Sample & Hold: Estimate jitter delay of an ADC I've got a question regarding the effects of sample and hold. 
My input signal is $x$, and my output signal $x_{SH}$. The error between the signals is $e_{SH} = x_{SH}-x$.

The sampling frequency is set to $f_s = 1000kHz$ and the jitter delay to $t_{jitter}=4\cdot 10^{-4}s$. 

The influence of the jitter is implemented in Matlab as the following: 

t = (0:N-1)/f_S; 
x = sin(2*pi*f*t); 
t_SH = t+Tjitter*(2*rand(size(t))-1); 
x_SH = sin(2*pi*f*t_SH); 
e_SH = x_SH-x; 
rxx = xcorr(x,x,'biased'); 
ree = xcorr(e_SH,e_SH,'biased'); 


Now I'd like to estimate $t_{jitter}$ using the formula:

$SNR = 20 \log_{10}\left[\frac{1/\sqrt{2}}{\Delta v_{rms}}\right]=20 \log_{10} \left[\frac{1}{2\pi f t_{jitter}}\right]\\$
$\Rightarrow t_{jitter} = \frac{1}{ 2\pi f \left(\sqrt{ \frac{P_{signal}}{P_{noise}} }\right) }=\frac{1}{ 2\pi f \left(\sqrt{ \frac{max(r_{xx})}{max(r_{ee})}} \right) }$

Now I only achieve the same result of $t_{jitter}$ if I add a factor of $\sqrt{3}$, which I can't explain why.

$\Rightarrow t_{jitter} = \frac{1}{ 2\pi f \left(\sqrt{ \frac{P_{signal}}{P_{noise}\cdot 3} }\right) }$

I'd be happy for some help! Thanks in advance!
I think the jitter to SNR formula is based on a gaussian jitter.

You use "rand" which yields uniformly distributed numbers. You should use randn() instead which yields numbers distributed according to a gaussian distribution.