[time-nuts] Down-conversion to IF and sampling

Stephan Sandenbergh ssandenbergh at gmail.com
Sat Dec 23 16:00:39 EST 2017


Hi,

The goal would be to be able to tell what the phase and frequency of the
down-converted and sampled signal is. So no modulation on the carrier (for
now).

So given the RF signal is perfect sinusoid, and given that you know the
parameters x(t) = xo + yot (time and fractional frequency offset) of the
reference oscillator, one should be able to determine the phase and
frequency of the ADC output at any given time (in a perfect world).

In general, the ADC sampling frequency (and the LO frequency for that
matter) could be at non-integer multiples of the reference oscilator.
However, both the LO and sampling frequency will be a derivative of the
reference and will have the x(t) = xo + yot time and frequency offset.
Hence, that should be accounted for in both down-conversion and ADC
sampling.

However, I have not seen examples where time and frequency offsets have
been included in the ADC sampling. But, it seems logical that reference
oscillator's imperfections modulate both the down-conversion and the ADC
timebase.

I guess I'm just worried that I might be missing something obvious here?
And I know there is no better place to ask such a question other than on
time-nuts :)

Regards,

Stephan



On Sat, 23 Dec 2017 at 18:11 Bob kb8tq <kb8tq at n1k.org> wrote:

> Hi
>
> What is the Time Nut goal here? Are we after the carrier frequency or
> after the
> modulation on the signal?
>
> Bob
>
> > On Dec 23, 2017, at 10:46 AM, Stephan Sandenbergh <
> ssandenbergh at gmail.com> wrote:
> >
> > Oops, I noted a sign error in the previous diagram. The attached seems
> > better...
> >
> > On Sat, Dec 23, 2017 at 4:46 PM Stephan Sandenbergh <
> ssandenbergh at gmail.com>
> > wrote:
> >
> >> Hi All,
> >>
> >> Consider the following very common scenario: A perfect RF signal is
> >> heterodyne down-converted to baseband using an offset oscillator. Let's
> >> assume this oscillator has x(t) = xo + yot. This produces a time and
> >> frequency offset baseband signal. Then, this baseband signal is
> coherently
> >> ADC sampled using that same offset oscillator.
> >>
> >> What would the effect of this coherent ADC sampling be?
> >>
> >> See attached diagram. Here I assumed the ADC timebase is a
> time-dependent
> >> function of the oscillator offset. However, it feels like I'm making a
> >> logic error? I can't remember ever seeing anyone accounting for the ADC
> >> time-base errors in coherent heterodyne down-converter stages. I have
> >> limited experience though.
> >>
> >> Regards,
> >>
> >> Stephan.
> >>
> >>
> >>
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