• vutran
In summary, the Starlink phased array antenna can't be totally isotropic, so the power pattern is narrower than the amplitude beam width.

#### vutran

It looks very cool.
I have been using phased-array for direction finding & beam-forming, but recently I have come up with an idea that I find difficult to understand.
Let's take the star-link phased array as an example, if we used a long-wave (MHz -- much lower than the one it is designed for), the phase offset among antenna elements would be very small (go to 0) in any direction. Therefore, the amplitude gain in any direction would be N (N: number of elements), and the power gain would be N^2 in any direction which would violate the energy conservation law. Could anyone help me figure out what is wrong here?
Thanks.

vutran said:
violate the energy conservation law
Energy conservation applies over the whole sphere. The square of the amplitude gives the power radiated in a particular direction but remember that all the directions where the amplitude is one half, get only one quarter of the power. It can never all add up to greater than unity.
The power beam width is less than the amplitude beam width - is another way of looking at it.

vutran
Very closely spaced elements have large mutual coupling that spoils the gain. A way to look at it is that coupling makes many elements behave as one, so you have, effectively, a fraction of N elements.

vutran and berkeman
sophiecentaur said:
that all the directions where the amplitude is one half
In this case, I assumed the wavelength is much larger than the element spacing, so the radiation pattern is approximately a sphere, so the amplitude is the same in all directions, isn't it?

marcusl said:
Very closely spaced elements have large mutual coupling that spoils the gain. A way to look at it is that coupling makes many elements behave as one, so you have, effectively, a fraction of N elements.
But how can I take this into account in analyses in general cases with a spacing of D? Is it correct to compute the pattern regardless of this mutual coupling effect, then normalize it so that ∫(power_pattern) = 1 (or transmission power)?

vutran said:
In this case, I assumed the wavelength is much larger than the element spacing, so the radiation pattern is approximately a sphere, so the amplitude is the same in all directions, isn't it?
No, there is no such thing as an omni-directional EM antenna. The Starlink antenna uses microstrip patches on a ground plane so the radiation pattern is confined to a hemisphere. Such elements have maximal amplitude at broadside and fall to zero along the array plane, so the pattern is shaped more like a teardrop.

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vutran said:
But how can I take this into account in analyses in general cases with a spacing of D? Is it correct to compute the pattern regardless of this mutual coupling effect, then normalize it so that ∫(power_pattern) = 1 (or transmission power)?
No. If your antenna has a perfect impedance match, then the gain is approximately $$G=\frac{4\pi A}{\lambda^2}$$where A is the array aperture array. To get an exact value requires analysis with an EM simulation code or measurement in an antenna test range.

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vutran said:
In this case, I assumed the wavelength is much larger than the element spacing, so the radiation pattern is approximately a sphere, so the amplitude is the same in all directions, isn't it?
Even a very small array can be 'unidirectional', if desired, with deep or slight null(s) in some directions. See this Radio Ham link In any case, as stated earlier, it can't be totally isotropic. As you'd expect, the Power pattern would be narrower (but not all that narrow). The integrated power will still add up to unity.