The random numbers from the R230-USB True Random
Number Generator originates in a thermodynamical noise process, ofthen
referred to as Johnson Noise. This page present
high resolution noise spectra taken from the R200-USB noise amplifier.
These amplifiers must have a very high gain, and it is important to
check that no ringing, no influence from the USB bus, and no 50Hz/60Hz
from the mains, disturb or block the correct operation of the
amplifier. The noise spectra is taken with a HP8568B 1.5 GHz Spectrum
Analyzer. Unfortunately is the measurement not available for
downloading in digital format right now. The pictures may be downloaded
for detailed analysis.
Picture 1: START: 0Hz, STOPP 200kHz, Signal
scale 5dB/div logaritmic, Frequency scale 20 kHz/div linear,
Measurement bandwith 1000Hz.
Picture 1 show that slow frequencies, where we find disturbances such
as humming or click noise, is attenuated approx 25dB. This is
implemented by a filter. The filter pass the noise signal above a
frequency of approx 100kHz. We see that the signal is random, producing
a wide band some 25 dB thick. We can also see that all frequencies
contribute to the output signal with no gaps in the spectrum or any
dominating harmonic tones.
Picture 2: START: 0Hz, STOPP 10MHz, Signal
scale 5dB/div logaritmic, Frequency scale 1MHz/div linear, Measurement
Picture 2 show the spectrum used by the R200-USB. The reduction of the
signal amplitude as a function of frequency occurs due to a high
frequency cut-off in the amplifier. The output signal can be found up
to a frequency of 50MHz, but the amplitude above 12MHz is too low to
significantly influence the random numbers sampled from the amplifier.
In the important 1MHz to 5MHz frequency band we find no gaps or strong
Picture 3: CENTER: 2MHz, SPAN 1KHz, Signal
scale 10dB/div logaritmic, Frequency scale 100Hz/div linear,
Measurement bandwith 10Hz.
Picture 3 show a detail of a small part of the frequency spectrum. A
2MHz center frequency was selected, in an arbitrary way, for the
picture. Note the very low frequency span of just 1kHz from left to
right of the picture. We see that not even at this microscopic scale
can we find harmonic tones or other non-random signals. The note
"BATTERY" found on the pictures is to indicate that the HP8568B
possibly need a new backup battery to save instrument status at power
At last, an ordinary occilloscope picure of the R200-USB signal:
Picture 4: Ordinary time domain picture of the
R200 noise signal. 200ns/div and 200mV/div.