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## Re: [Discuss-gnuradio] Number sink unit to dBm

 From: Marcus D. Leech Subject: Re: [Discuss-gnuradio] Number sink unit to dBm Date: Thu, 28 Apr 2011 14:18:25 -0400 User-agent: Mozilla/5.0 (Windows; U; Windows NT 6.1; en-US; rv:1.9.2.15) Gecko/20110303 Thunderbird/3.1.9

```On 28/04/2011 1:55 PM, Matt Ettus wrote:
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There is a full WBX characterization with USRP1 here:

http://code.ettus.com/redmine/ettus/projects/public/documents

Noise figure with N200/N210 is 1-2 dB better.

Matt

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[Just because I'm in an expansive and tutorial-esque frame of mind this afternoon].
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Equivalent noise figures of ADCs are (relative to RF amplifiers) *just awful*. Equivalent noise figures of ADCs can be anywhere between 20 to 30dB (or more). For ADCs of equivalent "quality", the equivalent noise figure decreases with increasing number of bits, so all else being equal, you'd naturally expect that the equivalent noise figure of the 12-bit USRP1 ADC to be noticeably worse than the 14-bit N2xx ADC, and in fact, that is the case. This is a natural consequence of ADC "physics".
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Now the total noise figure of a system tends to be dominated by the noise-figure of the first gain stage in a sytem, that is because the noise figure at any given stage N, is always conceptually *divided* by the gain of the previous stage (N-1), so:
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Ntot(N) = Ntot(N-1) + (Noise(N) / GAIN(N-1))

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From this, you can see that the first-stage noise-figure and gain is quite important in determining the overall noise-figure of the system--as you move further away from the antenna, a given stage noise figure contributes less and less to the overall noise figure, provided that it is
```  preceded by a low-noise gain stage.

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With boards like the BASIC_RX and LF_RX, there are no gain elements, so observed noise-figure is entirely dominated by the less-than-wonderful equivalent noise figure of the ADC. Which means that for those boards, you need some low-noise gain ahead of them to achieve decent weak-signal performance. I've used 40dB of low-noise gain (ERA-3 GaAs MMIC), with 25-45MHz bandpass filters to make repeatable observations of galactic background noise at 38MHz with a BASIC_RX and USRP2.
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For other cards, the RX chain typically has an LNA at the head of the chain, followed by some amount of variable-gain amplification. Something to keep in mind about variable-gain amplifiers in the RF domain is that their equivalent noise figure gets *worse* as you reduce their gain. That's typically because the gain-control is implemented as an electrically-controlled step attenuator, and the noise-figure of an attenuator is identical to its attenuation--so a 10dB attenuator "contributes" 10dB of noise figure at whatever stage in the gain chain it is placed. This made obvious in the plots for the WBX--the noise-figure curve approaches a limit of 5dB as the gain is increased, with a peak noise
```  figure of roughly 22dB at the lowest (0dB) gain setting.

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