# phase noise in NCO

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Hello,

I want to make a phase measurement at 100MHz with a NCO at 200+ MHz
This NCO will have a 32 bit phase accumulator and a 32 bits phase offset. The
output will be only one bit.
I will use a phase comparator followed by an integrator (digital or analogic
if needed).
At 100MHz the NCO output will be very very noisy but if I integrate it for a
rather long time (10ms) will it have a 0 mean ?
Can I implement this in an FPGA or should I use a DDS chip (AD9854) ?
Where can I find some maths on this subject ?

Thanks

Marc Battyani

Re: phase noise in NCO

A 32 bit accumulator will have very, very low noise in the digital
domain due to the high resolution.  If you need to convert this to
analog, you will find significant noise from the discrete time
sampling.  However the noise level will be affected by your filter.

The phase noise is an AC measurement so it will not integrate to zero
over time.  With a 32 bit phase accumulator, I expect nearly all of your
phase noise will be due to your osciallator source giving time error of
the samples.

--

Rick "rickman" Collins

snipped-for-privacy@XYarius.com
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Re: phase noise in NCO

The

A 1-bit output will give you NCO phase noise that has a range of 5nS
peak-to-peak based only on the single bit output.  The only exception to
this value is when you run at a fractional value such as 100 MHz from the
200MHz clock where the accumulator acts as a divide-by 2.  [I guess all
frequencies will be a fractional relation - 1329046/2^32 is still a
fraction.  The arguement applies to small whole number fractions such as
3/16.]  The way to get good performance from the system is to use the full
DDS - an NCO with a D/A such as those very nifty Analog Devices parts.

analogic
a

If you compare the phase to a noise-free reference that is precisely the
desired frequency, the low-passed output of the phase comparator will
conceptually be the phase offset between your NCO and the noise-free
reference.  I say conceptually because this is not a practical test.  If
you're trying to figure out of the phase noise is "lopsided," you should
find the phase comparator output is some form of sawtooth.  If the frequency
is very close to a fraction of the 200MHz clocking frequency, your phase
comparator output will appear to recover from a step function while the
reality is that it's a very long sawtooth.  Your frequency give you results
with phase variations that are much closer in time where it's hard to see
the longer term sawtooth characteristics beyond the very large, high
frequency variations you see without the lowpassing.

The NCO can be implemented in the FPGA.  You could drive a D/A with the FPGA
though it's recommended that the D/A's clock be sourced direclty from your
low phase-noise source rather than passing the clock through the FPGA.  The
DDS chips with integrated D/As are the best for this kind of thing.

Unfortunately, the maths are a little loose on the phase noise results.
I've only seen textbook treatment of simple jitter: a sinusoidal phase
variation.  The Bessel function is a result of the Fourier of the

sin(wt+Psin(at))

kind of form (ah, my kingdom for an ohmega, phi, or alpha on this keyboard).
The Bessels give you only a slight idea of what happens in the NCO realm.
The investigations I did went through a theoretical setup I described above.
Determine the time domain of the phase comparator output from your NCO
compared to the "ideal" noise-free reference mathematically.  The pattern
will repeat when the NCO accumulator values repeat which will happen at
least every 2^32 cycles.  This time-domain result might be what you seek.
The frequency domain interested me, so I took the FFT of the time domain.

If you're only interested in close-in phase noise and higher frequencies are
a non-issue, there are ways to increase the peak-to-peak phase noise while
decreasing the close-in phase noise.  A google on "MASH" and "frequency
synthesis" might bring up results on that advanced subject.

Re: phase noise in NCO
I have been playing around with the idea of a 32-bit DDS circuit at 200
MHz ( as a digitally controlled VCO) and I know some tricks to reduce
the timing uncertainty from the obvious 5 ns by a factor of 4. Then I
was going to use an external PLL to reduce it further.
These are just ideas...

Peter Alfke
=============
Marc Battyani wrote:

Re: phase noise in NCO

I'm trying to have an almost all digital solution. I would rather use a DDS
rather than a PLL as I'm not generatin a frequency.
I just want to lock on the phase. (I have the reference frequency) I'ts a
kind of DLL...

Marc

Re: phase noise in NCO

Sounds challenging : If I have this right
You have 100MHz 'incomming' (hopefully very clean and phase stable :)
You want to lock to 0.1%, (or 10ps), nominally 200MHz local Osc
You can tolerate longer lock acquire times

Analog Phase locked loops work because they integrate
the phase-magnitude errors,
- In a digital system, edge resolution of 10ps may be just possible, but
I'm not sure you can get any error-proportional siganl.
Go-right/Go-Left control is likely to be swamped by the phase-noise of
the DDS signal.....
-jg

Re: phase noise in NCO
On Tue, 8 Jul 2003 14:33:20 +0200, "Marc Battyani"

Do you need to know the spectrum of the noise, or just the peak to
peak value?

I sometimes find myself in the situation of having to work out the
spectral characteristics of the phase noise (jitter) of the msb of a
phase accumulator.  E.g. if I am using a post-NCO PLL (as Peter A.
suggested) then I only care about the phase noise components at offset
frequencies less than the loop bandwidth of the PLL.

I don't know of a closed form expression for spectrum of the noise,
but it's trivial to work out the spectrum with a spreadsheet (once you
know how).  This is much easier that trying to measure the spectrum in
the lab.
(Reply if you are interested in the method.)

BTW, Peter's trick of reducing the jitter by a factor of 4 (I assume)
relies on using a 4 phase clock.  This is almost certainly worth the
effort if you are trying to reduce the jitter.
I have a worked example that uses a 2 phase clock (actually it uses
both edges of a single clock) in my free fractional N divider
generator, at this web site:
http://fractional_divider.tripod.com /
(Note: some web proxies don't like domain names with underscores.)

Allan.

Re: phase noise in NCO

The
analogic
a

The spectrum I think. In fact I need to have a very precise phase lock
(0.1%). The frequency lock is already ok as I have the reference clock.

I thought about filtering and integrating the phase error after the phase
comparator. I don't think I need a PLL as I'm not synthesising a frequency.

Sure, please explain how to do it, I'm really interested.

Thanks, I will look at it.

Marc

Re: phase noise in NCO
On Wed, 9 Jul 2003 01:08:36 +0200, "Marc Battyani"

Hmmm, 0.1% of what?  "Phase lock" is usually specified as an angle
(degrees, radians or unit intervals) or as phase noise (dBc/Hz).

What are you actually trying to do?

You are synthesising a frequency with the NCO, even if that wasn't

Rough description here:

Re: phase noise in NCO
On Tue, 8 Jul 2003 14:33:20 +0200, "Marc Battyani"

I've used the Ad9954 DDS and the phase noise is about -140dBc/Hz @
10KHz 0ffset. Your clk ref needs to be better than that if you want an
accurae measurement. I used a DRO for the reference and an Agilent
E5500 phase noise test set to measure it. Download the Analog Devices
dds tutorial for all the math involved.