SNR and Receiver Gains - Charles's Questions Answered

[Charles77]

Dear all,

I have questions regarding to the relations betw SNR and receiver gains (digital and analog):

We have a system that allows us to set the analog receiver gain (ARG) and digital receiver gain (DRG). The signal doubles if we increase one integer of either ARG or DRG (eg from 12 to 13), and the filling factor of ADC also doubles (eg from 45% to 90%). My question is: Whether the SNR changes or not in this case? We tested but could not confirm.

Thanks!

Charles

 

[chroot]

There isn't enough information here about your system for us to be able to help.

- Warren

 

[Bob S]

Your SNR is determined almost entirely by the first-stage input analog amplifier, the KTB noise, and the noise figure of the first stage. The noise between the first and second stages will contribute some, and less if the gain of the first stage is increased. Mixers (I.e., down-converting) introduce some gain loss and noise. If you are digitizing the output, then the granularity of the ADC will contribute some additional noise, so filling the ADC will help.
Bob S.
[added] I was once told that by "dithering" the input signal (deliberately adding a little noise signal before digitizing), I could average over any granularity of the ADC and improve the SNR. I proved this to be untrue, both mathematically and empirically. Conversely, dithering reduces the SNR.

 

[Charles77]

Thank you very much!
Do I understand that (1) the Analog Receiver Gain does NOT change the SNR (because the amplifier does not distinguish noise and signal)? (2) the Digital Receive Gain does not change the SNR significantly if the digitization noise is NOT a problem?

Thanks!

 

[Charles77]

There isn't enough information here about your system for us to be able to help.

- Warren

Thank you very much!
We have analog and digital amplifiers and can adjust the Analog Receiver Gain and DRG.

Do I understand that (1) the Analog Receiver Gain does NOT change the SNR (because the amplifier does not distinguish noise and signal)? (2) the Digital Receive Gain does not change the SNR significantly if the digitization noise is NOT a problem?

Thanks!

 

[berkeman]

Thank you very much!
Do I understand that (1) the Analog Receiver Gain does NOT change the SNR (because the amplifier does not distinguish noise and signal)? (2) the Digital Receive Gain does not change the SNR significantly if the digitization noise is NOT a problem?

Thanks!

No on (1). If the first gain stage were noiseless (or had negligible noise comparred to the channel noise), then it wouldn't affect the SNR. But that is not usually the case. I believe that Bob pointed this out in post #3.

 

[sophiecentaur]

What do you mean by the term "digital receiver gain"?
If the word 'gain' is used, it sort of implies you're dealing with an analogue signal. Or are you talking of a digitally implemented receiver which samples and analyses the received signal? This will, surely, have an analogue front end (of course it will- you would, at least, need an ADC)?

 

[Charles77]

Thank you all!

I was talking about a GE MRI scanner.

It has Analog Receiver (Gain) and Digital Receiver (gain). both ARG and DRG can be automatically determined or manually changed. If automatically determined, the values change from scan to scan. And I want to know the SNRs with different ARGs and DRGs.

We made tests. When we increased the ARG (with fixed DRG), or DRG (with fixed ARG) by one (eg, from 12 to 13 for ARG, or 25 to 26 for DRG), the signal clearly doubled and noise seemed also doubled. That's why I thought SNR did not change with the two gains, if the signal was not too small.

 

[sophiecentaur]

If the noise originates in the front end of the receiver then changing gain will not affect it. However, the subsequent processing - such as bandwidth control and averaging / noise reduction, can improve SNR. Even things like the 'gamma' (linearity of the brightness of the display) - can alter the subjective effect of noise.
There is no easy answer to the original question. The manufacturers would know best, probably. In principle, however, once you have noise mixed with a signal, then merely changing gain makes no difference.

 

[Bob S]

If the noise originates in the front end of the receiver then changing gain will not affect it..

Even if you have a low-noise (NF=noise figure) input amplifier, excessive noise between amplifier stages will [STRIKE]increase[/STRIKE] decrease the SNR. If a low NF input amplifier has 10 dB gain, and the second amplifier has a high NF, the SNR will be reduced. In this case, increasing input amplifier gain will improve SNR.
Bob S

 

[sophiecentaur]

I agree in principle but what sort of a design introduced more noise along the chain? This kit must be very costly so I would imagine they have done their very best. 10dB seems to be a low value for the gain of a first stage (before any gain control) but I don't know the frequency involved so perhaps that is representative.