[USRP-users] Resolution of center frequency settings

Marcus Müller marcus.mueller at ettus.com
Wed Dec 17 05:21:32 EST 2014

Hello Mahaveer,

tuning USRPs is a two-stage process:
1. the daughterboard has gets tuned.
2. the DSP logic performs digital frequency shifting.

1. Daughterboard tuning

The daughterboards have local oscillators (LO) which they use to mix
down the RF signal to baseband (or vice versa).
These LOs are generated from the motherboard reference clock, usually by
fractional interpolation; thus, the LO can only tune to a discrete set
of frequencies.
How many of these frequencies exists, and how they are distributed,
depends on the daughterboard.

2. DSP frequency shifting

RX side:
The FPGA has logic that generates a complex sine (it's actually a
12-stage CORDIC) and multiplies the ADC samples with it, before
anti-aliasing filtering and decimating the ADC samples (coming in at
100MS/s) to the user-requested sampling rate.
This allows the USRP to transparently tune to "any" real frequency in
the daughterboard's frequency range.

"any" is in parentheses, because this is where accuracy comes in: the
sine calculation of course happens with fixed point numbers, and so do
the multiplication and the rest of the DSP. Thus, everything is
quantisized (at 16bit, most of the time); this, by considering
quantization noise, will give a maximum SNR you can get. With that
maximum SNR you could calculate the maximum accuracy a given frequency
estimator could achieve. And that will be your lower boundary for
frequency resolution.

exactly the same, other way around.

Overall frequency accuracy considerations

1Hz *is* very small. At 2.45GHz, that would be 0.4 parts per billion
accuracy. The accuracy of the reference clock is (I don't have exact
numbers in my head, just putting down something intuitively good) about
50 times worse. With other words: the variation you'll see because of
your reference clock should be expected to be 50 times as big as the
steps you want to do.

Even when driving the N210 at rather low user sampling rates, for
example 1MS/s, and considering the frequency shift in baseband, a
frequency accuracy of 1ppm is something that most receiving systems try
to autonomously correct by design.

This question comes up once or twice every year, and it's always
interesting to hear the motivation behind it, so would you mind
explaining why you want to tune so finely?

Best regards,
Marcus Müller

On 12/17/2014 10:52 AM, mahaveer gupta via USRP-users wrote:
> Hello,
> Could you please tell me the resolution at which I can vary the center
> frequency settings in USRP N210.
> For example, I can set the center frequency to be at 2.45 GHz. If I
> want to increase the center frequency by 1 Hz, I could use 2.450000001
> Hz. Not sure, how accurate the small increment would be and if it
> would make any difference at all.
> I know 1 Hz is very small, but would like to know the step size at
> which frequency increments would have effects
> -- 
> Thanks,
> M
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> USRP-users at lists.ettus.com
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