I am getting a strange result that either indicates I misunderstand something about the FFT algorithm implemented by the PicoScope or that a product I just purchased is behaving oddly. I thought it reasonable to seek an opinion on this forum in case the strange result isn't strange, but rather my confusion about the PicoScope's FFT algorithm.

The product I am testing is an AlphaLab LNA 10 Oscilloscope preamplifier (https://www.alphalabinc.com/product/lna10/). For the cost ($270), it has some impressive specs: 10-1000 gain; built-in single-pole LPF on the output settable from 1Hz - 1 MHz; single-ended or differential input; 4 nV/sqrt(Hz) noise for frequencies above 100 Hz (higher for lower frequencies - see url above); AC or DC coupling; output impedance = 470 ohms; input impedance = 500 Kohms. Unfortunately, the documentation is very sparse. For example, there is no indication what is the bandwidth of the amplifier (I presume it is at least 1 Hz - 1 MHz, but that is a guess from the web page information).

I decided to test the unit by generating a signal at one frequency using my signal generator and displaying the resulting spectrum on my PicoScope 4262/PicoScope 6. I ran a number of tests, but the strange result is demonstrated by focusing on the tests for 10 KHz. The test setup comprised a Rigol DG1022 signal generator, the LNA 10 and the Picoscope. For the set of tests discussed here these 3 instruments were configured as follows: LNA10 (20 KHz LPF, 10, 100, and 1000 gain); DG1022 (1 mV P-P amplitude, 50 ohm load); PicoScope (1-20 KHz span, 40 KS/s, 16,364 bins, 819 ms timegate, 30 segments averaging, dBm@50 ohms, Blackman-Harris windowing, and no termination on the PicoScope input).

The last PicoScope configuration setting (no-termination) requires some explanation. First at 10 KHz, the RG-58 cables are of sufficiently short-length that reflections should not be a problem. Second, I ran both no-gain and amplified experiments. In the former case the DG1022 was directly connected to the PicoScope, while in the latter case it was connected to the + input of the differential input (this how single-sided configurations should be set up according to the instructions). The output impedance of the LNA 10 is 470 ohms, so a 50 ohm termination at the PicoScope would be unbalanced. After playing around with various termination options, it seemed like the unterminated approach was the best.

I ran experiments that displayed the spectrum in both dBV units and dBm units. I concentrate on the dBm results here.

With these preliminaries in mind, I now describe the result that is puzzling me. The spectrum of the 10 KHz signal with no-gain (without using the LNA 10) is show in figure 1. The spectrum of the10 KHz signal with 1000 gain is shown in figure 2. The no-gain power at 10 KHz is -55.13 dBm, whereas the power at 10 KHz with 1000 gain is 3.971 dBm. This seems a reasonable result - 60 dB gain. In detail, the gain of the amplifier is specified as voltage gain. So, power gain will be the square of voltage and so 10^3 voltage gain gives 10^6 power gain or 60 dB.

However, if you look closely at the two spectra, there is something odd. The noise on the no-gain plot is quite a bit lower in relation to the peak at 10 KHz than in the 1000 gain plot. To make this clear, I normalized the 1000 gain plot by subtracting 59.101 dB so the peak at 10 KHz is at the same level (this only makes it easier to compare the plots; it doesn't represent a meaningful spectrum in any other way). This is shown in figure 3. It is clear that the length of the 10 KHz level to the underlying noise is shorter. This is made even clearer when the two plots are superimposed - figure 4. Noise in the two plots are about 20 dB apart.

I don't think this can be explained by processing gain, since both plots used the same number of bins and therefore correcting for processing gain would raise the noise an equal amount. The one thing I have considered is there is something that happens in the FFT that treats coherent and non-coherent signals differently (other than processing gain). One possibility is the averaging that the PicoScope implements somehow affects the spectrum. As I understand, this is how processing gain occurs, but maybe there is some other effect at play.

The other possibility is the LNA 10 is the cause of the problem. One possibility is the LNA is adding noise that is raising the 1000 gain spectrum. The span of the spectrum is 20 KHz and the number of bins is 16,364. This means each bin is about 1 Hz in width. If the specs of the LNA 10 are correct, only about 4 nV of noise would be added to each bin. 4 nV is equivalent to -167 dBm and the 1000 gain plot is well above -60 dBm, so the additional noise would have no observable effect.

Well, that is about where I am now. I would welcome any ideas that might solve this conundrum.

## PicoScope analysis of an LNA

### Re: PicoScope analysis of an LNA

It appears the shrinkage of carrier power in relation to noise power is an artifact of the LNA 10. I ran some further experiments at 50 KHz so I could also look at the spectrum with my Siglent SA, which has a lower frequency bound of 9 KHz. While the results of the Siglent analysis of the amplified signal had problems (due, I think to the impedance mismatch between the LNA 10 output - 470 ohms- and the Siglent input - 50 ohms, which caused reflections that corrupted the spectrum), I also captured the experiments with the PicoScope. This shows clearly that for the 10X, 100X and 1000X spectra, the distance between carrier power level and the noise level is approximately the same. The difference between the no-gain and amplified spectra still exists. I have attached 4 screenshots of the PicoScope showing the results for no-gain, 10X gain, 100X gain and 1000X gain. (It is clear from the level of the carrier in each spectrum which attachment corresponds to which level of amplification. The peak power value, corresponding to the carrier power, is shown at the bottom of each spectrum labeled "Amplitude at Peak").