Allan deviation power expansion

Question

In the 'Hand Book of Frequency Analysis' S3.2, by W.J Riley the frequency stability of an oscillator is expressed as a combination of power-law noises of the form $S(f)\propto f^\alpha$, where $f$ is a Fourier frequency and $\alpha$ the power law exponent. For example, some of the leading exponents are related to noise terms

1. White noise, $\alpha=0$
2. Flicker(pink) noise, $\alpha=-1$
3. Random walk(brown) noise, $\alpha=-2$

These noise terms have been identified with different slopes $\mu$ on the Allan deviation curve

1. White noise, $\mu=-\frac{1}{2}$
2. Flicker(pink) noise, $\mu=0$
3. Random walk(brown) noise, $\mu=\frac{1}{2}$

The value of the line with $\mu=0$ slope is referred to as bias instability, does this mean that any source of flicker noise in a system causes bias instability in that system? And to reduce the bias instability in that system you would need to locate and remove those flicker noise sources?

Answer 1

I'd say yes. Flicker noise is what limits the averaging in a Allan deviation. If you have only white noise, you can measure infinitely long and you will always decrease your error. Flicker noise will give you a noise floor.