RF Sampling

[jmsigler]

Hello, I have a quick question regarding sampling RF. Say I have an ADC referenced to 3.3v and am receiving a signal from a satellite at -130dBm. My thinking is that I need 144dB of gain to bring it up to 14dBm, which should be about 3v into a 50ohms. Is this correct thinking, or are there other things I haven't considered? My worry is that the thermal noise floor is somewhere around -111dBm, so would I need less gain to fit the noise into the range?

[T3sl4co1l]

You'll be getting the SNR back by processing, not analog filtering.  Give it enough gain to improve the noise figure of the ADC (related to its ENOB, noise performance and bandwidth -- you'll have to look up the data and figure this out) and do the rest in DSP.

Too much gain and not enough filtering in the front end, and you'll be screwed out of dynamic range.  Just a few dB more of a nearby interfering signal and *splat* goes the SNR of your desired signal (mostly due to IMD)...

Tim

[jmsigler]

That's a very low level signal and probably unrealistic to process due to noise and the high gain required unless there are particular characteristics of the signal modulation and receiver architecture that facilitate the acquisition.  Some signals can be received at levels below the noise floor if redundancy in the signal characteristics make it possible to apply some kind of simple (or complex) averaging/correlation techniques to effectively improve the the signal to  noise ratio.  But usually for such signals with mainstream relevance with complex modulations there are dedicated receiver ICs that have digital and analog filtering and so on to recover them.

So this is for experimenting with a GPS front end, which as you suggested, uses Gold Codes to pull the signal out of the noise in the DSP side of things. From what I've found, you can use a very low resolution (4-1 bits) adc to decode the signal. What is confusing me is how the amplification stage before the adc is calculated.

Give it enough gain to improve the noise figure of the ADC (related to its ENOB, noise performance and bandwidth -- you'll have to look up the data and figure this out) and do the rest in DSP.

Could you elaborate on this a little more. Say for example I use a TI THS1009 ADC (datasheet attached, relevant info on page 4), which has a SNR of 58-60dB. I've calcualted the NF of the ADC to be 62dB using the equation on page 4 of the attached MT-006 application note on the subject with SNR=60 B=4e^6 and Pfs = 14.1 (not sure if this is correct). How does increasing the gain improve the ADC's NF? I assume I'm using the wrong Pfs?

[bson]

I think Pfs = 14.1dBm looks completely wrong.  The THS1009 doesn't seem to present a AINP load other than 1) 10pF input capacitance and 2) 10uA peak leakage current.   Pfs is very small for FS @ 3.2V; 32uW is the FS leakage power (so Pfs is more like -45dBm) and I doubt the 10pF is a factor at 4MHz, but it depends on your source impedance.  If you buffer the input to drop the source impedance to some fraction of an ohm the 10pF disappears at your frequencies.  (But then you add another NF to the chain, so balance the effect of a buffer on the Friis sum vs the benefit of dropping Pfs; if you already have a low source impedance gratuitously adding another buffer doesn't help.)
So, NF=-45+174-60-66 = 3dB

That looks a lot more reasonable, no?

[jmsigler]

That does look a lot more reasonable, but the Analog Devices app note does say that it should be higher than you would expect and calculated 30dB in their calculation example.

[bson]

Sure, but their example has 52-something ohm external terminator in parallel with the 1k internal impedance, so their Pfs is much higher.  3.2V over 50ohm is 64mA!

[radar_macgyver]

The ADI app note uses that termination resistor to ensure that the input impedance is 50 ohms. Without it, the frequency response of the ADC would not be flat, due to interactions with the input capacitance and the source impedance.

To answer the OPs question, use MT-006 to calculate the ADC noise figure. Your results look ok (as they note, 60 dB NF seems high compared to most microwave parts, but is expected). Then do a cascade of the ADC with the preceding stages (LNA, filtering, additional amplification, etc) with Frii's formula, to get the total gain and noise figure of the system. This should tell you how it behaves for a -130 dBm input. Increasing the LNA gain will decrease the system's NF (as T3sl4co1l mentioned).

Also, consider the use of an impedance-matching transformer. As noted in MT-006, this helps to reduce the ADC's noise figure. As long as you're operating in a frequency range that lets you do this (10's of MHz) it's a nice way to improve the NF. It can be done at higher frequencies, but you use a transmission line balun instead of a transformer.

Finally, unless your -130 dBm signal has a bandwidth < 10 kHz, this doesn't seem feasible since thermal noise with 10 kHz bandwidth is -133.8 dBm, and a 3.8 dB system NF will kill the signal completely.

[valgamaa]

So this is for experimenting with a GPS front end, which as you suggested, uses Gold Codes to pull the signal out of the noise in the DSP side of things. From what I've found, you can use a very low resolution (4-1 bits) adc to decode the signal. What is confusing me is how the amplification stage before the adc is calculated.

If you want to start with something simple and add complexity, then the easiest way to start is to recognise that 16.368MHz is a common factor in the GPS system. With a 16.368MHz reference you can multiply it by 96 to get an LO (either multipliers or a PLL) that can down-convert the GPS signal to a 4.092MHz IF (actually 16.368/4). A simple analogue HP+LP to make a BP filter can condition the signal before hard-limiting the output. Sampling this at 16.368MHz makes the correlators relatively simple too.
This was a pretty standard architecture 15 years or so ago, and can work well without having to worry about signal level, AGC or anything else other than NF upto the mixer.
God luck with the project, the hardest thing about GPS is that there are no real specifications and everything is noise-limited.

[jmsigler]

The ADI app note uses that termination resistor to ensure that the input impedance is 50 ohms. Without it, the frequency response of the ADC would not be flat, due to interactions with the input capacitance and the source impedance.

To answer the OPs question, use MT-006 to calculate the ADC noise figure. Your results look ok (as they note, 60 dB NF seems high compared to most microwave parts, but is expected). Then do a cascade of the ADC with the preceding stages (LNA, filtering, additional amplification, etc) with Frii's formula, to get the total gain and noise figure of the system. This should tell you how it behaves for a -130 dBm input. Increasing the LNA gain will decrease the system's NF (as T3sl4co1l mentioned).

Also, consider the use of an impedance-matching transformer. As noted in MT-006, this helps to reduce the ADC's noise figure. As long as you're operating in a frequency range that lets you do this (10's of MHz) it's a nice way to improve the NF. It can be done at higher frequencies, but you use a transmission line balun instead of a transformer.

Finally, unless your -130 dBm signal has a bandwidth < 10 kHz, this doesn't seem feasible since thermal noise with 10 kHz bandwidth is -133.8 dBm, and a 3.8 dB system NF will kill the signal completely.

Frii's formula is interesting, I didn't realize that most of your systems noise comes from your initial amplification stage and clears up some confusion I had about why you would want a low noise LNA at the input and have higher noise gain stages later anyway. The GPS signal bandwith is 4mhz and I think 8mhz if you want to use the Galileo constellation.

If you want to start with something simple and add complexity, then the easiest way to start is to recognise that 16.368MHz is a common factor in the GPS system. With a 16.368MHz reference you can multiply it by 96 to get an LO (either multipliers or a PLL) that can down-convert the GPS signal to a 4.092MHz IF (actually 16.368/4). A simple analogue HP+LP to make a BP filter can condition the signal before hard-limiting the output. Sampling this at 16.368MHz makes the correlators relatively simple too.
This was a pretty standard architecture 15 years or so ago, and can work well without having to worry about signal level, AGC or anything else other than NF upto the mixer.
God luck with the project, the hardest thing about GPS is that there are no real specifications and everything is noise-limited.

Thats good advice, and I think I may start with this instead before trying a more complicated receiver.

[radar_macgyver]

The GPS signal bandwith is 4mhz and I think 8mhz if you want to use the Galileo constellation.

I seem to have missed the point that this was for GPS. In that case, the comment I had earlier about the -130 dBm signal approaching the noise limit needs to be revised. You also need to take into account the 'processing gain' of the correlator. IMO, this is a misnomer, the correlator is really a band-limiting filter which limits the noise bandwidth (and hence, noise power) without limiting the power of the correlated signal. Same principle as pulse compression in radars.

[valgamaa]

If you want to start with something simple and add complexity, then the easiest way to start is to recognise that 16.368MHz is a common factor in the GPS system. With a 16.368MHz reference you can multiply it by 96 to get an LO (either multipliers or a PLL) that can down-convert the GPS signal to a 4.092MHz IF (actually 16.368/4). A simple analogue HP+LP to make a BP filter can condition the signal before hard-limiting the output. Sampling this at 16.368MHz makes the correlators relatively simple too.
This was a pretty standard architecture 15 years or so ago, and can work well without having to worry about signal level, AGC or anything else other than NF upto the mixer.
God luck with the project, the hardest thing about GPS is that there are no real specifications and everything is noise-limited.

Thats good advice, and I think I may start with this instead before trying a more complicated receiver.

Remember to either filter the image noise or use an image-reject mixer for the down-conversion (filtering will require a narrow filter after the LNA, so the latter may be easier). The startling thing is that a 1-bit ADC (limiting IF) only reduces the sensitivity of the receiver by around 2dB compared with a 4-bit ADC and AGC.
If you want to make things easier then you could look for an SE4100 chip (I don't think they are made any more, but the company is owned by Skyworks now). This takes the output from an integrated antenna+LNA and gives the 4MHz output. If nothing else the data sheet would be worth reading.

[uncle_bob]

Hi

The GPS signal is roughly 20 to 30 db *below* the thermal noise in the same RF bandwidth. Yes, below the noise, not above the noise. There is very little advantage in going crazy with lots of bits in the A/D.

A *normal* GPS antenna has an amp in it. That amp runs between 20 and 60 db of gain. Unless you have a LOT of loss in your coax, there is still plenty of gain in that preamp to dominate the system noise with any rational amp in front of the A/D.

How does this even work? Well, if you take a 4 MHz wide signal and process it down to a 4 Hz bandwidth you get a signal processing gain of at least 60 db. You signal that was 20 to 30 db below the noise is now 30 to 40 db above the noise. (It's not quite that simple, but that's the right idea). The whole trick to a GPS receiver is how you lock on to the codes when they are buried in the noise. This is where things like 50 to 500 correlators come into the picture.

Lots of fun.

Bob