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 ).
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.
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:
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.
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.
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:
The maximum directivity is given by:
where P inj is the real power, in watts, injected into the circuit.
The maximum gain is given by:
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.
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.
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.
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.
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.
- 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.
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:
- Choose Projects > Select Project.
- Select the name of the Momentum or Agilent EMDS project that you want to use.
- Click Select Momentum or Select Agilent EMDS.
- Choose Projects > Read Field Solution.
- When the data is finished loading, it can be viewed in far-field plots and as antenna parameters.
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 .
- 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 .
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
- 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.
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
In the antenna parameters, the magnitude of the E-fields is in volts.