Limiting Values of TDEV of Bottom Branch of Model

 Expressions for the asymptotic behaviour of the TDEV of the noise produced by the bottom branch of the noise model will now be obtained. From the form of (6.2) it is evident that  

$$\mathrm{TDEV}_w\to 0 \quad \mathrm{as} \quad \tau\to\infty$$ (54)

To obtain an expression for $\mathrm{TDEV}_w$ for small $\tau$ it is useful to recast (6.2) in the form

$$\mathrm{TDEV}_w(f)\approx \frac{K_w}{5\sqrt{\tau}}\sqrt{\frac{1}{1+\left(\frac{\tau B}{0.3}\right)^2}}$$

Then substituting $\tau=0.1s$ the following expression (6.7) for $\mathrm{TDEV}_w$ may be obtained

$$\mathrm{TDEV}_w(\tau=0.1s)\approx\frac{K_w}{1.58}\sqrt{\frac{1}{1+\left(\frac{B}{3}\right)^2}}$$

i.e.  

$$\mathrm{TDEV}_w(\tau=0.1s)\sim K_w\sqrt{\frac{1}{1+\left(\frac{B}{3}\right)^2}}$$ (55)