in the paper: SΦ(Δf) is power density of phase, and L(Δf) is phase noise that we can get by doing pss and pnoise to a real vco, is this right?

and calculation of n and fc is based on the result of pss+pnoise.

how to use equation 21,26,29 to calculate n?

what does the fΔ in equation 25 mean? corner frequency, is it fc?

if i choose a Δf that is well above fΔ and well below fo, n=cfo^2*pi=L(Δf)*Δf^2*2,is this right?

in the figure below, at frequency 10^5Hz, the slope changes from -30dB to 20 dB, so fc is 10^5 Hz.

I choose Δf=100M to do the calculation. n= 2*10^(L(100M)/10)*2*(100M)^2=1.32.

then veriloga model of VCO is:

**Code:**// VerilogA for pllphasenoise, vco, veriloga
`include "constants.vams"
`include "/home/wzliu/project/phase.vams" // from Listing 2, includes disciplines.vams.
module vco(in, out);
input in; output out;
voltage in;
phase out;
parameter real gain = 40e6 from (0:inf); // transfer gain, Kvco (Hz/V)
parameter real n = 1.32 from [0:inf); // white output phase noise at 1 Hz (rad2/Hz)
parameter real fc = 100K from [0:inf); // flicker noise corner frequency (Hz)
analog begin
Theta(out) <+ 2*`M_PI*gain*idt(V(in));
Theta(out) <+ flicker_noise(n, 2, "wpn") + flicker_noise(n*fc, 3, "fpn");
end
endmodule