Antennas are devices that match the artificial channeling system of electromagnetic waves (EMW) with the surrounding natural environment of their propagation.
Antennas are an integral part of any radio communication system that uses electromagnetic waves for technological purposes. In addition to matching artificial and natural environments for the propagation of electromagnetic waves, antennas can perform a number of other functions, the most important of which is the spatial and polarization selection of received and emitted electromagnetic waves.
Reference:
Coordinated systems are systems that transmit to each other the maximum of the electromagnetic power intended for transmission.
There are receiving and transmitting antennas.
Transmitting antennas
Structural scheme
1 – antenna input to which the supply waveguide from the transmitter is connected;
2 – a matching device that ensures traveling wave mode in the supply waveguide;
3 – a distribution system that provides the required spatial amplitude-phase distribution of radiating fields;
4 – radiating system (emitter), provides specified polarization and directional radiation of electromagnetic waves.
Receiving antennas
Structural scheme
1 – antenna output, to which the waveguide connecting the antenna to the receiver is connected;
2 – matching device;
3 – integrator – a device that provides weighted coherent-in-phase summation of spatial electromagnetic fields;
4 – the receiving system provides polarization and spatial selection of electromagnetic waves entering the antenna from the natural environment surrounding it.
Reference:
Elements of the structure of the transmitting and receiving antennas, designated by the same numbers, may have identical designs, as a result of which, in isolation from the system in which the antennas operate, it is impossible to distinguish the transmitting antenna from the receiving antenna and vice versa.
There are transmitting and receiving antennas.
Antenna classification
To systematize the various types of antennas, they are combined according to a number of common characteristics. Classification criteria can be:
operating wave range;
commonality of design;
robot principle;
appointment.
Classes can be divided into subclasses, etc.
According to their purpose, all antennas are divided into two large classes:
transmitting;
receptions.
These two classes include subtypes:
standing wave antennas;
traveling wave antennas;
aperture antennas;
antennas with signal processing;
active antenna arrays;
scanning antenna arrays.
Main tasks of antenna theory
There are two tasks:
the task of analyzing the properties of specific antennas;
the task of designing antennas according to the given initial requirements for them.
The analysis problem should be solved based on the conditions: the required electromagnetic waves must satisfy Maxwell's equations, boundary conditions at the interface and Sommerfeld radiation conditions.
In such harsh conditions for posing problems, analysis is possible only for some special cases (for example, for a symmetrical electric vibrator).
Approximate methods for solving analysis problems are widespread, according to which these problems are divided into two parts:
Internal task;
External task.
The internal task is designed to determine the distribution of currents in the antenna, real or equivalent. The external task is to determine the radiation field of the antenna from the known distribution of its currents. When solving an external problem, the superposition method is widely used, which consists of dividing the antenna into elementary radiators and subsequent summation of the fields.
The task of designing an antenna is to find the geometric shape and dimensions of the structure that ensure its required functional properties. Solving antenna design (synthesis) problems is possible:
by applying the results of analysis of specific types of antennas and the method of successive approximations, that is, by changing parameters (parametric optimization stage) with subsequent comparison of the electrical characteristics of new versions of known antennas thus obtained;
through direct synthesis, that is, bypassing the parametric optimization stage. In this case, antenna design tasks are divided into two subtasks:
classical synthesis problem;
the task of constructive synthesis.
The first consists of describing the amplitude-phase distribution of the current (or field) at the antenna emitter, which provides the specified functional properties of the antennas. The solution to this subtask does not yet determine the design of the antenna; it only determines the requirements for its distribution.
The second is aimed at finding the complete geometry of the antenna based on a given amplitude-phase distribution of the current (or field) at the antenna emitter. This problem is much more complicated than the first one and is structurally ambiguous; it is often solved approximately.
However, for some types of antennas, a rigorous theory of constructive synthesis has been developed.
Transmitting antennas
Their characteristics and parameters
Structure of the electromagnetic field (EMF) of the antenna
Each antenna can be considered as a system of elementary emitters concentrated in a certain limited volume of linear space (), its EM field as a superposition of the EM fields that make up its elementary emitters. To identify the structure of the EMF antenna, consider the structure of the EMF element of a rectilinear element that changes harmoniously with angular frequency , current with constant amplitude and length of this element in a linear unlimited isotropic medium with constant parameters, ,.
– absolute dielectric constant of the medium;
ε – relative dielectric constant of the medium;
Electrical constant;
– absolute magnetic permeability of the medium;
Relative magnetic permeability of the medium;
Magnetic constant;
– specific electrical conductivity of the medium;
λ – wavelength.
M – EMF observation point;
r – radial coordinate of point M (distance from the center of the spherical coordinate system to point M);
– azimuthal coordinate of point M;
Meridional coordinate of point M.
To consider a Hertz vibrator located along the z axis, the middle of which is aligned with the center of the spherical coordinate system, the solution to Maxwell’s equation has the form (1.1), where
Unit vectors;
– moment of electric current;
Orthogonal complex amplitude components along spherical coordinates, electric field strength vector;
, , - orthogonal complex amplitude components along the spherical coordinates of the magnetic field strength vector;
- wave number;
Wavelength in infinite space.
From the expressions it follows that the EMF of a linear current element represents waves of electric and magnetic field strength orthogonal in space. In this case, the rate of change in the amplitude of each wave is determined by the relative distance of the point from the center of the vibrator.
There are three areas of the field:
For the far field region, the expressions take the form:
In the far region, EMF has the following properties:
For air: .
In the regions of intermediate and near fields, in addition to the spherical transverse wave, there are local reactive fields, the intensity of which increases very quickly with decreasing r. These fields contain a certain supply of EM energy, which they periodically exchange with the antenna (with a period). These fields determine the reactive component of the antenna input impedance.
The properties of the EMF determine the functional properties of the antenna, and the properties of the near and intermediate EMF determine the stability of the functional properties and the broadband of the antennas.
The far EMF region is often called the emission region, and the near EMF region is often called the induction region.
For real antennas, the boundaries of the far, intermediate and near field regions are determined taking into account the phase difference of the waves arriving at the observation point from the edges of the antenna and its center.
With an allowable phase difference in the far-field region equal to:
The far-field EMF region will be at ;
Intermediate field area;
Near field region where
Distance from the center of the antenna to the observation point;
- the maximum transverse size of the radiating antenna system.
Main characteristics and parameters of the transmitting antenna
Antenna properties are divided into:
Radio engineering;
Constructive;
Operational;
Economic;
Functional properties are entirely determined by signal parameters.
Characteristics and parameters of the transmitting antenna:
Complex vector directional characteristic
Complex vector XNA is the dependence on the direction (polarization, phase) of the electric field of waves emitted by the antenna at points equidistant from it (on the surface of a sphere of radius r).
In general, a complex XNA consists of three factors:
where are the spherical coordinates of the observation point of the field of the wave emitted by the antenna.
Amplitude Henna
Amplitude XNA is a dependence on the direction of the amplitude of the intensity of the electromagnetic wave emitted by the antenna at points equidistant from it.
Normalized amplitude CNA is usually considered:
,
where is the direction in which the amplitude CNA value is maximum.
Antenna radiation pattern (APP)
The antenna radiation pattern is a section of the amplitude XNA by planes passing through the direction or perpendicular to it.
The most commonly used section is by mutually orthogonal planes.
The radiation pattern has a lobe structure. Petals are characterized by amplitude and width.
The width of the bottom lobe is the angle within which the amplitude of the lobe changes within the permissible specified limits.
Petals are:
Main petal;
Side petals;
Back petal.
The width of the petals is determined by zeros or by the level of half the maximum power.
By field = 0.707;
By power = 0.5;
On a logarithmic scale = -3 dB.
The normalized amplitude CNA in terms of power is related to the amplitude CNA in the field by the relation:
To image the bottom, polar and rectangular coordinate systems and three types of scale are used:
Linear (across the field);
Quadratic (power);
Logarithmic
Phase Henna
Phase XNA is a dependence on the direction of the phase of a harmonic electromagnetic wave in the far field region at points equidistant from the origin at a fixed point in time.
Reference:
The phase center of the antenna is a point in space relative to which the phase value in the far zone does not depend on the direction and changes abruptly to when moving from one HNA petal to another.
For a point source of an electromagnetic wave emitting a spherical wave, the surface of equal phases has the shape of a sphere.
Polarizing HNA
An electromagnetic wave is characterized by polarization.
Polarization is the spatial orientation of the E vector, considered at any fixed point in the far field during one oscillation.
In the general case, the end of the vector E during one period of oscillation at any fixed point in space describes an ellipse, which is located in a plane perpendicular to the direction of wave propagation (polarization ellipse).
Polarization is characterized by:
ellipse parameters;
spatial orientation of the ellipse;
direction of rotation of vector E.
Antenna radiation resistance
The radiation resistance of an antenna is the wave resistance of the space surrounding the antenna, transferred by it to the input, or to any section of the waveguide feeding it, where the concept of total current has meaning and can be defined.
Radiation resistance can be calculated using the formula:
ss ,
where I is the value of the total current at a given location of the antenna or the two-wire line feeding it, which is equivalent to the feeding hollow waveguide.
Antenna input impedance
The antenna input impedance is the ratio of the complex amplitudes of harmonic voltages and currents at the antenna input terminals.
The antenna input impedance characterizes the antenna as a load for the supply line.
This parameter is used mainly for linear antennas, i.e. antennas whose input voltages and currents have a clear physical meaning and can be measured.
For microwave antennas, the cross-sectional dimensions of their input waveguide are usually specified.
Antenna efficiency (efficiency)
Determines the efficiency of transmission by the antenna to the surrounding space.
Loss resistance
Reference:
As f increases, the antenna efficiency increases from a few percent at long waves to 95-99% at microwave frequencies.
Electrical strength and antenna height
The electrical strength of an antenna is the ability of antennas to perform their functions without electrical breakdown of the dielectric in its structure or the environment when the electromagnetic wave power arriving at its input increases.
Quantitatively, the electrical strength of the antenna is characterized by the maximum permissible power and the corresponding critical electric field strength, at which breakdown begins.
Antenna height
Antenna height is the ability of antennas to perform their functions without electrical breakdown of the surrounding atmosphere when the height of this antenna increases at a given transmit power.
Reference:
With increasing altitude, the electrical strength first decreases, reaching a minimum at altitudes of 40-100 km, and then increases again.
Antenna operating frequency range
Frequency interval from f max to f min, within which none of the parameters and characteristics of the antenna goes beyond the limits specified in the technical specifications.
Typically, the range is determined by the parameter whose value, when the frequency changes, goes out of the permissible limits before others. Most often, this parameter turns out to be the input impedance of the antenna.
Quantitative estimates of the range properties of an antenna are the bandwidth and transmittance:
Often use relative bandwidth
Antennas are divided into:
Directional coefficient (DC)
The directional coefficient of an antenna in a given direction is a number showing how many times the value of the Poynting vector in the direction under consideration at a fixed point in the far zone differs from the value of the Poynting vector at the same point if we replace the antenna in question with an absolutely omnidirectional (isotropic) antenna, subject to equality their radiated powers.
Reference:
Typically, the maximum antenna efficiency value is indicated in the direction of its maximum radiation.
Vibrator: KND=0.5;
Half-wave symmetrical vibrator: KND=1.64;
Horn antenna: KND;
Mirror antenna: KND;
Spacecraft antennas: KND;
The limiter for the upper limit of the efficiency factor is technological manufacturing errors and the influence of operating conditions.
The minimum values of the maximum efficiency of real antennas are always >1, because There are no completely omnidirectional antennas.
The directivity factor is related in field to the normalized amplitude XNA:
,
Where – the maximum value of the directivity in the direction of maximum radiation of the antenna, in which .
KND show This is the gain in power that the use of a directional antenna provides, but does not take into account the thermal losses in it.
Co. uh antenna gain
The gain of an antenna in a given direction is a number showing the gain in power from using a directional antenna, taking into account the heat losses in it:
Equivalent isotropically radiated power
Equivalent isotropically radiated power is the product of the power supplied to the antenna and the maximum value of its gain.
Antenna dispersion coefficient
An antenna's dissipation factor is a number indicating the proportion of radiated power attributable to the side and back lobes.
Determines the power attributable to the main lobe of the XNA
Effective antenna length
The effective length of the antenna is the length of a hypothetical rectilinear vibrator with a uniform current distribution along its entire length, which, in the direction of its maximum radiation, creates the same value of field strength as the antenna in question with the same value of current at the input.
In a medium with characteristic impedance, the effective length of the antenna is determined by the expression.
When considering the principle of operation of a parabolic mirror, we assumed that a point source was located at its focus. Real irradiators have dimensions comparable to the wave and often even larger than it.
The question is, how should the irradiator be placed relative to the focus? Which vibrator is active or passive for the irradiators shown in Fig. 43 and 44, should be in the focus of the mirror?
These kinds of questions always confront engineers developing antenna devices. And they give the following answer: the focus of the mirror must coincide with that point of the irradiator, which can be mentally considered as phase center irradiator, i.e. as the starting point of spherical waves.
The location of the phase center is determined experimentally. Experience shows that the irradiators shown in Fig. 43 and 44, the phase center is located between the active and passive vibrators, somewhat closer to the first. For horn feeds, the phase center is located inside it, in the vicinity of the horn throat.
Provided that if the phase center of the feed does not coincide with the focus, two cases are possible.
First, we will consider the option of longitudinal defocusing of the feed-mirror system, when the feed is shifted to one side or another from the focus along the axis OZ.
Let's turn to Fig. 51 and construct the path of rays reflected from the mirror, assuming that at each point of the paraboloid the radio wave is reflected according to the laws of optics as from a flat mirror tangent to the parabola at a given point.
If, when the irradiator is placed at the focus of a parabolic mirror, the reflected rays go parallel to the focal axis OZ, then when the irradiator moves from focus away from the mirror (point IN) the angles of incidence of the rays at each point of the mirror will increase compared to the correct location of the irradiator (j 2 > j 0). Due to the well-known law of optics that the angles of incidence are equal to the angles of reflection (j 1 = j 2), the rays reflected from the mirror will travel in a diverging beam. When the irradiator is shifted to the point A, lying behind the focus, the reflected rays will be inclined to the axis OZ.
Since the wave surfaces (wave front) are perpendicular to the rays, then in the second case (point A) the wave front in the mirror opening is not flat, but concave; in the first case, the wave front becomes convex.
In both cases, the wave front is symmetrical about the axis OZ, therefore, the radiation pattern of the antenna also remains symmetrical when the feed is shifted, but its main lobe expands, merging with the first side lobes.
If the antenna is very defocus, the main lobe may even split.
An idea of the degree of influence of wave front distortions in the antenna aperture on its gain is given in Fig. 52, which shows the dependence of the decrease in the gain of a parabolic antenna on the absolute value of the deviation, and the phase of the reflected wave at the edges of the mirror relative to the phase at the center of its opening.
In this graph, the gain of an ideal antenna is taken as unity, in which a plane wave with a uniform amplitude distribution is created in the radiating hole.
In practice, phase deviations not exceeding 1/8l are considered acceptable. The reduction in antenna gain in this case does not exceed 8% (see Fig. 52).
For specific antenna samples, this requirement is met through special design measures that eliminate the possibility of erroneous installation of the feeds and at the same time ensure the interchangeability of the latter.
Let us now consider how the transverse movements of the feed will affect the directional properties of the antennas.
If the phase center of the feed is moved out of focus in a direction perpendicular to the optical axis, this will lead to an asymmetrical change in the wave front in the mirror aperture: it will tilt in the direction opposite to the shift of the feed (Fig. 53). But since the main maximum of antenna radiation is always directed perpendicular to the wave front, as a result of transverse defocusing, the main maximum of the radiation pattern will rotate by an angle equal to the wave inclination angle.
At the same time, the main petal itself is somewhat deformed. The degree of this deformation will be determined by how far the irradiator is moved out of focus.
This property of changing the direction of the main lobe of the radiation pattern when the feed is moved transversely is widely used in radar for swinging (scanning) the beam.
Concluding a brief examination of parabolic antennas, we point out that symmetrical and asymmetrical phase distortions in their apertures can occur not only due to defocusing of the feed, but also due to the deviation of the mirror profile from parabolic. The source of field distortions can also be the feed source itself if its wave front differs from spherical.
Under operating conditions, the causes of all these distortions can be either mechanical damage to the mirror and the irradiator, or precipitation in winter.
Ice and snow build-ups on the mirror and irradiator, as a rule, change the calculated path of the rays and turn out to be electrically equivalent to curvature of the mirror profile or defocusing of the irradiator. Therefore, you should carefully follow all the rules for operating antennas, which are usually set out in the instructions and manuals for specific equipment. The last remark, of course, applies to antennas of all types.
phase center hodograph calculation techniqueYu. I. Choni - Ph.D., Associate Professor, Kazan National Research Technical University named after. A.N. Tupolev - KAI
Email: [email protected]
The features of calculating the coordinates of the local phase center (LPC) of an antenna are considered, generated both by the degree of uncertainty in the very concept of LPC, and by the need to eliminate phase jumps when calculating inverse trigonometric functions. It is noted that the coordinates of the LFC depend on the direction of observation, when changing which, in the general case, the LFC describes a surface in three-dimensional space, and in a two-dimensional situation it describes a hodograph line, often of a bizarre configuration. Using examples of a ring antenna array with cardioid individual patterns, the calculation results for three types of algorithms are compared and the LFC hodographs are demonstrated. It is shown that calculating the LFC as the center of curvature of the phase front curve can lead to erroneous results that contradict the physical meaning.
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When calculating in high-frequency technology using mirror reflecting systems (parabolic mirrors), the task of finding the phase center of the antenna (PCA) always arises, because Correct operation of the mirror is only possible if there is an antenna at the focus (called a feeder, feedhorn) which has a phase wave front in the form of a sphere, and the center of this sphere is at the focus of the mirror. For any deviations, both the shape of the phase front from the sphere and the displacement of the PCA from the focus of the mirror, the efficiency of the mirror system drops because its directional pattern is distorted.
Although the topic of searching for FCA is quite relevant even in everyday life, because in addition to traditional satellite television antennas, parabolic antennas for WiFi, WiMAX and cellular communications (UMTS/3G, LTE/4G) have become widespread - nevertheless, this topic is poorly covered in the literature and users often they confuse the phase pattern with the usual radiation pattern.
In videos about computer simulation programs, you can sometimes find practical instructions on how to search for FCA, but usually there are not even minimal explanations of what we are looking for and what we get.
Therefore, to fill the gap, we will write a short article with practical examples.
Phase radiation pattern is the dependence of the phase of the electromagnetic field emitted by the antenna on the angular coordinates.
(A.P. Pudovkin, Yu.N. Panasyuk, A.A. Ivankov - Basic Antenna Theory)
Since in the far zone of the antenna the field vectors E and H are in phase, the phase pattern is equally related to the electrical and magnetic components of the EMF emitted by the antenna.
The phase pattern is designated by the Greek letter Psi:
Ψ = Ψ (θ, φ) , with r = const.
If Ψ(θ, φ) = const at r = const, then this means that the antenna forms the phase front of the wave in the form of a sphere.
The center of this sphere, where the origin of the coordinate system is located, is called the phase center of the antenna (PCA).
The phase center of an antenna is the point at which a single spherical wave emitter equivalent to the antenna system under consideration can be placed with respect to the phase of the field produced.
(Drabkin A.L., Zuzenko V.L. Antenna-feeder devices)
Not all antennas have FCA. For antennas that have a phase center and a multi-lobe amplitude pattern with clear zeros between them, the field phase in adjacent lobes differs by π (180°).
The relationship between the amplitude and phase radiation patterns of the same antenna is illustrated
In real antennas, the phase center is usually considered within the limited angles of the main lobe of the radiation pattern. The position of the phase center depends on the frequency of the signal used, the direction of radiation/reception of the antenna, its polarization and other factors. Some antennas do not have a phase center in the generally accepted sense.
In the simplest cases, for example in a parabolic antenna, the phase center coincides with the focus of the paraboloid and can be determined from geometric considerations. In more complex cases, such as horn antennas, the position of the phase center is not obvious and requires appropriate measurements.
Field measurements of the phase center are very labor-intensive (especially in a wide frequency band).
In CAD simulators of electromagnetic fields, calculating the FCA is a very simple task, but it still requires several manual manipulations, because it is performed by “brute force” and requires a small initial setup of the function that we are going to brute force.
For practical calculations, let's take a real parabola feeder for the Ku-band - LNB from Inverto, Black Ultra series.
This feeder looks like this (in section)
A pea-sized ball will be the FCA, but we don’t know this yet and our task is to find its position.
In the example we will use the following inputs:
Calculation frequency 11538.5 MHz (wavelength 25.982 mm)
- linear horizontal polarization (in the Y axis)
- the antenna itself is directed along the X axis, i.e. main direction of radiation θ=90, φ=0
Calculating traditional Far Field parameters in Ansys HFSS gives this radiation pattern in 3D and 2D
Instantaneous values of intensity (Volts/meter) of the electric field (E-field) depending on the phase
Integral E-field strength (for >1 wave revolution)
All such Far-Field parameters, both in field measurements and in CAD simulations, are calculated on an infinite sphere - Infinite Sphere. The antenna under test or its computer model is placed in the center of such a sphere, and the measuring probe moves along the perimeter of such a sphere and measures the amplitude, polarization (the amplitude of one of the components) and phase of the EM wave. The probe can be fixed permanently and the antenna under test can be rotated.
The main thing that:
The distance was always the same (i.e. it was precisely the measuring sphere)
- the radius of the sphere was large enough so that measurements were carried out only in that region of space where the vectors of the electric field E and magnetic field H are in phase, i.e. none of the components predominates and is not shifted in phase (has no reactivity) due to the charge carriers that exist in the metal conductors of the antenna or due to charged dielectric molecules.
IN Ansys HFSS To carry out far field measurements, you must create at least one infinite sphere: Radiation -> Insert Far Field Setup -> Infinite Sphere
φ and θ can always be specified from 0 to 360, but in order to save time on calculations, it is sometimes rational to limit the angle under study to a certain sector. When setting a step of 1 degree, the full sphere will occupy 360 * 360 = 129,600 calculated points, and with a step of 0.1 degree almost 13 million. To create 3D/2D reports of the radiation pattern, a step of 2-3 degrees is usually sufficient (14,400 calculated points with a step 3 degrees). It makes sense to use a step of 1 degree or less only for slice analysis
In the “Coordinate System” tab, each sphere must have its own coordinate center. By default, the project's global coordinate center is always there. You can add any number of other relative coordinates if desired. Both model geometry elements and the custom sphere “Infinite Sphere” can be assigned relative to the global coordinate center or relative to the user one. We will use this below.
The diverging phase front of the wave was visible in the E-field animation above. The EM wave forms concentric circles, similar to circles on water caused by a thrown stone. The phase center is the point at which such a stone was thrown. It can be seen that its position is somewhere in the bell of the horn, but its exact position is not obvious.
The FCA search method is based on the fact that we look at the direction of the E-field vector (its phase) along the surface of an infinitely distant sphere.
For demonstration, we will create 2 animations with E-field vectors on a sphere with a radius of 4 lambda (this is not an infinite sphere, but for the best scale of the drawing this radius is quite enough).
In the first animation, the center of the sphere is located exactly in the FCA
In the second animation, the center is placed at the project point 0, 0, 0 (looking ahead, let’s say that it is 25.06 mm behind the FCA)
On the surface of the first sphere (it is curved, it is not a plane) it is clear that the vectors move synchronously. Their amplitude (magnitude) is different, because the antenna pattern has a maximum in the center (up to 14.4 dBi) which smoothly fades by a factor of 2 (-3 dB) at angles of ±20°.
We are not interested in the color/length, but in the direction of the vector. So that they all move synchronously (in phase).
In the first animation, all the vectors move synchronously, as if the ball were rotating right and left.
In the second animation, the vectors are asynchronous, some have already changed the direction of movement, others have not yet. The surface of this sphere is constantly undergoing surface tension/strain.
The first sphere is located in the FCA, the second is not in the FCA.
The task of searching for a PCA using this method is to move (brute force) the Infinite Sphere with small steps until the phase spread in the area of this sphere that interests us (we are only interested in the main radiation lobe) becomes minimal (ideally zero).
But before moving on to brute force, let’s first figure out how phase patterns can be displayed in HFSS.
In the far field reports “Results -> Create Far Field Report” we can display either a traditional rectangular plot (Rectangular plot) or a 2D circular plot (Radiation pattern) where along one axis (for example X) we can display the dependence of the angular coordinate (for example θ), and along the Y axis - phase values at these angles θ.
The report we need is rE - “radiated E field”.
For each angle [φ, θ] on an infinite sphere, the complex number (vector) of the electric field is calculated.
When constructing conventional amplitude graphs (directional pattern, distribution of radiation power in direction), we are interested in the amplitude (mag) of this field, which can be obtained either as mag(rE) or immediately using the more convenient variable Gain (the power is given relative to the power at the excitation port and relative to isotropic emitter).
When constructing a phase pattern, we are interested in the imaginary part of a complex number (vector phase) in polar notation (in degrees). To do this, use the mathematical function ang_deg (angle_in_degrees) or cang_deg (accumulated_angle_in_degrees)
For the LNA Inverto Black Ultra antenna, the phase pattern in the XZ plane (φ=0) with horizontal excitation polarization (rEY) has the following form
Angle Theta=90 is radiation forward, Theta=0 up, Theta=180 down.
Values ang_deg vary from -180 to +180, an angle of 181° is an angle of -179°, so the graph has a saw shape when passing through the points ±180°.
Values cang_deg accumulate if the direction of phase change is constant. If the phase has made up to 3 full revolutions (crossed 180° 6 times), then the accumulated value reaches 1070°.
As was written at the beginning of the article, the phase and amplitude patterns of antennas are usually connected to one another. In adjacent amplitude lobes (beams), the phases differ by 180°.
Let's superimpose the phase (red/light green) and amplitude (purple) graphs on top of each other
The humps on the amplitude pattern clearly follow the phase breaks, as written in the books.
We are interested in the phase front only in a certain sector of space, within the main radiation lobe (the remaining lobes still shine past the parabolic mirror).
Therefore, we will limit the graph to only the sector 90 ±45° (45-135°).
Let's add markers MIN (m1) and MAX (m2) to the graph, which show the greatest phase dispersion in the sector under study.
In addition, we will add a mathematical function pk2pk() that automatically searches for the minimum and maximum on the entire chart and shows the difference.
In the graph above, the difference is m2-m1=pk2pk= 3.839 °
The task of searching for the FCA is to move the Infinite Sphere with small steps until the value of the function pk2pk(cang_deg(rE)) is minimized.
To move Infinite Sphere, you need to create another additional coordinate system: Modeler -> Coordinate System -> Create -> Relative CS -> Offset
Since we know for sure that for a symmetrical horn the PCA will be located on the X axis (Z=Y=0), then for Z and Y we set 0, and it will move only along the X axis, for which we assign the variable Pos (with an initial value of 0 mm)
To automate the brute force process, let's create an optimization task.
Optimetrics -> Add -> Parametric, and set the variable step Pos to 1 mm, in the range from 0 to 100 mm
In the "bookmark" Calculations -> Setup Calculation"Select the report type “Far Field” and the function pk2pk(cang_deg(rEY)). In the “Range Functions” button, specify the range from -45 to +45 degrees (or any other one of interest)
Let's launch ParametricSetup1 -> Analyze.
The calculation is performed quite quickly, because All far-field calculations are Post-Processing and do not require re-solving the model.
After completing the calculation, click ParametricSetup1 -> View analysis results.
We see a clear minimum at a distance of X=25mm
For higher accuracy, we edit the parametric analysis in the range of 25.0-25.1 mm in increments of 0.01 mm
We get a clear minimum at X=25.06 mm
To visually assess where the FCA is in the model, you can draw spheres (Non-model) or points.
Here, at point X = 25.06 mm, 2 spheres are placed (with a radius of 2 and 4 lambda)
Here's the same thing in animation
Here is a closer-up drawing of a plane and a pea at point X=25.06
A common misconception is that in HFSS (and other programs such as CST), when you overlay a 3D Plot on an antenna geometry, the plot is automatically placed in the FCA.
Unfortunately, it is not. A 3D plot is always superimposed at the center of the coordinate system that was used to set the "Infinite Sphere" for that plot. If the default global coordinate system was used, then the 3D Plot would be placed at 0,0,0 (even if the antenna itself is far away).
To combine graphs, in the 3D Plot settings you need to select the “Infinite Sphere” (create another one), for which “Relative CS” is set at the FCA point that we found manually.
It should be noted that such an overlap will be true only for the sector under study (for example, the main beam of the pattern), in the side and rear lobes the FC may be located in a different place or be non-spherical.
Also note that the Infinite Sphere settings have nothing to do with the Radiation Boundary boundary condition. The Rad layer can be defined as a rectangle, cone, cylinder, ball, ellipsoid of revolution, and its position, shape and rotation can be moved as desired. The position and shape of “Infinite Sphere” will not change in any way. It will always be a sphere (ball) with an infinite (sufficiently large) radius and with a center in a given coordinate system.
The LNB_InvertoBlackUltra.aedt model file for study is available at the link: https://goo.gl/RzuWxW (Google Drive). Ansys Electronics Desktop v19 or higher is required to open the file (at least 2018.1)
Calculation of the phase center of a corrugated antenna horn
Calculating the phase center is a very labor-intensive task in terms of accuracy. The location of the phase center depends on many parameters, such as the direction of polarization, the direction of the scanning angle, and the width of the aperture. The device modeled in this example is a cylindrical corrugated horn with linear vertical polarization.
Correct settings are essential to obtain accurate results. The polarization of the E-field coincides with the E-plane (vertical orientation). Figure 2 shows the phi component of the E-field in three-dimensional representation. It can be noted that this field component is well defined along the horizontal direction, which in this case is the H-plane. The phase center settings according to which this image is presented are shown in the same figure on the left. Alternatively, if the E-plane is selected, the theta component of the E-field must be selected. Note that the phase centers of the E and H fields are different from each other.
Figure 2 – Setting the field scanning direction in the H-plane
When the CST MWS postprocessor calculates the field of a given device, the phase graph can be constructed both in three-dimensional format and along a certain direction. The power consumed by the postprocessor is explained by the fact that the calculation takes into account the fact that the origin of the field can be changed. This feature is used to adjust and/or set the initial field coordinates to the location of the calculated phase center. In this case, the phase change will be displayed in 2D and for a specific aperture angle. Figure 3 shows how the field center is set to three different positions - the phase center location, as well as +/- 5% of the full horn length (z-axis offset).
Figure 3 – Three different field origin locations
Figure 4 shows three-dimensional E-field plots for the three different field origin locations discussed earlier. The middle graph shows the smallest phase change along the horizontal direction. A more visual representation of the phase change is shown in Figure 5, in which the phase is represented along the H-plane. The phase slope is an indicator that the phase center has been established in the simulation and/or the antenna has been realigned in the actual measurement setup.
Figure 4 – From left to right: phase center shifted by +5%, in the center and by -5%
Figure 5 – Phase change along the H-plane
The position of the phase center changes according to the considered aperture angle. The smaller the aperture angle, the smaller the change in the location of the phase center. This fact is shown in Figure 6. Again, note that the phase center estimates in the E and H planes are different. The standard deviation is another criterion for the accuracy of determining the phase center (Figure 7).
Figure 6 – Dependence of the phase center on the aperture angle
Figure 7 – The smaller the aperture angle, the smaller the standard deviation
Comparison of theory and practice
At two different frequencies (+/-2% relative to the average frequency), the phase center was calculated. Polarization is in the E-plane. The antenna rotates in the H-plane (azimuthal). Depending on the phase-slope versus scan angle the antenna is slightly repositioned along its propagation axis and measured again until a flat phase was found. Figure 8 shows the actual locations of the phase centers. And Figure 9 shows the same picture, but in an enlarged form. As can be seen, the values obtained from modeling agree quite well with practical data.
Figure 8 – Actual location of the phase centers of the corrugated horn
Figure 9 – Deviation of theoretical values from practical ones; note that the location of the phase center calculated for different frequencies is different
