How well time synced do channels in a phased array need to be to be coherent?

In order for a narrowband phased array to be coherent channel to channel, what is the maximum timing jitter that can be tolerated between channels? I assume there can be a constant timing error between channels because this can be calibrated out, but randomly varying timing errors between channels are another matter.

From a naive mathematical perspective, I would assume the channels need to be synced to a small fraction of the wavelength of the carrier (i.e., within a few degrees of phase error at most). This would make it increasingly difficult to build phased arrays at higher frequencies (even ignoring the size and spacing of the antenna elements!). At 5 GHz for example, the time jitter between channels would have to be less than 5 picoseconds (9 degrees phase error) under this assumption.

Is there something I'm missing, or hardware tricks people employ to get around this that I'm not understanding?

• What do you mean by a channel? An RF path? a beam (in a multi-beam system)? Oct 27, 2022 at 15:08
• And when you talk about jitter, do you mean sampling error in an ADC someplace in the chain? Oct 27, 2022 at 15:09
• Right general idea, but I suspect your limit may be too small. Useful addition and suppression can still be had at the times that level, useful addition is still OK at 10x Oct 27, 2022 at 15:10
• Most phased arrays, at least those with more than a handful of elements, do not digitize the individual elements RF (yet). The elements are combined analog wise and that combined output is down converted (mixed) to a lower IF frequency before being digitized. Oct 27, 2022 at 15:30
• @SteveSh, I'm talking about digital channels in a phased array, such that you can perform digital beamforming with collected data. Oct 27, 2022 at 15:38