[hpsdr] "Infinite Precision?"

[Robert McGwier]

Murray:

There won't be just one QSE unless you do the phase shifting in analog
or at the LO for each individual element in the array.    Frequency
response (and I think you mean bandwidth)  comes in because of your
last sentence, which is RIGHT ON.   To the extent that we can treat
the phase component as DC,  the phased array is a "narrow band" phased
array and we completely ignore the frequency dependence.   It is, of
course,  not precisely true. BUT,  up to your ability to tell the
difference in the performance of the antenna,  it might as well be
true.

Bob
N4HY


Murray Lang wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
>
>
> What about the situation where QSE is the only "mixing" stage and I/Q is from a sound card? Where does frequency response come into it? You've only talked about word size. You seem to be saying that phase is a DC component of I/Q.
>
> Murray
> VK6HL
>
> At 01:08 PM 6/09/2006, Robert McGwier wrote:
>
>
>> Murray:
>>
>> You are getting there.  Keep asking questions since you are not the
only person here who needs these questions answered.
>>
>> You might as well have continuous phase since the difference
between you and continuous phase is so small as to not be worth
mentioning.
>>
>> Let P1, P2, ..., Pn   be the phase offset of the LO's or clocks in
the N stages of a receive system
>>
>> The phases are COMPLETELY commutative.
>>
>> (P1+ phi) + P2 + P3 + ... + Pn   =
>> P1 + P2 + P3 + ...+ (Pn + phi)
>>
>> Where P1 is the first LO and Pn is the last "LO" in the system.
Since Pn will be the software oscillator in your SDR system,  the
precision for phi is determined by the precision of a floating point
number.   Since this is 2^23 bits  we have 138 dB of range in an IEEE
float.     Since ALL of the oscillators in your coherent phasing
system are derived from the SAME source for each of the antennas,
the RELATIVE phase offset,  which will be determined by the software
LO has this 138 dynamic range.  Your phased array can't possibly have
enough elements in it to use all of that precision since they half
power beam width of any real antenna system is going to be about 12
orders of magnitude worse than you could possibly use.
>>
>> Bob
>>
>>
>>
>>
>> Murray Lang wrote:
>>>
>>> ***** High Performance Software Defined Radio Discussion List
>>> *****
>>>
>>> Thanks Robert,
>>>
>>> I need to go away and try to get my head around it some more. I need to
>>> understand the relationship between the sampling resolution of I/Q and
>>> the
>>>
>>> resolution (ie step size) of phase adjustments that it can apply to RF.
>>> It's not going to be continuous. I'm starting to work on the math, but I
>>> have a way to go.
>>>
>>> Cheers
>>> Murray
>>> VK6HL

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