiation pattern. After computation, the far-fields and derived antenna parameters will be stored in a dataset with the name you specified. An f will be appended to the dataset name. The __f indicates that the dataset contains radiation pattern data. The dataset is stored in the / data directory of the current project.
After the radiation calculations are performed, data is saved depending on the display tool selected above:
- 2D Data Display was selected: all data is stored in a single dataset with the name you specified with _f.ds appended. The _f indicates that the dataset contains radiation pattern data. The dataset is stored in the /data directory of the current project.
- 3D Visualization was selected: the far-fields and derived antenna parameters will be stored in respectively proj.fff and proj.ant in the mom_dsn/<design_name> directory of your project.
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.
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.
For more information, please refer to About Antenna Characteristics.
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> */
Maximum radiation intensity <U> /* in Watts/steradian */
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)>
Power radiated <excitation #i> <prad> /* in Watts */
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.
Displaying Radiation Results
In Momentum 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 Momentum RF mode, radiation results are not available for display. For general information about radiation patterns and antenna parameters, refer to About Radiation Patterns.
Loading Radiation Results
In Momentum, 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. The radiation results file contains only the radiation results for a single frequency (the one that was last calculated). Since this file is loaded only when a new Momentum project is opened, you must reopen the project to load radiation results calculated at another frequency.
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:
- Choose Projects > Select Project.
- Select the name of the Momentum or Agilent EMDS project that you want to use.
- Click Select Agilent EMDS or Select Momentum.
- Choose Projects > Read Field Solution.
- 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:
- Choose Far Field > Far Field Plot.
- Select the view in which you want to insert the plot.
- 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
- 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.
- 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.
- Click OK.
Selecting Far-field Display Options
You can change the translucency of the far-field and set a constant phi angle:
- Click Display Options.
- 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.
- Adjust the translucency of the far-field by using the scroll bar under Translucency.
- 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:
- Choose Far Field > Cut 3D Far Field.
- If you want a conical cut, choose Theta Cut. If you want a planar cut, choose Phi Cut.
- 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.
- Click Apply to accept the setting. The cross section is added to the Cut Plots list.
- Repeat these steps to define any other cross sections.
- 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:
- Choose Far Field > Plot Far Field Cut.
- 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.
- Select the view that you want to use to display the plot.
- Select the E-field format.
- Select the plot type, either Cartesian or Polar.
- If you want the data normalized to a value of one, enable Normalize.
- 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.
- 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:
- Radiated power, in watts
- Effective angle, in degrees
- Directivity, in dB
- Gain, in dB
- Maximum radiation intensity, in watts per steradian
- Direction of maximum radiation intensity, theta and phi, both in degrees
- E_theta, in magnitude and phase, in this direction
- E_phi, in magnitude and phase, in this direction
- E_x, in magnitude and phase, in this direction
- E_y, in magnitude and phase, in this direction
- E_z, in magnitude and phase, in this direction
| Note In the antenna parameters, the magnitude of the E-fields is in volts. |
Viewing Radiation Patterns
Specific information about the data available in the far-field dataset is given in this section.
Variables in the Far-field Dataset
| Note The normalized far-field components (Elhp, Erhp, Eco, and Ecross) are normalized with respect to  . |
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