This chapter describes how to calculate radiation fields. It also provides general information about the antenna characteristics that can be derived, based on the radiation fields.
In Momentum RF mode, radiation patterns and antenna characteristics are not available. 
Once the currents on a circuit are known, electromagnetic fields can be computed. They can be expressed in the spherical coordinate system attached to your circuit as shown in Figure 1. The electric and magnetic fields contain terms that vary as 1/r, 1/r^{2} etc. The terms that vary as 1/r^{2}, 1/r^{3}, ... are associated with the energy storage around the circuit and are called the reactive field or nearfield components. The terms having a 1/r dependence become dominant at large distances and represent the power radiated by the circuit. These are called the farfield 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 also be present. 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 farfields. 
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 farfields can only be computed at frequencies that were calculated during a simulation. The farfields are computed for a specific frequency and for a specific excitation state. They are computed in all directions (theta, phi), in the open half space above and/or below the circuit. Besides the farfields, derived radiation pattern quantities such as gain, directivity, axial ratio, etc. are computed.
Directivity and radiated power can be derived based on the radiation fields, polarization and other antenna characteristics such as gain .
The farfield can be decomposed in several ways. You can work with the basic decomposition in (E_{θ}, E_{φ}). However, with linear polarized antennas, it is sometimes more convenient to decompose the farfields into (E_{co}, E_{cross}) which is a decomposition based on an antenna measurement setup. For circular polarized antennas, a decomposition into left and right hand polarized field components (E_{lhp}, E_{rhp}) is most appropriate. In the following equations you can see how the different components are related to each other:
Z_{ω} is the characteristic impedance of the open half sphere under consideration.
The fields can be normalized with respect to
The following equations show how the left hand and right hand circular polarized field components are derived. From these components, the circular polarization axial ratio (AR_{cp}) can be calculated. The axial ratio describes how well the antenna is circularly polarized. If its amplitude equals one, the fields are perfectly circularly polarized. It becomes infinite when the fields are linearly polarized.
The following equations decompose the farfields into a co and cross polarized field (α is the co polarization angle). From these, a “linear polarization axial ratio” (AR_{lp}) can be derived. This value illustrates how well the antenna is linearly polarized. It equals one when perfect linear polarization is observed and becomes infinite for a perfect circular polarized antenna.
Eco is defined as collinear 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 ARlp = infinity. 
Figure 1. Copolarization 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:
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 is dimensionless and is represented by:
The maximum directivity is given by:
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:
The efficiency is given by:
The effective area, in square meters, of the antenna circuit is given by:
The radiation patterns analysis in Momentum GX is performed in postprocessing time. Before calculating a radiation pattern, you need the Sparameters of the circuit has been calculated in microwave (UW) mode.
1. Open
the MomentumGX Options dialog, Far Field Options page, and set checkbox
“Calculate Far Field”;
2. Set radiation pattern
type 3D to calculate full Far Field data and antenna
characteristics or
one of 2Dcuts to get specific cut of the far field
data:
Conic cut (sweep θ)
Principal plane cut (sweep φ)
Eplane cut (sweep θ, φ=0) or
Hplane cut (sweep φ,
θ=90˚)
3. Select excitation frequency. It may be one or all of the EM simulation frequencies for 3D radiation pattern mode, and one of the EM frequencies for 2Dcuts modes.
4. If
you define a 2Dcut,
set the checkbox "Normalize fields" to calculate normalized
EM filed data (in dB), normalized to the maximum value of the data.
Otherwise the field data will be calculated in absolute values (Volt/meter).
5. Select excitation ports from the EMports list and set their amplitudes and phases. MomentumGX calculates the linear superposition of all far fields, created from all excited EM ports.
6. Set the data clipping level (default=50dB). It sets the numerical noise floor of the data, improving scaling of the data plots.
In the Far Field simulation, MomentumGX uses port impedance values from Sparameters simulation, which may be changed to new values in postprocessing time, after Sparameters have been calculated. Each time after a new Sparameters simulation the port data will be reinitialized from the simulated design. 
Any 2D radiation pattern cut may be plot from 3D Far Field data by setting the cut properties in the Antenna Measurement Options dialog (draw antenna plot dialog):
To plot the 2Dcuts radiation patterns use default settings (All values and All Frequencies) of the Antenna Measurement Options dialog. 
For example, MomentumGX has calculated the 3D radiation pattern data, which when viewed in ADS Far Field viewer, is:
You may get any 2D radiation pattern cut from
the data, using the Antenna plot dialog.
For example, the “Conic” cuts (sweep Phi, for Theta=const), created from
the 3D data are:
The “principal plane” cuts (sweep Theta, Phi=const), created from the 3D data, are:
The 3D far field data is always normalized to the maximum value of each data variable, and the 2D cuts are always normalized to the maximum value of each variable in the full 3D data. This is different from 2D normalized data, when Momentum calculates 2D radiation pattern cuts. In this case, Momentum does not have the full set of 3D field data, and uses for normalization the maximum value of the variable for the pattern 2D set of data points.
There are other differences between 2D radiation pattern data that is calculated from MomentumGX 3D data, or calculated directly by MomentumGX, defining 2D cut parameters in the MomentumGX Far Field options. When MomentumGX calculates a 2D radiation pattern cut, it also calculates a set of antenna and far field measurements, related to the radiation pattern cut:
ANT_ARCP  axial ratio for circular polarization
ANT_ARLP  axial ratio for linear polarization
ANT_ECO  copolarization component of electric field decomposition Eco
ANT_ECROSS  crosspolarization component of electric field decomposition Ecross
ANT_ELHP  left handpolarization component of electric field decomposition Elhp
ANT_ERHP  right handpolarization component of electric field decomposition Erhp
ANT_EFFECTIVEAREA  effective area of the antenna
ANT_EFFICIENCY  antenna efficiency
ANT_HPHI  Phi plane component of magnetic field decomposition H_{φ}
ANT_HTHETA  Theta plane component of magnetic field decomposition H_{θ}
ANT_POWER  radiated power
All the data are the swept data of the variable angle (Phi (ANT_PHI) or Theta (ANT_THETA)) of the 2D radiation pattern cut.
The 3D radiation pattern data include full electric field data for basic decomposition system E_{φ}, E_{θ} and integrated antenna parameters:
ANT_EFFANG_STERAD  antenna effective angle in sphere steradians (Ωeff)
ANT_EFFANG_DEG  antenna effective angle in degrees of equivalent cone (αeff)
ANT_EX_MAX, ANT_EY_MAX, ANT_EZ_MAX  maximum electric field amplitude in the direction
ANT_DIRECTIVITY  maximum antenna directivity
ANT_GAIN  maximum antenna gain
ANT_RAD_POWER  antenna radiated power
ANT_RAD_INTENS_MAX  maximum radiated power intensivity (Watts per steradian) Umax = max(U(φ,θ ))
ANT_PHI_UMAX  angle φ of Umax
ANT_THETA_UMAX  angle θ of Umax
All the data for the 3D radiation pattern are scalars.
The ‘”effective angle in degrees” (αeff) is the opening angle of a cone with radius 1 that has the same “effective angle in steradians” (Ωeff) as the antenna. The following math applies to calculate
the area of the cone: and
Consequently, the “effective angle in degrees”
is 
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 (in most cases Momentum GX sets that automatically after Sparameters analysis finished) 
For the planar cut, the angle phi (Cut Angle), which is relative to the xaxis, is kept constant. The angle theta, which is relative to the zaxis, 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. Figure 2 illustrates a planar cut.
Figure 2. Planar (vertical) cut
Note In layout, there is a fixed coordinate system such that the monitor screen lies in the XYplane. The Xaxis is horizontal, the Yaxis is vertical, and the Zaxis 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 zaxis, is kept constant. Phi, which is relative to the xaxis, 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. Figure 3 illustrates a conical cut.
Figure 3. Conical cut
You can take a 2D cross section of the farfield 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.
where
Measurement name 
Dependence 
Array size 
Description 
Units 
ANT_DIRECTIVITY 
ANT_FREQ 
Nf 
Directivity 
dB 
ANT_EFFANG_DEG 
ANT_FREQ 
Nf 
Effective angle in equivalent cone degrees 
degrees 
ANT_EFFANG_STERAD 
ANT_FREQ 
Nf 
Effective angle in sphere steradians 
degrees 
ANT_EPHI 
ANT_PHI, ANT_THETA, ANT_FREQ 
Nφ * Nθ * Nf 
E_{φ} – electric field φcomponent 
dB 
ANT_EPHI_MAX 
ANT_FREQ 
Nf 
Maximum value of E_{φ} 
V/m 
ANT_ETHETA 
ANT_PHI, ANT_THETA, ANT_FREQ 
Nφ * Nθ * Nf 
E_{θ} – electric field θcomponent 
dB 
ANT_ETHETA_MAX 
ANT_FREQ 
Nf 
Maximum value of E_{θ} 
V/m 
ANT_ETOTAL 
ANT_PHI, ANT_THETA, ANT_FREQ 
Nφ * Nθ * Nf 
Total electric field E = E_{φ}+ j*E_{θ} 
dB 
ANT_EX_MAX 
ANT_FREQ 
Nf 
Maximum value of xcomponent of E ( E_{x}) 
V/m 
ANT_EY_MAX 
ANT_FREQ 
Nf 
Maximum value of ycomponent of E ( E_{Y}) 
V/m 
ANT_EZ_MAX 
ANT_FREQ 
Nf 
Maximum value of zcomponent of E ( E_{Z}) 
V/m 
ANT_F 
No 
Nφ * Nθ * Nf 
Independent variable for frequency in field sweeps 
GHz 
ANT_FREQ 
No 
Nf 
Independent variable for frequency F in antenna parameters sweeps 
GHz 
ANT_GAIN 
ANT_FREQ 
Nf 
Gain 
dB 
ANT_Log 
No 

Antenna parameters text Log 

ANT_PHI 
No 
Nφ * Nθ * Nf 
Independent variable for angle φ in field sweeps 
degrees 
ANT_PHI_UMAX 
ANT_FREQ 
Nf 
Angle φ of maximum radiation electric field 
degrees 
ANT_RAD_INTENS_MAX 
ANT_FREQ 
Nf 
Maximum radiation power intensity 
W 
ANT_RAD_POWER 
ANT_FREQ 
Nf 
Radiation power 
W 
ANT_THETA 
No 
Nφ * Nθ * Nf 
Independent variable for angle θ in field sweeps 
degrees 
ANT_THETA_UMAX 
ANT_FREQ 
Nf 
Angle θ of maximum radiation electric field 
degrees 
Where Nφ, Nθ, Nf – is the number of sweep points for azimuth angle φ, elevation angle θ, and analysis frequency F, correspondingly.
Radiation pattern not normalized 2D cut data are shown in the Momentum GX dataset snapshot:
The normalized 2Dcut data includes also the normalization constant for each of the normalized swept variables, which has the suffix "_MAX" in its name. For example, ANT_ECO_MAX is the normalization constant for ANT_ECO (Eco) swept data.
Measurement name 
Dependence(s) 
Array size 
Description 
Units (normalized units) 
ANT_ALPHA 
No 
1 
Copolarization angle α 
degrees 
ANT_ARCP 
<swept angle> 
Nang 
Circular polarization axial ratio 
dB 
ANT_ARLP 
<swept angle> 
Nang 
Linear polarization axial ratio 
dB 
ANT_DIRECTIVITY 
<swept angle> 
Nang 
Directivity 
dB 
ANT_ECO 
<swept angle> 
Nang 
Linear polarized field cocomponent Eco 
V/M (dB) 
ANT_ECO_MAX 
No 

Maximum value of Eco 
V/M 
ANT_ECROSS 
<swept angle> 
Nang 
Linear polarized field crosscomponent Ecross 
V/M (dB) 
ANT_ECROSS_MAX 
No 
1 
Maximum value of Ecross 
V/M 
ANT_EFFECTIVE_AREA 
<swept angle> 
Nang 
Effective area 
M^{2} 
ANT_EFFICIENCY 
<swept angle> 
Nang 
Efficiency 
% 
ANT_ELHP 
<swept angle> 
Nang 
Circular polarized field left hand component Elhp 
V/M (dB) 
ANT_ELHP_MAX 
No 
1 
Maximum value of Elhp 
V/M 
ANT_EPHI 
<swept angle> 
Nang 
Electric field φcomponent E_{φ} 
V/M (dB) 
ANT_EPHI_MAX 
No 
1 
Maximum value of E_{φ} 
V/M 
ANT_ERHP 
<swept angle> 
Nang 
Circular polarized field right hand component Erhp 
V/M (dB) 
ANT_ERHP_MAX 
No 
1 
Maximum value of Erhp 
V/M 
ANT_ETHETA 
<swept angle> 
Nang 
Electric field θcomponent E_{θ} 
V/M (dB) 
ANT_ETHETA_MAX 
No 
1 
Maximum value of E_{θ} 
V/M 
ANT_FREQ 
No 
1 
Frequency of analysis 
GHz 
ANT_GAIN 
<swept angle> 
Nang 
Gain 
dB 
ANT_HPHI 
<swept angle> 
Nang 
Magnetic field φcomponent H_{φ} 
V/M (dB) 
ANT_HPHI_MAX 
<swept angle> 
Nang 
Maximum value of H_{φ} 
V/M 
ANT_HTHETA 
<swept angle> 
Nang 
Magnetic field θcomponent H_{θ} 
A/M (dB) 
ANT_HTHETA_MAX 
No 
1 
Maximum value of H_{θ} 
A/M 
ANT_PHI 
No 
Nang or 1 
azimuth angle _{φ} 
degrees 
ANT_POWER 
<swept angle> 
Nang 
radiated power 
W 
ANT_THETA 
No 
1 or Nang 
elevation angle _{θ} 
degrees 
Where <swept angle> is ANT_PHI, or ANT_THETA, depending on what angle is swept in the radiation pattern cut. The other angle (not swept) is a constant in the 2Dcut dataset; Nang  number of angle swept points.