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I'm fairly new to RF technology, but a direction-finding application has come up where a highly directional antenna can offer a convenient solution, so I started searching for such antennas.

Most, like Yagi antennas, that can be purchased seem to have gain patterns that are not very focused, with half-power beamwidths of no less than 30 degrees, often much greater.

Is it possible to design PCB antennas (or alternatively, purchase pre-made antennas) with a very narrow/focused radiation pattern -- Ideally, I'm looking for a small (size < 10 cm) antenna with a half-power beamwidth under 10 degrees? Assume any transmission frequency between, e.g., 433 Mhz up to 10 GHz is acceptable (because the application has some leeway in this).

What keywords should I research for this, or are such antennas impossible due to scientific limitations?

For example, Wikipedia contains this image within a radiation-pattern article, but I haven't yet been able to find an antenna with such favorable pattern:

enter image description here

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    \$\begingroup\$ You don't even specify for which frequency you want the antenna - antenna size mainly depends on frequency! Neither do you specify why you need a directional antenna. Is it for direction finding, or for normal operation? \$\endgroup\$ – jcoppens Jun 3 '15 at 4:34
  • \$\begingroup\$ @jcoppens: I have added these details; but frankly, as stated before, transmission frequency is an open variable in my case. I wanted to give as much freedom as possible to resolving other constraints, especially the small antenna size and of course the narrow beamwidth. \$\endgroup\$ – boardbite Jun 3 '15 at 4:54
  • \$\begingroup\$ @jcoppens: And yes, the application is direction-finding-related. Any thoughts? \$\endgroup\$ – boardbite Jun 3 '15 at 4:54
  • \$\begingroup\$ Better directivity would be accomplished using a dish or a helical but it could prove a challenge to fit this on a pcb. \$\endgroup\$ – captcha Jun 3 '15 at 5:12
  • \$\begingroup\$ Perhaps you're looking for "grid antenna radiation pattern"? \$\endgroup\$ – davidcary Jun 3 '15 at 12:13
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Your requirements will never be met.

A dish antenna is the best for providing focus and if you looked at voyager II, it used a 3.7 metre dish at about 3 GHz. This would give a 3dB half-beam-width of about 0.91 degrees.

I'm using the example of Voyager II because they would not ship something to the planets that had not been thought about (o-rings excluded from this statement).

At 1 GHz this half beam angle increases to 2.74 degrees

At 1 GHz and a 1m dish this increases to 10.2 degrees

See this calculator to check. To help you get further ideas about this follow these rules: -

  • If you double the frequency, the gain of an antenna will quadruple.
  • If you double the frequency, the beam-width of an antenna will halve.
  • If you double the antenna diameter (keeping the frequency the same), the gain of the antenna will quadruple.
  • If you double the antenna diameter (keeping the frequency the same), the beam-width of an antenna will halve.
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It's easy to calculate the narrowest beamwidth possible from an antenna structure. This will give you an idea of the size antenna required to achieve a certain beam width.

You need to know the dimension of the antenna and the wavelength. Draw a two-dimensional view of the geometry of a wave impinging on the antenna. Work out the smallest angle at which the wave at the edge will be 180 degrees out of phase with the wave at the middle. This is the angle of the first null, the 3dB beamwidth might be about half this.

This method is for flat antennas. Slow-wave antennas (yagi, helix, dielectric rod) have an effective area larger than their physical front area. But don't expect a free lunch here either.

A suggestion though: Look up something called a monopulse antenna.

It's made from two antennas of some kind, connected to a sum and difference network. The sum channel just has the combined pattern of the two antennas, still fairly broad. But the difference channel has a null on boresight which is very narrow, if the signal is strong enough.

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For typical parabolic antennas (which include mesh antennas and solid dish antennas), a common rule of thumb is

B = k λ / d

where

  • B = the half-power beamwidth in degrees
  • λ = wavelength
  • d = antenna diameter
  • k = antenna illumination factor, typically close to 70

I'm looking for a small (size < 10 cm) antenna with a half-power beamwidth under 10 degrees

Rearranging the terms in the above formula, I get

λ = B d / k =~ 10 degrees * 0.10 m / 70 ~= 0.014 m

frequency = c / &lambda ~= (3e8 m/s)/(0.014 m) ~= 21 gigahertz

which gives a frequency of 21 gigahertz. Making the size d and the beamwidth B smaller will increase the required frequency.

If your antenna has a small size, it's impossible to get around fundamental physical limits to its beamwidth and gain, no matter if it's Yagi, parabolic, log-periodic, or any other kind of antenna. See Randy Bancroft. "Fundamental Dimension Limits of Antennas: Ensuring Proper Antenna Dimensions in Mobile Device Designs".

direction finding

Many transmitter hunting and direction finding systems, such as the ones used in the sport of amateur radio direction finding, find the direction of some transmitter by turning the antenna to (counterintuitively) find the minimum signal (the "null position"), rather than the maximum signal that one might expect. The nulls are sharper (and so easier to find an exact direction) than the maximums for most (all?) antennas.

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    \$\begingroup\$ It's 21 GHz, not too difficult! \$\endgroup\$ – tomnexus Jun 3 '15 at 17:26
  • \$\begingroup\$ @tomnexus: whoops, you're right. What's a few orders of magnitude between friends? Maybe it's not quite as impossible as I thought. \$\endgroup\$ – davidcary Jun 3 '15 at 23:18

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