RF downconverting

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...Jim Thompson

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OK, Let me give you guys some more details/background. The original signal is a doppler shifted Terahertz signal. The return signal (light) is mixed with a 3dB coupler(all optical) that provides the optical output (both the optical carrier and the shifted optical carrier). The optical output is then fed to an EO receiver that puts out 80MHz +/- 80MHz shift, thus the 0 Hz to 160 MHz range. A 1 MHz shift corresponds to 0.5 knots.

David: Somewhere in this range of 0 - 160 MHZ is one or more carriers, I presume, with Doppler. If the carrier(s) always appear in relatively constant portions of the band, you can use your sampler as a downconverter by appropriately selecting the sampling rate (Fs) . Of course, there are a number of caveats with this, but first things first. Think of the spectrum from 0 -160 MHz as a linear scale, and plot the various carriers at their locations.

Next, think of partitioning that spectrum into equal sized chunks of frequency. The width of each chunk is exactly half the sample rate wide (Fs/2). The first chunk reaches from 0 Hz to half of the selected sample rate. The next chunk reaches from Fs/2 to Fs. These chunks continue until they extend beyond 160 MHz. Clearly, if Fs is large, there are only a few chunks and if Fs is small, there are many chunks. Start with a candidate Fs, you will adjust it later. For my discussion, I'm going to select 60 MHz as Fs, just so I can clarify with some numbers. So Fs = 60 and Fs/2 = 30 MHz. Each chunk is 30 MHz wide.

Now alternately mark the chunks with "+" and "-" characters. The chunk at 0 Hz (0 - 30 MHz) is a "+", the one from Fs/2 to Fs (30 to 60 MHz) is a "-", etc. The Chunks with "+" signs are uninverted spectra. Those with the "-" sign will have their frequency content inverted after conversion. Handling that will be explained later.

Now picture the frequency spectrum has been drawn lengthwise on a long unfolded piece of computer fan-fold printer paper, such that the paper perforations are the chunk partition lines. Each page is one frequency chunk wide. Furthermore, imagine that the paper is transparent, and that we have drawn our carriers with a marker or grease pencil. Now imagine folding the printout paper until its in a stack. You can look through the transparent paper and see all your carriers, but the whole thing is only one page (30 MHz) wide, and every carrier appears to have a frequency between 0 and 30 MHz.

Also notice that if I had a carrier at 59 MHz (just below Fs), it would now look as though its at 1 MHz when I look at it through the transparent paper. But if I slid it to 59.5 MHz, it would appear to move toward 0 Hz. This is the effect of the chunks with the "-" sign - they end up looking like they are still 30 MHz wide, but it looks like they are backwards.

Your task is to select Fs such that all the carriers of interest are located somewhere in the center 80% of their respective chunk. If the carriers get too close to the partitions, there will be some processing problems later on. If there are only a few carriers, this is not usually a difficult task. If you need to grab signals anywhere in the band, this criteria cannot be met and you may have to do the brute force approach with high sample rate. You also need to try to get maximum separation between your signals. Imagine the folded paper - the farther apart the signals are, the easier it will be to isolate them with filters. If two carriers land on top of each other after folding, you will not be able to differentiate them later on.

Your A to D sampling will perform the fan-fold operation for you. Once sampled, you won't know the original carrier frequency unless you can infer it because you had a limited number of them to start with. But to use my example above, if I see a signal at 1 MHz, I could infer that it was the 59 MHz, as long as I was confident no unexpected extra signals would appear at the input of my sampler (signals at 1, 59, 61, 119, 121 MHz would all appear at the same place).

Now the caveats I mentioned :

Remember the Doppler shifts reverse, just as the spectrum reverses, for alternate bands. If you just need velocity, no problem, But if you need direction, you have to know what band your signal came from to know its sign.

Your A to D must have more than a 160 MHz analog bandwidth, no matter how slowly you sample it. Analog bandwidth usually exceeds the allowable clock rate for high speed parts, check the specs.

Phase noise increases for each successive sampling band. This means the chunk from 120 - 150 MHz in my example will have higher converted phase noise than the one from 0 -30 MHz. Since Doppler and phase noise are both low frequency FM / PM sideband phenomena, make sure your A to D clock is clean enough for the highest sub-sampled band.

Do not use clock oscillator modules that have internal phase locked loops for this kind of application. Most of the microprocessor oscillators are built with PLL's because its cheap, flexible, and because the processor only cares about frequency, not jitter or phase noise. You want a fundamental mode oscillator unless you are just looking for gross performance. If the data sheet does not give you phase noise specs, its probably a PLL type.

Signals that fall on the Fs/2 partitions will be unrecoverable - at least as far as direction is concerned. You may be able to get the velocity info, but I'd think it would be unreliable.

Good luck Steve

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email: snipped-for-privacy@jomega.com

Don't follow Nyquist. If you sub-sample the signal you don't have to down convert. Downconverting adds noise anyways.

Hello David,

Assuming you don't mean the Doppler spectrum could be 160MHz wide but that you want to be able to detect a carrier anywhere in this band with some Doppler shift riding on it: IMHO this may be the stage in the design process where to think about analog pre-processing. I/Q down conversion, range gating (if required) and some baseband low pass filtering, then send the I and Q baseband outputs off to the DSP.

The rest is "just software". Last time I said that I almost had a coffee mug thrown at me ;-)

Regards, Joerg

I read in sci.electronics.design that snipped-for-privacy@oads.com wrote (in ) about 'RF downconverting', on Mon, 26 Sep 2005:

What characteristics of the signal do you need to preserve? For example, if you want only to know the frequency, a broadband frequency discriminator would give you a DC voltage proportional to frequency.

You would need to mix with, say, a 1 GHz signal to transfer your range to 1080 MHz +/- 80 MHz.

Oh, sorry, that's an analogue method, and therefore useless. (;-)

...but processing gain reduces noise;-)

Hello Thomas,

So does sampling ;-)

Regards, Joerg

Hello Dave,

Then you really have to deal with +/- 80MHz bandwidth. Either you can use one heck of an expensive array of DSP or go analog. I would certainly think some more about an analog solution. The challenge on that one will be the allpass phase shifters.

On a side note: Can you move this stuff a bit higher in center frequency? The range below 30MHz is heavily polluted with EMI these days.

Regards, Joerg

I'm assuming that you are trying to measure just the frequency of the shifted signal in order to determine the velocity of some object. Just a few questions: What is the desired frequency resolution? What is the capture/processing time aloud? What is the signal to noise ratio?

Thomas

Hello John,

They are there to re-combine upper and lower sideband. Look at the "direct conversion method", "zero IF" or "Weaver method" of SSB reception. In Doppler that would be approaching target and retracting target.

This brings up a thought (David): Is the target direction known? If yes, one might forego directional capability which makes an analog Doppler design a lot easier. Won't work with multiple targets though if they are on either side of center frequency.

Regards, Joerg

I read in sci.electronics.design that Joerg wrote (in ) about 'RF downconverting', on Mon, 26 Sep 2005:

What are the phase-shifters for? Are you assuming that the OP wants to recover the phase of the signal, not just the frequency?

Hmm. Assuming you could square up the signal before I/Q downconversion it'd just be quadrature decoding -- it'd have to be done in an FPGA or with darn fast logic, but quadrature decoding at 80MHz should be quite doable.

As I understand it, he has 160 MHz of signal bandwidth. He can't undersample.

--Mac

Is only a single target, or could there be several?

If you know there is only a single target with Doppler, or if you are only interested in the Doppler of the strongest return, you can just just divide the frequency by two or four prior to sampling (or skip sampling and just use some kind of frequency counter)

If worse comes to worst, maybe you will just have to sample at 400 MHz. ;-(

Analog Devices makes some 12- or 14-bit 400 MHz ADC's now, I think. There is also an outfit called Aquiris (IIRC--maybe try without the 'u') which makes some fast, precise ADC's.

Sounds like an interesting project. ;-)

--Mac

It is not a question of sampling rate, it is a question of dynamic range. What is your minimum detectable signal requirement and how far down from the carrier is that? The doppler is a tone, so it is only a matter of first deterring which band of your bandpass sampling contains it, then decimate the sample record, window the data to increase frequency resolution, and integrate the complex multiplied phase corrected data as necessary- or something like that. The A/D front ends are very good these days with bandwidths well in excess of 320MHz, so that the only resource requirement will be memory.

In article , Mac wrote: [...]

The truth is that you can always undersample. It just causes the signal to be folded back on its self by aliasing. If you can live with not knowing whether the signal is at XHz, (N-X)Hz, (X-2N)Hz, ... etc undersampling may be ok.

If you know that the signal doesn't changing in frequency, you can use different undersampling rates to figure out the true frequency. The time taken to get the answer is longer than if you maintained the full bandwidth.

You took the words right out of my mouth Ken. I have used this technique before where I switched the sub-sampling rate to determine true frequency. Works great. If fact, I also have tried a technique where I sub-sampled at a pseudo-random rate then processed it with the same PR rate. It worked but was a little noisy.

It really depends on the dynamics of the OP signal. Sub-sampling might not work or might be the best solution. Looks like we might have lost the OP in this thread and will never know.

Thomas

Hello Thomas,

Pseudo-random can work nicely. AFAIR Skolnik's Radar Handbook or a similar publication has a set of staggered PRFs in there (in this case that would become sampling rates) that was optimized to calculate out target ambiguity in a reasonable time.

David mentioned knots. If that means ships there should be plenty of time. He mentioned 1MHz shift being 0.5 knots, meaning 40 knots full scale over 80MHz so it couldn't be aircraft. Unless it was the Wright flyer ;-)

Regards, Joerg