# TDUs or phase shifters?

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New for May 2019.  This question comes up when you are first designing a phased array.  When are phase shifters used, and when are time delay units needed?

In a phased array, ideally, signals are delayed by something that changes length (a TDU).  For a three-foot array, steering 45 degrees, you’d need three feet of length added to one end, and then gradually smaller lengths added across the array until you get to zero added length at the opposite end.

It is impractical to add that much length.

At 10 GHz, if you consider phase, you need 10,980 degrees of phase to hit that three foot (914.4mm)  length. Don't try to do that in your head, visit our download area and grab a copy of the delay/length/phase calculator (in Excel).  Here's a screen shot, it's already out of date as we just improved that calculator. Don't forget to use K=1 as we are talking about phase in free-space!

You already should know that in RF engineering, at a fixed frequency, you can usually ignore whole numbers of wavelengths in transmission phase: recall that S-parameter phase is always between -180 and +180 degrees.  In the 10 GHz case, you can ignore 10,800 degrees of the length (30 wavelengths x 360 degrees) and use a constant-phase phase shifter set to 175 degrees (for the longest case) to point the beam in the right direction.

A problem happens when you try to operate over a non-zero frequency band. At 9.5 GHz, 10,427 degrees is ideally needed to delay the signal by three feet. That is 28 wavelengths (10,080 degrees), plus 347 degrees.  You can still ignore the 28 wavelengths, at your peril.  Oops, your phase shifter is set to 175 degrees (to form the beam at 10 GHz)…. The beam will not add up correctly at 9.5 GHz.

In practice, a combination of phase shifters is used at the elements, with some time delay at sub-array level to alleviate the problem, and arrays can operate over 10% bandwidth or more.  However, for a perfect, wideband array, (such as 6 to 18 GHz) conventional phase shifters cannot be used, every element needs full time delay to form the beam over frequency.  Smaller TDU bits are put into the elements, and longer bits are at the sub-array level.

Continuing the example, let's look at TDUs used at sub-array level.  Let's convert that three-foot length to units of time: three feet is 3050 ps. Because the TDUs are used at subarray level, you don't get to choose the exact length that is needed for every element. Perhaps you can command the TDU to 2500 ps, which is 25 wavelengths at 10 GHz (9000 electrical degrees). How close will the phase shift setting be to ideal?  We already know that we want 175 degrees of phase shift at 10 GHz.

Now back to 9.5 GHz.  That TDU is providing 23.75 wavelengths, or 8550 degrees of unwrapped phase.  Ignoring whole wavelengths (8280 degrees at 9 GHz) the TDU transmission phase (S21 angle) is 270 degrees. Add the phase shifter phase of 175 degrees and we see 445 degrees phase shift.  Ideally, we wanted 347 degrees.  The error is 98 degrees, considerable, but not a disaster like 180 degrees would be.