# Quantization error and standard deviation of noise : concepts?

#### TarikElec

Joined Oct 17, 2019
124
This question might be ambiguous as I am not sure what I do not know .
I have been reading about the quantisation error which is considered as standard deviation too.

1-the quantization error is calculated as the rms value of :
$P_{\text{noise}} = \frac{\text{V_FS}^2}{12 \times 2^{2n}}$
2-the standard deviation of quantization noise:
$\sigma = \frac{\text{LSB}}{\sqrt{12}}$

I am trying to understand this so i can start learning ow noise shaping and the use of average reduce noise.

#### MisterBill2

Joined Jan 23, 2018
18,934
Quantization error is not the same as noise. It is the uncertainty of the actual value versus the stated value of the center of that bit's spread of values. So the error can vary from zero to half of the step size. The way to reduce the uncertainty is to increase the number of steps for the overall span.

#### TarikElec

Joined Oct 17, 2019
124
The way to reduce the uncertainty is to increase the number of steps for the overall span.
if I understood well, you mean N number of bits?

#### MisterBill2

Joined Jan 23, 2018
18,934
if I understood well, you mean N number of bits?
YES, the number of bits is closely driven by the number of steps in the conversion ramp. MIcrovolts per step defines the maximum possible resolution. Of course, resolution does not guarantee accuracy, although adequate resolution is a requirement. Linearity also matters. So some converters show a best-fit straight line response as well.

#### TarikElec

Joined Oct 17, 2019
124
YES, the number of bits is closely driven by the number of steps in the conversion ramp. MIcrovolts per step defines the maximum possible resolution. Of course, resolution does not guarantee accuracy, although adequate resolution is a requirement. Linearity also matters. So some converters show a best-fit straight line response as well.
Understood. and how then we increase number of bits in sigma delta for example using noise which is a normal distribution?

#### MisterBill2

Joined Jan 23, 2018
18,934
Ok, that is a fair question, because to increase number of bits in sigma delta converter it is probably a challenge to increase the resolution of the control of the on and off times in the switching control signals. That is the basic limitation of accuracy in almost all binary controlled processes. Since I am not an expert in exactly how sigma-delta systems function, my advice goes no farther.
But in all cases, settability to an exact value is limited by the elements that define the resolution.