[hpsdr] "Infinite Precision?"

[Robert McGwier]

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



-- 
AMSAT VP Engineering. Member: ARRL, AMSAT-DL, TAPR, Packrats,
NJQRP/AMQRP, QRP ARCI, QCWA, FRC. ARRL SDR Wrk Grp Chairman
"You see, wire telegraph is a kind of a very, very long cat.
You pull his tail in New York and his head is meowing in Los
Angeles. Do you understand this? And radio operates exactly
the same way: you send signals here, they receive them there.
The only difference is that there is no cat." - Einstein
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