Charts/Science charts

Radiation Pattern

<RadiationPattern /> · 10 examples

How strongly an antenna sends or hears in each direction, drawn as a polar plot in decibels.

Overview

An antenna is not a lamp. A lamp sends light roughly everywhere and you are happy with that. A good antenna sends its energy where you want it and as little as possible elsewhere, and the picture that says how well it manages is the radiation pattern: stand at the antenna, face every direction in turn, and mark how much signal there is.

The shape is the product. A broad round blob is an omnidirectional antenna, good for a phone, useless for a link to a hilltop. A narrow main lobe with a ring of small side lobes is a dish. A lobe that points forward with almost nothing behind it is a directional antenna you can aim. Each of these shows up instantly in polar form, and almost none of it shows up in a table of numbers.

The plot is almost always in decibels, because the range is vast: the main lobe may be ten billion times stronger than the sidelobes, and on a linear scale they would not exist. The chart puts your gain figures on a decibel scale with the strongest direction at the rim and the floor at the centre, so every lobe, down to the ones you wish were not there, gets a place on the page.

Props

API

<RadiationPattern data={lobes} angle={|l: &Lobe| l.angle}>
    <TrendSeries name="E-plane" y={|l: &Lobe| l.e_plane} />
    <TrendSeries name="H-plane" y={|l: &Lobe| l.h_plane} />
</RadiationPattern>

Prop	Type	Default
`data`		required
`angle`	`Fn(&T) -> f64`: degrees, clockwise from the top	required
children	`<TrendSeries>`: gain in dB, one pattern each	required
`max`	`f64`: dB at the rim	the highest gain, rounded up to 10
`min`	`f64`: dB at the centre	`max − 40`
`levels`	`usize`: dB rings	`4`
`fill_opacity`, `line_width`		`0.1`, `2.`
`legend`, `tooltip`, `class`	as on `<Spider>`

Spokes every 30°, rings labelled in dB. A pattern that covers the full circle is closed and filled. Hover to read every pattern's gain at the nearest angle.

Run them

10 examples

Press Run to load an example into the live render at the top of the page. Open one to read its code.

How to read it

01Find the main lobe: the longest petal, pointing in the direction of peak gain. Check that it points where you intended.
02Measure its width at the ring 3 dB below the peak. That is the half-power beamwidth.
03Look at the smaller petals. The tallest side lobe sets your sidelobe level, and the lobe opposite the main one is the back lobe, the front-to-back ratio being the gap between them.
04Hover to read the gain of every pattern at the nearest sample angle. Hover snaps to samples, so a coarse measurement will snap coarsely.

When to use it, and when not to

Reach for it when

You are comparing an antenna design against its specification: main lobe direction, beamwidth, sidelobe level, front-to-back ratio.
You have two cuts of the same antenna, such as the E-plane and the H-plane, and want them drawn on the same axes.
You are reviewing measurements from an anechoic chamber, or a simulation, and want to see where the unwanted lobes are.
You want a picture that an RF engineer will read without a caption.

Skip it when

You want the full three-dimensional pattern. A polar chart is one slice. You can draw several, but not a sphere.
Your data are linear power or voltage. Convert to dB first, because the radial scale is linear in dB and will crush the small lobes.
You want to compare values exactly. Rings are labelled in steps. A table or a plain XY Chart of gain against angle is better for reading numbers.
You are plotting something that is not directional. Categories arranged round a circle belong in a Spider or a Nightingale Rose, not a pattern.

The math behind it

From gain to radius

Each sample is an angle $\theta$ in degrees, clockwise from the top, and a gain $g$ in dB for each pattern you add as a child. A sample lands at radius $r$ and angle $\theta$ with the rule below, where $g_{\max}$ is the dB at the rim (max) and $g_{\min}$ the dB at the centre (min), and $R$ is the plot's radius in pixels. Gains below the floor are clamped to the centre, and gains above the rim to the rim.

r = R\,\operatorname{clamp}\!\left(\frac{g - g_{\min}}{g_{\max} - g_{\min}},\; 0,\; 1\right)

Defaults, rings and spokes

If you give no max, it is the highest finite gain in any of the patterns, rounded up to a multiple of 10 dB; if there is none, it is 0. The floor defaults to $g_{\max} - 40$ dB. So a pattern normalised to 0 dB at its peak spans 0 to minus 40 dB, and the radial scale is linear in decibels: each ring is an equal step in dB.

levels rings (4 by default) are drawn at equal dB steps and labelled in dB, and twelve spokes mark every 30 degrees. A pattern that covers the full circle is closed and lightly filled (fill opacity 0.1). An open pattern covering a partial sweep is drawn as a line only, so a one-sided measurement does not claim data it does not have.

Relationship to the physics

The chart does not compute a pattern; it plots what you measured or simulated. For orientation, a uniform linear array of $N$ isotropic elements with spacing $d$ and wavelength $\lambda$ has the array factor below, and the gain in dB is $20\log_{10}|AF|$ of the field, which is $10\log_{10}$ of the power. The half-power beamwidth is where the pattern has fallen 3 dB from its peak, which is the figure most data sheets quote.

AF(\theta) = \frac{\sin(N\psi/2)}{N\sin(\psi/2)}, \qquad \psi = \frac{2\pi d}{\lambda}\cos\theta

g(\theta)\,[\text{dB}] = 10\log_{10}\frac{P(\theta)}{P_{\max}}

Real life usage

The dish that heard the neighbours

Ruth worked for a rural internet provider that ran radio links between hilltops, and she had a complaint: a customer in a valley complained that the link dropped every evening around seven. The link margin was fine. The weather was fine. The only thing that happened at seven was that, as far as anyone could tell, somebody three kilometres away turned on a microwave link of their own.

The antenna was a small panel with a stated beamwidth of 20 degrees and a stated sidelobe level of minus 25 dB. Those are the numbers on the box. They tell you the antenna passes its test, not what it does at 140 degrees, where it turns out the interference was coming from.

She wanted the whole picture, from every direction, for the actual antenna as installed, with the measured pattern of the panel on top of the manufacturer's. She had a rotator and a signal generator and an afternoon in a field, which is the complete equipment list for most antenna measurements and a good reason to enjoy them.

She recorded the gain every five degrees and passed both sets to <RadiationPattern> as two <TrendSeries> children, with the floor at minus 40 dB. The manufacturer's pattern was a tidy lobe with small, even petals. Her measurement had the same main lobe, and then, around 140 degrees, a bump that rose to minus 14 dB: a side lobe 11 dB higher than the specification.

A plot like that is a small argument by itself. The neighbour's link sat at 142 degrees from her boresight. The bump was listening to the neighbour's transmitter, which raised its power in the evening peak. The data sheet pattern was a drawing of a good antenna. Hers was a picture of a specific one, with a bracket bent by two degrees and a mounting pole that reflected into the back half.

She straightened the bracket, moved the dish 40 centimetres to take the pole out of the way, and re-measured. The lobe at 140 degrees dropped to minus 26 dB, inside the specification. The link has not dropped at seven since, and the neighbour has never been told that they were, briefly, the most powerful thing within three kilometres.

Ruth has since asked for the measured pattern on every installation. The manufacturer's drawing, she says, is a promise, and the plot is a receipt.

Pitfalls

Angle convention. Angles are in degrees, clockwise from the top. A pattern stored counter-clockwise from the right will look rotated and mirrored. Convert it before plotting.
Linear data in dB clothing. If the values are linear power, the whole lobe looks like a thin spike and the sidelobes vanish. Convert with $10\log_{10}$ first.
Min and max chosen badly. The defaults assume a peak near 0 dB and a 40 dB floor. A broad pattern of 8 dBi gain with a floor of minus 32 dBi has no detail near the rim. Set min and max explicitly.
Comparing plots with different scales. Two patterns drawn with different floors look equally sharp but are not. Fix min and max for every plot in a comparison.

From around the web

Watch and read

Inside Wireless: Radiation DiagramRF elementsExplains how to read antenna radiation diagrams: lobes, beamwidth and nulls.

Radiation Patterns of Antenna (Isotropic Antenna, Directional Antenna & Omnidirectional Antenna)Engineering FundaLecture-style comparison of isotropic, directional and omnidirectional patterns.

Overview

API

<RadiationPattern data={lobes} angle={|l: &Lobe| l.angle}>
    <TrendSeries name="E-plane" y={|l: &Lobe| l.e_plane} />
    <TrendSeries name="H-plane" y={|l: &Lobe| l.h_plane} />
</RadiationPattern>

Prop	Type	Default
`data`		required
`angle`	`Fn(&T) -> f64`: degrees, clockwise from the top	required
children	`<TrendSeries>`: gain in dB, one pattern each	required
`max`	`f64`: dB at the rim	the highest gain, rounded up to 10
`min`	`f64`: dB at the centre	`max − 40`
`levels`	`usize`: dB rings	`4`
`fill_opacity`, `line_width`		`0.1`, `2.`
`legend`, `tooltip`, `class`	as on `<Spider>`

Spokes every 30°, rings labelled in dB. A pattern that covers the full circle is closed and filled. Hover to read every pattern's gain at the nearest angle.

How to read it

01Find the main lobe: the longest petal, pointing in the direction of peak gain. Check that it points where you intended.
02Measure its width at the ring 3 dB below the peak. That is the half-power beamwidth.
03Look at the smaller petals. The tallest side lobe sets your sidelobe level, and the lobe opposite the main one is the back lobe, the front-to-back ratio being the gap between them.
04Hover to read the gain of every pattern at the nearest sample angle. Hover snaps to samples, so a coarse measurement will snap coarsely.

When to use it, and when not to

Reach for it when

You are comparing an antenna design against its specification: main lobe direction, beamwidth, sidelobe level, front-to-back ratio.
You have two cuts of the same antenna, such as the E-plane and the H-plane, and want them drawn on the same axes.
You are reviewing measurements from an anechoic chamber, or a simulation, and want to see where the unwanted lobes are.
You want a picture that an RF engineer will read without a caption.

Skip it when

You want the full three-dimensional pattern. A polar chart is one slice. You can draw several, but not a sphere.
Your data are linear power or voltage. Convert to dB first, because the radial scale is linear in dB and will crush the small lobes.
You want to compare values exactly. Rings are labelled in steps. A table or a plain XY Chart of gain against angle is better for reading numbers.
You are plotting something that is not directional. Categories arranged round a circle belong in a Spider or a Nightingale Rose, not a pattern.

The math behind it

From gain to radius

r = R\,\operatorname{clamp}\!\left(\frac{g - g_{\min}}{g_{\max} - g_{\min}},\; 0,\; 1\right)

Defaults, rings and spokes

Relationship to the physics

AF(\theta) = \frac{\sin(N\psi/2)}{N\sin(\psi/2)}, \qquad \psi = \frac{2\pi d}{\lambda}\cos\theta

g(\theta)\,[\text{dB}] = 10\log_{10}\frac{P(\theta)}{P_{\max}}

The dish that heard the neighbours

Ruth has since asked for the measured pattern on every installation. The manufacturer's drawing, she says, is a promise, and the plot is a receipt.

Pitfalls

Angle convention. Angles are in degrees, clockwise from the top. A pattern stored counter-clockwise from the right will look rotated and mirrored. Convert it before plotting.
Linear data in dB clothing. If the values are linear power, the whole lobe looks like a thin spike and the sidelobes vanish. Convert with $10\log_{10}$ first.
Min and max chosen badly. The defaults assume a peak near 0 dB and a 40 dB floor. A broad pattern of 8 dBi gain with a floor of minus 32 dBi has no detail near the rim. Set min and max explicitly.
Comparing plots with different scales. Two patterns drawn with different floors look equally sharp but are not. Fix min and max for every plot in a comparison.

Overview

API

10 examples

How to read it

When to use it, and when not to

Reach for it when

Skip it when

The math behind it

From gain to radius

Defaults, rings and spokes

Relationship to the physics

The dish that heard the neighbours

Pitfalls

Watch and read

Related charts

Overview

API

10 examples

How to read it

When to use it, and when not to

Reach for it when

Skip it when

The math behind it

From gain to radius

Defaults, rings and spokes

Relationship to the physics

The dish that heard the neighbours

Pitfalls

Watch and read

Related charts