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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?

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  • \$\begingroup\$ What do you mean by a channel? An RF path? a beam (in a multi-beam system)? \$\endgroup\$
    – SteveSh
    Oct 27, 2022 at 15:08
  • \$\begingroup\$ And when you talk about jitter, do you mean sampling error in an ADC someplace in the chain? \$\endgroup\$
    – SteveSh
    Oct 27, 2022 at 15:09
  • \$\begingroup\$ 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 \$\endgroup\$
    – Neil_UK
    Oct 27, 2022 at 15:10
  • \$\begingroup\$ 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. \$\endgroup\$
    – SteveSh
    Oct 27, 2022 at 15:30
  • \$\begingroup\$ @SteveSh, I'm talking about digital channels in a phased array, such that you can perform digital beamforming with collected data. \$\endgroup\$
    – Gillespie
    Oct 27, 2022 at 15:38

1 Answer 1

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Digital beam forming is performed at the IF that is much lower in frequency than the carrier and is often centred on DC with in-phase and quadrature channels.

The phase jitter requirements at IF are correspondingly relaxed because of the lower frequency. At 10MHz for example timing accuracies of hundreds of picoseconds may be tolerated depending upon SNR requirements.

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  • \$\begingroup\$ Thanks for the answer Kevin! Follow up: how is a phase error characterized at DC? I understand a 1 nanosecond error at 10 MHz would be a 3.6 degree error (1e-9*10e6*360), but I don't quite understand how that works at DC. \$\endgroup\$
    – Gillespie
    Oct 27, 2022 at 16:13
  • \$\begingroup\$ All of the radars I've dealt with (air to air tracking, SAR imaging, etc) have their final IF in the range of 400 MHz - 800 MHz, with an instantaneous bandwidth (IBW) of 100 MHz to 400 Mhz, depending on the mode and mission. I've never seen one centered on DC. \$\endgroup\$
    – SteveSh
    Oct 27, 2022 at 20:27
  • \$\begingroup\$ @SteveSh - most of the modern chipsets for automotive and other consumer use use a zero frequency IF with FMCW (or similar) modulation. The local oscillator is modulated with a ramp or steps then mixed with the received signal. This is then digitized for signal processing. A stationary reflection at zero range would give a zero frequency IF, there is no separate LO. \$\endgroup\$
    – Kevin White
    Oct 27, 2022 at 20:55
  • \$\begingroup\$ @Gillespie - at DC static timing error is not relevant. For a target at any distance from the transmitter there will be a non-zero frequency signal in the IF. The ones I have worked with (eg AWR2243) are designed with an IF bandwidth of up to 20-25MHz. \$\endgroup\$
    – Kevin White
    Oct 27, 2022 at 20:59
  • \$\begingroup\$ @Kevin White - Not disputing what you've said, but OP has indicated (at least that's the way I've interpreted his question and comments) he's talking about a relatively large phase array system, perhaps with digital beamforming being done at a subarray level. This is significantly different from the automotive/consumer market. \$\endgroup\$
    – SteveSh
    Oct 27, 2022 at 21:16

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