A question on adding noise and low-pass filer in Ltspice
For your first question: the voltage source has specified a resistance. In parallel with it, there's a current source which, by default, outputs a 0.5Vpp signal (the white() function). This means that this current is generated onto the (now) parallel resistance, Rser, resulting in a R*I amplitude. Therefore, Rser will set the amplitude of the noise. In your case, \$R_{ser}=3 =&gt; 3 * 0.5 = 1.5V_{pp}\$. If you need \$2V_{pp}\$, simply add an \$R_{ser}=4\Omega\$.

For your second question: the white() function generates a flat bandwidth that starts dropping at around 2*f_specified, when it's some 6dB lower. That's why you have white(2*f*time). So, the easiest approach would be to simply set your noise source for white(2*900*time). If, on the other hand, you need a lowpass filter, then, besides the obvious R8+C1, you also have R7+R_CE(Q1), to which you can also consider R8+R10+R(D3). D1 and D2 also have some parasitic capacitances, but they won't matter here. Still, R8||[R10+R(D3)] will make a voltage divisor with R7, soo they won't matter as much, provided you keep R9 much larger than R7 parallel with the whole dynamic resistance (impedance) of Q1&amp;co. A 10k should be fine. Then, a simple 1st order is calculated with: \$\omega=2\pi{f}=\frac{1}{RC}=&gt;C=\frac{1}{2\pi{f}{R}}=\frac{1}{2\pi{900}*{10k}}=17.68n\$. Choose an 18nF. To berify this, here's what LTspice has to say:



The input is reduced a bit by the previously mentioned divisor, plus there's a minor "shelf" filter due to interaction, while the final RC does the job.



Edit: Forgot to add that for your noise to be correctly displayed and calculated in LTspice, you'll need at some 10 times its highest bandwidth, so if your highest frequency of interest is 9kHz, then make your timestep as 1/90kHz. As per the suggestion in the comment, you can use a behavioural source, directly, incorporating the signal and the noise. For my part, unless it's just some quick sketch, I'd advise to only use behavioural sources when they absolutely cannot be replaced, as they have an inherent dynamic range loss (for orders of magnitude difference) due to their calculation "on the fly" of any point that is time-dependent, and they add quite the burden of computation, even when used with the undocumented flag nojacobi. Of course, the choice is entirely yours.

I'll add one more thing: for noise and, in general, for "delicate" low/high frequencies, .opt plotwinsize=0 should be a must, to preserve the waveshape.