Ethan,
you can easily calculate the noise voltage density distribution Vn(f) in V/sqrtHz of
an NRZ unipolar pseudorandom bit sequence of amplitude A (15V, in your case) driven by a clock
signal with frequency Fck and period Tck=1/Fck, like this:
At DC: Vn(0)= A/2
At all other frequencies: Vn(f)=A*Tck*sin(x)/x where x = pi*f*Tck
Here sin(x)/x is the classical sinc(x) function with nulls at the clock frequency
Fck and all its integer multiples.
Trace this curve with a dB vertical scale [20*log(Vn)], and you will then see that
the noise voltage density distribution is almost flat only up to about 1/10th of the clock
frequency.
At 1/4th of the clock frequency it goes about 1 dB down, at 0.5*Fck the level is about
4 dB down, and 0.75*Fck it's about 10 dB down.
In theory -and considering ideal NRZ pulses- the effective noise spectrum coming out
from your circuit is this same characteristic combined with the frequency
response of the subsequent filters.
But be careful: when simulating the circuit with LTspice there is another parameter
that could play a role in shaping the displayed FFT trace of the filtered noise:
the maximum timestep (Tmax) used by the simulation engine. Its effect is to convolute
the noise signal with a second sinc function that can somewhat distort the real response, hence it
is a good rule to keep it at least ten times smaller than the clock period of the
PRBS noise generator.
You can play with this parameter looking at the FFT of an LTspice's behavioral noise
generator, like for instance a "white" with V=0.1*white(1e6*time). Begin with a transient
simulation setting a maximum timestep of 0.1u, and then repeat it but setting it to 1u and then
then to 10u, and see the differences in the displayed traces
A last comment: maybe I’m wrong, but it seems that the primitive polynomial of your generator
is x^31+x^13+1. Now, in order to get the maximum length of the sequence this polynomial should
be x^31+x^28+1 (or its complementary x^31+x^3+1).
I have uploaded in the Temp folder the file <PRBS_Maxlenght_31.asc>, a modified version of your
circuit reflecting the latter structure, plus an initialization circuit added to the first register that avoids
the need for an AC coupling in the feedback.
Ethan Winer
John Woodgate
