Radiation Patterns and Antenna Characteristics

 

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.

About Radiation Patterns     

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/r2 etc. The terms that vary as 1/r2, 1/r3, ... are associated with the energy storage around the circuit and 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. These are called the far-field components (Eff, Hff).

 

 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 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 frequencies that were calculated during a simulation. The far-fields 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 far-fields, derived radiation pattern quantities such as gain, directivity, axial ratio, etc. are computed.

 

About Antenna Characteristics     

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

Polarization   

The far-field can be decomposed in several ways. You can work with the basic decomposition in (Eθ, Eφ). However, with linear polarized antennas, it is sometimes more convenient to decompose the far-fields into (Eco, Ecross) 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 (Elhp, Erhp) is most appropriate. In the following equations you can see how the different components are related to each other:

 

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

The fields can be normalized with respect to

Circular Polarization   

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 (ARcp) 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.

Linear Polarization   

The following equations decompose the far-fields into a co and cross polarized field (α is the co polarization angle). From these, a “linear polarization axial ratio” (ARlp) 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. 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 Pinj 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:

Calculating Radiation Patterns     

The radiation patterns analysis in Momentum GX is performed in post-processing time. Before calculating a radiation pattern, you need the S-parameters 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 2D-cuts to get specific cut of the far field data:
 

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 2D-cuts modes.

 

4.   If you define a 2D-cut, 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 EM-ports 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 S-parameters simulation, which may be changed to new values in post-processing time, after S-parameters have been calculated. Each time after a new S-parameters 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 2D-cuts 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:

 

 

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 Eφ, Eθ and integrated antenna parameters:

 

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 S-parameters analysis finished)

 

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. 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 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. Figure 3 illustrates a conical cut.

Figure 3. Conical cut

 

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.

Radiation patterns and Antenna analysis data

3D Far Field and Antenna analysis data

 

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

 

Eφ – electric field φ-component

 

dB

ANT_EPHI_MAX

ANT_FREQ

Nf

Maximum value of Eφ

V/m

ANT_ETHETA

ANT_PHI, ANT_THETA, ANT_FREQ

 

Nφ * Nθ * Nf

 

Eθ – electric field θ-component

 

dB

ANT_ETHETA_MAX

ANT_FREQ

Nf

Maximum value of Eθ

V/m

ANT_ETOTAL

ANT_PHI, ANT_THETA, ANT_FREQ

 

Nφ * Nθ * Nf

 

Total electric field E = Eφ+ j*Eθ

 

dB

ANT_EX_MAX

ANT_FREQ

Nf

Maximum value of x-component  of E ( Ex)

V/m

ANT_EY_MAX

ANT_FREQ

Nf

Maximum value of y-component  of E ( EY)

V/m

ANT_EZ_MAX

ANT_FREQ

Nf

Maximum value of z-component  of E ( EZ)

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.

 

2D radiation analysis data

Radiation pattern not normalized 2D cut data are shown in the Momentum GX dataset  snapshot:

 

 

The normalized 2D-cut 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

Co-polarization 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 co-component Eco

V/M (dB)

ANT_ECO_MAX

No

 

Maximum value of Eco

V/M

ANT_ECROSS

<swept angle>

Nang

Linear polarized field cross-component Ecross

V/M (dB)

ANT_ECROSS_MAX

No

1

Maximum value of Ecross

V/M

ANT_EFFECTIVE_AREA

<swept angle>

Nang

Effective area

M2

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 φ-component Eφ

V/M (dB)

ANT_EPHI_MAX

No

1

Maximum value of Eφ

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 θ-component Eθ

V/M (dB)

ANT_ETHETA_MAX

No

1

Maximum value of Eθ

V/M

ANT_FREQ

No

1

Frequency of analysis

GHz

ANT_GAIN

<swept angle>

Nang

Gain

dB

ANT_HPHI

<swept angle>

Nang

Magnetic field φ-component Hφ

V/M (dB)

ANT_HPHI_MAX

<swept angle>

Nang

Maximum value of Hφ

V/M

ANT_HTHETA

<swept angle>

Nang

Magnetic field θ-component Hθ

A/M (dB)

ANT_HTHETA_MAX

No

1

Maximum value of Hθ

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 2D-cut dataset; Nang - number of angle swept points.