The simple answer is that a suitably-designed phased array of the same size (same cross-sectional area) as an equivalent dish would be expected to perform approximately equally (in terms of directivity and signal-strength). On those basic measures, it can't really perform better than a dish.

In a receiver, the signals from the individual array elements are electronically summed (at some stage of the signal processing) with subtle time-delays between the elements in order to "phase" the array and create the required directivity. Signals from the wanted direction will sum constructively, while signals from other directions will tend to be non-coherent (at random phases) from the different received elements, and thus average down to a proportionately lower level in the summation.

The key advantage of phased-arrays is that the beam-direction can be "electronically" steered (i.e. by changing timings in the signal-processing), as opposed to having to physically move a dish. The electronic beam-steering can be essentially instantaneous, whereas the rate at which you can move a dish on motors is limited by physical mass, inertia, motor-power, ... and will be subject to mechanical wear. This high-speed steering is near-essential for tracking low-earth satellites, or military radar, among other applications.

There may then be second-order benefits such as physical simplicity, lighter-weight, less wind-loading etc. But if you need super-speed scanning, then moving a physical dish of more than a certain size is simply impractical. Very large dishes are major engineering projects, as the dish needs to retain it's shape to within a fraction of a wavelength (say 1/10th of a wavelength) as the dish is moved and steered. In contrast, a phased array can be fitted on a flat (or even uneven surface/terrain) and "electronically" flattened (corrected for physical distortions).

A further benefit of phased arrays (for relevant applications) is that you can double up (or triple, or...) in your signal-processing, and then receive from two or more directions simultaneously with the same physical antenna. That's something you simply cannot do with a dish. Again useful for Starlink-type applications where you have multiple low-earth satellites, or military radar when you want to track multiple fast-moving targets.

If you have a phased array with a lot of elements then you may be able to control side-lobes better than with a dish, which may be important if you not only want to maximise the signal strength of a wanted signal, but also reject or suppress an unwanted signal of the same frequency but coming from a different physical direction.

Phased array antenna with many elements are likely to be more expensive than dishes, often considerably so, although the cost of RF electronics is continually falling.

(I don't have any first-hand experience with phased-array antenna, but have a lot of experience with signal-processing in other applications, where the underlying reasoning would be similar)

u/noshowtho If you understand how a phased array can steer its output, then you are well on your way.

With a dish setup, all the energy for "pings" originates from a relatively concentrated point (which sometimes IS a small phased array) sitting at the focal point of the dish. You probably know that this is why dish systems have some sort of tripod or mechanical arm sitting out front, to hold the transmitter at that point. The transmitter "lights up" the dish, and the dish in turn focuses the emitted energy into a beam (with a major lobe). It's just like a flashlight, where the bulb throws off energy that is reflected and focused by the reflector behind it. Just like a flashlight, a dish antenna is aimed at targets by physically moving the dish around, although these days most dishes have a limited ability to do digital steering.

When the return signal (energy reflected off the target) comes back, the dish, being large, captures some of that energy and focuses it back on the focal point, onto a receiver sitting there. So the job of the dish is to take very low level energy arriving across a relatively large area and focus it down onto a specific point where the sensor sits. At this point it's operating a little like a telescope.

Unlike dish systems that transmit and receive energy from a concentrated point, phased arrays spread the transmit power out over many transmit modules arranged across a flat array. In the dish, the total power level out is the power of the one transmitter. In a phased array, the power out is the sum of the power of all the transmit modules.

For transmit, the phased array mimics the function of a dish by controlling the timing (phase) of the energy leaving each transmit module. This opens up all sorts of possibilities for creating different sorts of "pings" and avoids a lot of mechanical steering, as the array can be aimed digitally by controlling the energy coming from transmit modules individually.

Finally to your question. The return signal coming back to that flat phased array surface is again low level and spread across the entire array surface. But now, instead of a dish "multiplying" the intensity by focusing the energy like a telescope, the phased array simply sums the energy received at each receive module across the array surface. And since the returning wave front is captured at many point across the array, the post processing options are many times greater than that of a dish system.

The "better than" part of your question is significant. Better depends on what one is doing with the antenna system in the first place. Dish systems are relatively cheap, can be relatively simple, and depending on the scenario can outperform even really good phased arrays. But the electronic beam steering, beam forming capabilities, and post processing options for phased arrays make their expense and complexity worth it for many applications.

There's also one more fact that I think other commentators glanced over. One of the many approaches you can have towards gain and directivity of an antenna is the idea of an effective cross section of an antenna.

Think about a simple dipole. It basically has no cross sectional area, but yet it is still capable of capturing free air propagation and confining it to a conducted EM wave (into coax, for example).

This is because the presence of the dipole creates a disturbance in the way free air propagating EM waves (which can be approximated greatly since it's in free air), and creates more complex "near field" phenomena which essentially increases the cross sectional area of the antenna.

In this sense, all antennas disturb the free air propagation and create near field cross sectional areas that it will use to capture EM energy and send it through a conductor.

Indeed, there's actually a relationship between directivity/gain and this imaginary cross sectional area. I haven't done this in a while but I believe for parabolic antennas (or any antenna where the physical size >> wavelength) this cross sectional area is essentially the same as the physical size, and hence this is one way to think about the high gain of parabolic antennas like the ones used for radio astronomy.

In that sense, in certain degenerate scenarios, the flat plate might have a larger cross sectional area than an actual semi-spherical dish (hint: it has to do with physical size vs wavelength of the wave you're dealing with)

> how does any sort of flat plate collect incoming radio waves as well as or better than a semi-spherical (?) dish?

So the really counterintuitive fact here is that the amount of far field energy that an antenna can collect is a tradeoff between how directive it is and how much it can collect from a particular direction.

i.e. assuming your antenna is 100% efficient, and say antenna A collects energy from all directions, and say antenna B collects energy only from the "top" hemisphere, antenna B collects energy from that direction twice as much as antenna A. In more technical terms, the directivity integral is always constant.

What's also kind of wacky is that generally speaking the bigger the antenna is, the more directive the antenna is--e.g. an antenna that's big generally collects better from its "boresight". The first paragraph still applies, so a big antenna is poor at collecting energy off-boresight.

A phased array is a curious idea. Start with a passive phased array, where you have one antenna element, and you add the contributions from that one antenna element copy-pasted in space.

generally speaking the further an antenna element is spaced apart, the more directivity you get, since the physical size is larger. If you have many of these elements copied across a large surface, your directivity increases a lot.

A passive array is kind of dumb since you might as well just have a parabolic reflector antenna ("dish")--but an active array is where it shines.

You can tune the exact phase and amplitude contribution from each phased array element, and when you do that, you can tune the exact radiation pattern of the phased array. You can steer the "boresight" by delaying the input from some elements; you can make the antenna less directive or more directive; you can make it so that there are multiple boresights (useful if you want to track multiple radar targets); etc.

For pure efficiency and directivity, a parabolic reflector is best. That's why it's used in radio astronomy. Active phased arrays are used in military and high performance radios since you can change the radiation pattern pretty much instantaneously.