Notes on radiation patterns

Radiation patterns are far-field visualizations, not physical shapes around an antenna. Azimuth, elevation, 3D, and polarization patterns are all derived from the same far-field data, each using a different geometric “slice” through the 3D pattern. Understanding how those slices are defined is essential to interpreting what the plots actually mean.

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Introduction

Each of the antenna designers in this site allow the user to display one or more radiation patterns:

• an elevation pattern
• an azimuth pattern
• a polarization pattern
• a 3D pattern

For any particular antenna, each of these radiation patterns shows a different aspect of the same thing: namely, how the RF signal energy from the antenna at a particular frequency spreads out, or radiates, from the antenna.

Specifically, the code (NEC v4.2) which generates the gain values used to create these patterns, computes the radiation pattern (gain or directivity vs. azimuth/elevation angles) in the far-field approximation.  In this region, the electric and magnetic fields fall off as 1/r, and the angular pattern does not depend on distance (aside from the 1/r amplitude scaling).

The far-field condition - the region around the antenna where the E- and H- fields form radiating waves - is usually approximated by :
R ≳ 2D²/λ
where R = distance from the antenna, D = largest dimension of the antenna, and λ = wavelength.  Hence, for a 20-meter band dipole, this would be greater than a few tens of meters distance from the antenna.  The gain values correspond to the normalized power density radiated in a given direction, relative to an isotropic radiator, independent of the observation distance - as long as it's in far-field.  This means that, in the far-field region, the radiation pattern is already formed and its shape does not change with distance, unless and until the radiated waves meet an obstruction.

Example - Antenna and the far-field - comparative sizes

Let's look at an example antenna, an 80-meter EFHW inverted-L, to see how the size of the antenna compares to the size of its radiation patterns.   First, the antenna itself:

The azimuth, elevation and 3D patterns for this antenna, on its 6th harmonic at 15 meters, look like this:

Fig.b - the antenna's azimuth pattern

Fig.c - the antenna's elevation pattern

Fig.d - the antenna's 3D pattern

Inspecting a larger, and more detailed, version of the elevation pattern as here:

we have included the following elements in Fig. (e), drawn at relative scales intended to illustrate the approximate sizes of the antenna, its far-field region, and its radiation pattern:

• the blue curve represents the elevation radiation pattern of this example 80-meter antenna operating on the 15-meter band (its sixth harmonic);
• the green shaded region represents the minimum distance beyond which the antenna’s far-field region begins and within which a stable radiation pattern cannot yet be defined.  On this scale, the green region is shown larger than it would be in reality, in order to make it visible;
• the red inverted-L shape represents the antenna itself.  This figure corresponds to the maximum physical extent of the antenna on these scales; in reality, relative to the radiation pattern, the antenna would be even smaller than shown.

We should now understand that the radiation pattern - which is defined only at distances greater than approximately R ≳ 2D²/λ - exists only in a spatial region (the far field) far larger than the antenna itself, even when depicted (as in Fig. (e)) at the minimum possible distance from the antenna at which a far-field pattern can be meaningfully defined.

The antenna determines the radiation pattern, but the pattern itself is defined only in the far field as a description of how radiated power varies with direction, rather than as a physical structure surrounding the antenna.

Now, if we inspect radiation patterns from other websites or programs or other publications we may often see graphics like these:

where we can see (as we do in this example produced by the 4NEC2 program) small versions of the antenna (the white lines) protruding from the 3D pattern in certain places.

However, as the far-field relation informs us, the antenna is far smaller than the smallest possible far-field radiation pattern, and hence would never be so large as to be able to protrude anywhere through the 3D pattern surface. We understand such diagrams, therefore, to be representative of the shapes of radiation patterns and their antennas, but to be not representative of their actual sizes.

What the radiation patterns are NOT

First and foremost, the radiation patterns we are familiar with do not actually exist as physical structures anywhere in the real world.  There are no corresponding "shapes" to be found in either the electric or magnetic fields of the radiation emitted by an antenna.  The forms we see in radiation pattern diagrams are simply conventional visualizations, or graphical encodings, of field strength evaluated at a fixed distance on an imaginary sphere in the antenna's far field.

This particular convention encodes field strength as radial displacement from the center of a polar diagram.  Popular usage and long-standing convention often lead us to suppose that the resulting shape somehow exists as a physical structure in space.  This is not the case_ the same information could just as easily be encoded in the form using color, shading, contour lines, or as a heatmap, as in this example:

Here we see a "classic" 3D radiation pattern diagram, superimposed on a heatmap representation of the same dataset - each diagram simply presents a different visualization of the same data, namely the RF strength in the RF field at some fixed radius in the antenna's far field.

Either of these visualizations - and many others - could be used to present this data. However, for consistency and familiarity, we will continue to use conventional radiation pattern diagrams in the discussion that follows, while keeping in mind that they represent only one possible way of visualizing far-field signal strength, rather than any physical structure in the electromagnetic field itself.

If you would like to know more about the heatmap representation of the 3D dataset, click on the "Alternative 3D radiation patterns" tab above.

The One Pattern To Bind Them All - the 3D radiation pattern

It's often assumed by many that the azimuth pattern is simply a "top-view" of the 3D radiation pattern, and that the elevation pattern is the "side-view" of the 3D radiation pattern. We will see, however, that this is not the case, not even in the simplest of examples.

In the following sections, we will attempt to explain how the patterns are generated, how each relates to the others, and to the whole. Some of these relationships are particularly easy to comprehend; others perhaps less so.  Let's start with the pattern which shows the most information first: the 3D radiation pattern.

For this discussion, we show a simplified version of a 3D radiation pattern: one for a 40-meter EFHW antenna (a multi-band antenna) being used on one of its resonant bands, the 10-meter band.  This antenna is set out in an east-west direction, so that the antenna wires are in the 0° - 180° vertical plane.

We have replaced the usual color information (which would normally be used to show the signal strength at a particular point on the 3D figure) in the 3D patterns diagrams in this discussion, with coloration according to height only, and to highlight certain details in the following sections.

Fig.1 - 3D pattern - basic

Fig.2 - 3D pattern - basic with tooltip

We present here just static images of a 3D pattern, but in a designer page, the 3D figure is capable of being rotated, panned and zoomed.  As the second image shows, the figure can also show a tooltip containing information on the point under the mouse pointer.

The azimuth and elevation radiation patterns

The azimuth and elevation radiation patterns each represent "slices" and projections made from the basic 3D pattern for an antenna at a particular frequency.  Each of these two patterns is related to the other, with either the program or the user deciding how or where the "slicing" is to take place.

Fig.3 shows an azimuth radiation pattern diagram for this antenna, and we see that the blue outline of the radiation pattern has a shape resembling either a top-down view of the 3D pattern, or a horizontal cross-section through the 3D pattern as displayed in Fig.1 - we will see later that neither of these assumptions in fact represents the true nature of the azimuth pattern.  The diagram in Fig.3 is annotated to highlight certain features in the diagram:

• the red dot on the radiation pattern curve represents the maximum gain (7dBi) in the whole pattern - this is at an azimuth angle of 42° from the 0° - 180° line representing the antenna plane;
• the main radial axis (the black line with values 0, -3, -6, -10, etc.) is placed by the program at the angle (42°) of the point of maximum gain;
• for this discussion, we add an extension (the black dashed line) to the radial axis, passing through the diagram center, and out to a point situated diametrically opposite to the point of maximum gain;
• the two lines taken together define the position of the vertical plane used to "slice" through the 3D pattern to produce the elevation pattern in Fig.4.

Here are two views of the 3D pattern after the vertical plane "slice" has been made:

Fig.5 - 3D pattern sliced at 42° azimuth angle, from above

Fig.6 - 3D pattern sliced at 42° azimuth angle, oblique view

Note in Fig.6 the outline of the edge (highlighted in red), formed by slicing through the 3D pattern, represents the elevation radiation pattern displayed in Fig.4 above.  This demonstrates that an elevation radiation pattern is defined as the profile revealed when the 3D pattern is sliced by a vertical plane aligned along a particular azimuth angle.  It's not simply a "side-view" of the 3D pattern.

When the program is in "automatic" elevation angle mode - i.e. when the user has NOT chosen a particular elevation angle from the "Choose reference elevation angle" dropdown provided - then the program chooses a point at which BOTH azimuth and elevation angles are set to the angles corresponding to the maximum gain in both azimuth and elevation.  Figs. 3 and 4 show the results when the choice is made automatically.

If, however, the user wishes to know what kind of performance the antenna has at an elevation angle OTHER than that chosen automatically by the program, then they can use the "Choose reference elevation angle" dropdown to set this angle manually.   Why might the user decide to do this? - reasons for this might include:

• to see how much gain might be got at that angle - the 3D diagram might display a second lobe above the main lobe at a higher angle;
• to compare results between this and other antennas, all at some particular elevation angle, perhaps to see how each compares with the others at an angle suitable for DX;
• because they can, and they're curious to see what the results might be;

...and so on.

Deriving the azimuth radiation pattern from the 3D pattern

Before we go any further, let's see just how the azimuth pattern is obtained from the 3D pattern - it's not an immediately intuitive process, as we hinted at earlier.  Let's take a look at the 3D pattern one more time, this time after "slicing" it at a particular elevation angle as chosen either by the program or the user - in this case the elevation angle θ is 21°:

Here, we need to imagine the solid black line, from the antenna center C through the point P on the 3d pattern exterior, as acting like a rotating knife with its point fixed at the center C, kept at a constant elevation angle θ = 21°, and completing a full 360° in azimuth Φ.  This action describes a cone with apex angle α = 2 × (90°-θ) cutting away the top portion of the 3D pattern, and leaving the bottom portion intact.  The "edge" or "path" revealed, where the 3D pattern has been "cut" or "sliced" in this way, represents the azimuth pattern as shown in Fig.3 above.

If we were to examine this view of the 3D diagram in the program, we would see that the tooltip shows the elevation angle of 21° at all points along this top edge of the "sliced" diagram, even though this edge looks uneven - it is in fact not at all horizontal!  The "slicing" through the 3D figure is not a simple horizontal cross-section of the 3D figure.

Let's now look at a more extreme example: the same antenna, same band, and same 3D pattern as above, but this time with elevation angle set by the user (us!) to a much higher angle of 60°.  We use the "Choose reference elevation angle" dropdown to set this angle, and click on the "Display plots" button to show the new azimuth and elevation patterns:

Fig.9 - azimuth pattern, with elevation angle set to 60°

Fig.10 - elevation pattern, with elevation angle set to 60°

We see the radial axis in the elevation pattern diagram (Fig.10) set to our choice of 60°, and also that the program has set the azimuth angle to 0°, which just happens to be the direction of maximum gain in this particular configuration.

Looking now at the 3D pattern for this configuration, we see in Fig.11 the 3D pattern sliced at 0° azimuth angle as viewed from the top.  In Fig.12, this sliced 3D pattern has been rotated by hand to display an oblique view, where the edge resulting from this slicing has been highlighted in red.

Fig.11 - 3D pattern sliced at 0° azimuth angle, from above

Fig.12 - 3D pattern sliced at 0° azimuth angle, oblique view

Again, as in the previous example, the red-highlighted edge reveals the same elevation pattern for this configuration as in Fig.10.

So far, so good - but what about the azimuth pattern in Fig.9?  Here we show two views of the 3D pattern after the 60° elevation angle slicing has been applied to it:

Fig.13 - 3D pattern sliced at 60° elevation angle, from above

Fig.14 - 3D pattern sliced at 60° elevation angle, oblique view

The first figure, Fig.13, reveals the same profile at the cut edge as is displayed in the azimuth radiation pattern Fig.9.  The oblique view in Fig.14 shows this profile - produced by an imaginary "knife" set at a constant elevation angle of 60°, and rotated around the center of the antenna - is very far from being a simple horizontal slice through the 3D pattern.

Polarization radiation patterns

Polarization radiation patterns are plotted in azimuth, and represent the degree to which the signal is polarized in different azimuthal (compass) directions around the antenna.  A single polarization patterns diagram displays three curves at once:

• a vertical polarization pattern,
• a horizontal polarization pattern,
• and a curve representing their summed values,

for a chosen frquency.

So, what is meant by "polarization"? - put simply, it is by convention taken to be the orientation of the electric field (the E-field) of an electromagnetic wave (the RF signal) as it radiates from an antenna; the magnetic field of the wave (the B-field) being here ignored.

Let's take a look at the polarization pattern for the antenna from the previous example, where we chose an elevation angle of 60°:

We see in this diagram that the horizontal and vertical polarization patterns have very different shapes, each describing the signal strength in their particular polarization, and in different azimuth (compass) directions around the antenna. The antenna itself is erected in the plane 0° - 180°, i.e. east to west.

In this example, we see that, in directions toward the east (0°) and a little less so toward the west (180°), the vertical component (blue curve) is stronger (> 10dB) than the horizontal; however, in directions orthogonal to the antenna plane, the horizontal component (red curve) wins out, but only just.  Those with sharp eyes may already have spotted that the dotted curve representing the combined horizontal and vertical components of the EM field is the exact same shape and size as the azimuth radiation pattern as seen in Fig.9 above.  This is, of course, entirely to be expected, since each represents how the whole signal is distributed in azimuth.

Let's take a look at another couple of examples. In the first, we'll look at the polarization patterns diagram for the configuration used for the figure Fig.3 above, where the elevation angle is 21°:

As in the previous example, the vertically polarized component of the radiation is at a maximum in the eastern (0°) and western (180°) directions, but in other directions the situation is mixed, with the horizontal component having several maxima stronger than the vertical.  The combined horizontal and vertical components form the dotted "Summed" curve here, which is exactly the same curve as in Fig.3 above.

One more example, this time using a different antenna altogether. Here, we use an inverted-vee dipole for the 20-meter band only, with apex angle of 70° (full apex angle 140°), with the apex at 7m AGL.

Again, we see the directions of maximum vertical polarization of signal as being along the east-west line, i.e. around the vertical plane of the antenna.  But isn't this somehow counter-intuitive? Haven't we all often heard that signals from a dipole are always horizontally polarized, and exclusively so?  Indeed, many of us have heard this, but it's a myth - except for dipoles set up VERY FAR above the ground, or situated in "free space."

For dipoles erected at heights AGL typical of portable set-ups - a few meters above the ground - the situation is in fact just as we observe in this example.  To get a rough idea of why this would be so, imagine we have set up this antenna on level ground somewhere.  We're able to walk around the antenna, viewing it from all azimuth (compass) directions.  If we view the antenna from the north or the south (azimuth 90° and 270°) directions, we see the antenna strung out as a long wire as in Fig.17: we would be correct in expecting the signal to be horizontally polarized in these directions, and in directions close to the north-south line.

Fig.17 - 20-meter inverted-vee dipole viewed from the side

Fig.18 - 20-meter inverted-vee dipole viewed from nearly inline

If, however, we walk around the antenna to a position near to the plane of the antenna - i.e. nearly inline with the antenna as portrayed in Fig.18 - the antenna will look very foreshortened, almost like a couple of near-vertical elements.  It's in these directions that we observe the maximum vertical polarization from the antenna, almost as if the antenna DID consist of near-vertical elements.  Imagining how the antenna looks from different azimuth angles can help us to understand - at least in part - how and why the polarization changes around the compass.

Alternative ways of viewing 3D antenna radiation data

The 3D radiation pattern produced by an antenna can be represented in several alternative graphical formats, each
representing the 3D radiation field in different ways. In this discussion, we present two such formats :

• The classic view shows a 3D figure in space, with which many of us will be familiar, and where signal strength at points around the antenna is represented both by radial distance from the figure's center, and also by color-coding;
• An alternative heatmap view, where the signal strength at points around the antenna is plotted in a 2-dimensional azimuth–elevation grid with signal strength at each point in the chart (i.e. at a particular azimuth and elevation angle) represented by color.

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The classic 3D antenna radiation pattern

Many of us have seen typical 3D radiation patterns as produced by antenna modelling software, two examples of which we present here:

Fig.1 - 3D radiation pattern of a 40-meter OCFD antenna on the 15-meter band

Fig.2 - 3D radiation pattern of a 20-meter delta-loop antenna

The first example in Fig.1 shows a view of the 3D radiation pattern of a 40-meter OCFD antenna operating on the 15-meter band.  The second example in Fig.2 shows a view of the 3D radiation pattern of a 20-meter OCFD antenna operating at its' fundamental frequency.  In this site, this classic 3D pattern is offered as a standard option in all of the antenna designer pages.

Such 3D figures are capable of being zoomed, rotated and panned, allowing the user to view the figure from different angles.

An alternative view: the heatmap chart

While the classic 3D radiation pattern is versatile, and displays the antenna's radiation field at a particular frequency, it does have the limitation that it must be rotated in order to view the pattern from different angles, or vantage points.

A heatmap chart, however, does not suffer from this particular limitation: the whole radiation field is presented in a single graphical context as can be seen in this example:

In the classic 3D pattern, signal strength around the antenna is presented as radial distance from the 3D figure's center (and also as color-coding), and azimuth- and elevation-radiation patterns correspond to conical or angular slices through the 3D pattern.

In the heatmap chart, however, such slices are made at constant values of either azimuth or elevation angles: these constant angles correspond to either vertical columns or horizontal rows in the chart.  Each such column or row therefore corresponds exactly to the data encoded in either an azimuth or elevation radiation pattern at the chosen angle.

One could, therefore, set up such a heatmap chart to respond to a mouse-click on a row or on a column, and for a 2-dimensional azimuth or elevation pattern respectively to be shown.   In fact, such a scenario has already been realized: the user can choose to highlight either a row or column in the chart (or choose no highlighting).  A click on any point in the figure will then trigger either row- or column-highlighting in the chart, and the corresponding azimuth- or elevation-radiation pattern will be shown in a separate floating panel. Here are two examples of this:

One could, of course, use a particular highlighting mode, either row or column, and click on individual rows or columns to quickly view a succession of azimuth- or elevation-radiation patterns corresponding to the particular angle chosen. In this way, one can quickly view ALL or ANY possible such patterns for the antenna, without having to force the main plots to be displayed again.

Notes on low-angle radiation and the pseudo-Brewster angle (PBA)

Many users of antenna modelling software implicitly assume that the results produced by the software are accurate and dependable in most, if not all, circumstances.  Like all simulations, however, such results should be regarded as representative of an antenna's real-world performance only up to a point.  Beyond this point (which cannot be strictly defined), increasing discrepancies between simulated and measured performance are to be expected.

This limitation is particularly relevant for vertically-polarized radiation at low elevation angles.  In real-world conditions, such waves experience significantly greater attenuation at low angles than is typically predicted by modelling software.  This additional attenuation occurs at angles below the so-called pseudo-Brewster angle (PBA), which depends on frequency and the electrical properties of the ground.

The tendency of modelling software — including version 4.2 of the NEC engine used by this site — to under-predict this attenuation arises primarily from the use of simplified and frequency-independent ground models.  These models underestimate the absorption of vertically-polarized waves by the ground, particularly in the near field of the antenna.

The fact that most antenna modelling tools commonly used in amateur radio share this limitation is not widely appreciated.  As a result, modelled antenna patterns may suggest stronger low-angle radiation — often associated with “good DX” performance — than can realistically be achieved in practice.  Care should therefore be exercised when interpreting and comparing model results at low elevation angles.

The discussion below explores this subject in more detail.

Polarization components

All wire antenna types used in portable operations emit RF waves with horizontal and/or vertical polarization, depending on the azimuthal (compass) direction around the antenna.  By convention, polarization is defined by the orientation of the electric field (E-field) of the electromagnetic wave as it propagates away from the antenna; the associated magnetic field (B-field) is not considered here.

Vertical antennas emit almost exclusively vertically-polarized radiation, with only a very small horizontal component.  Other antenna types — including dipoles, EFHWs, and delta loops — generally emit RF waves with mixed polarization, with either the vertical or horizontal component predominating depending on azimuthal direction.

Two example polarization diagrams for commonly-used portable antennas should help to illustrate this behaviour:

• the first example is an inverted-vee dipole for the 20-meter band only, with apex angle of 60° (full apex angle 140°), with the apex at 7m above ground level (AGL);
• the second example is an apex-up delta loop for the 20-meter band, fed at one-quarter wavelength down from the apex, with the horizontal base at 2m AGL.

Fig.1 - polarization patterns for 20-meter inverted-vee dipole

Fig.2 - polarization patterns for 20-meter delta loop

In the first example (Fig.1), the inverted-vee dipole clearly shows strong horizontal polarization (the red curve) in directions orthogonal to the main antenna plane - that is, at or near 90° and 270° in the diagram.  At azimuths close to the antenna plane (near 0° and 180°), however, a significant vertically-polarized component (the blue curve) is present and, in fact, dominates in these directions, albeit at lower absolute signal levels than the horizontal component at its maxima.  The inverted-vee dipole therefore exhibits clear mixed polarization, contrary to popular belief.

In the second example (Fig.2), the delta loop in this configuration exhibits very strong vertical polarization at all azimuthal angles around the antenna.  A horizontal polarization component is present, but it remains at levels 15 dB or more below the dominant vertical component.  Some mixed polarization therefore exists, but the vertical component overwhelmingly dominates in this antenna configuration.

Antennas that produce significant vertically-polarized radiation at low elevation angles are therefore subject to the low-angle ground-loss effects discussed in the previous section.

Effects of ground on vertical polarization

Let's now take a look at a couple of different example antennas, and examine their elevation radiation patterns at low elevation angles...

To be continued...