I experimented with a simple RF white noise generator using avalanche breakdown on an NPN BFR93A transistor. I've used a voltmeter and an ammeter to determine the breakdown voltage and associated spike in current.
Next, I want to verify the randomness of frequencies in the generated signal on my oscilloscope. I've attached a probe to a capacitor connected to the RF white noise generator. I've enabled FFT on the scope to view the frequency spectrum and flatness. The BFR93A is quite wideband, so I expect results up to about 1GHz, with good flatness from DC to about 200MHz. The image I've attached is what I saw in my testing and it looks reasonable, but I think there is an issue.
QUESTION: Should the yellow signal trace be the same tone of yellow instead of having a bright horizontal region? The bright horizontal region indicates amplitudes generated more often than the darker yellow tracings further away from the baseline. Right? I'd appreciate someone helping me understand what I see.
If there is an error, I'd appreciate hints about possible causes. Would using a larger or smaller capacitor help?
Thank you for your time and interest!

