# Quantization Noise Current Spectral Density

Started by August 10, 2003
```Hi,

I trying to calculate the Quantization Noise Current Spectral Density
with regard to the ADC input of my system. My system includes a C6711
DSK and an AIC23EVM Codec.

I think I'm right in saying that the formula for Quantization Noise
Current Spectral Density is given by -

((V/2^Q)^2)/6TR^2

where V is the voltage range at the ADC, Q is the number of bits -
quatization, T is the sampling time, and R is the load resistance.
Does this sound correct?

My ADC operates with a full-scale range of 1.0VRMS, 16 bit, 96kHz.
Therefor am I right in saying that my Quantization Noise Current
Spectral Density is -

(((2^3/2)/2^16)^2)/(6*1/96000*(R^2))

Should the Quantization Noise Current Spectral Density increase with
Sampling frequency??

Anyway, I'm implementing demodulation algorithms on the Codec input
signal, and outputting the result to the Codec DAC. I'd like to come
up with some way of representing the quantization noise that my system
will incur with respect an "identical" analogue system. How should I

Thanks.
```
```Your quantization noise will be at the ADCs and DACs, the quantization
noise will be negligible on the 32bit floating point processor. The
AIC23 is 16 bit for each channel if I remember correctly.

bg_ie@yahoo.com (Barry) wrote in message news:<731cea69.0308100958.5138bffa@posting.google.com>...
> Hi,
>
> I trying to calculate the Quantization Noise Current Spectral Density
> with regard to the ADC input of my system. My system includes a C6711
> DSK and an AIC23EVM Codec.
>
> I think I'm right in saying that the formula for Quantization Noise
> Current Spectral Density is given by -
>
> ((V/2^Q)^2)/6TR^2
>
> where V is the voltage range at the ADC, Q is the number of bits -
> quatization, T is the sampling time, and R is the load resistance.
> Does this sound correct?
>
> My ADC operates with a full-scale range of 1.0VRMS, 16 bit, 96kHz.
> Therefor am I right in saying that my Quantization Noise Current
> Spectral Density is -
>
>   (((2^3/2)/2^16)^2)/(6*1/96000*(R^2))
>
> Should the Quantization Noise Current Spectral Density increase with
> Sampling frequency??
>
> Anyway, I'm implementing demodulation algorithms on the Codec input
> signal, and outputting the result to the Codec DAC. I'd like to come
> up with some way of representing the quantization noise that my system
> will incur with respect an "identical" analogue system. How should I
>
> Thanks.
```
```
Barry wrote:

> Hi,
>
> I trying to calculate the Quantization Noise Current Spectral Density
> with regard to the ADC input of my system. My system includes a C6711
> DSK and an AIC23EVM Codec.
>
> I think I'm right in saying that the formula for Quantization Noise
> Current Spectral Density is given by -
>
> ((V/2^Q)^2)/6TR^2
>
> where V is the voltage range at the ADC, Q is the number of bits -
> quatization, T is the sampling time, and R is the load resistance.
> Does this sound correct?
>
> My ADC operates with a full-scale range of 1.0VRMS, 16 bit, 96kHz.
> Therefor am I right in saying that my Quantization Noise Current
> Spectral Density is -
>
>   (((2^3/2)/2^16)^2)/(6*1/96000*(R^2))
>
> Should the Quantization Noise Current Spectral Density increase with
> Sampling frequency??
>
> Anyway, I'm implementing demodulation algorithms on the Codec input
> signal, and outputting the result to the Codec DAC. I'd like to come
> up with some way of representing the quantization noise that my system
> will incur with respect an "identical" analogue system. How should I
>
> Thanks.

The r.m.s quantisation noise is given for rounding as

sigma = delta/sqrt(12)

where delta = dynamic range/ no of quantisation levels

no of quantisation levels = 2^B where B = no of bits.

Tom

```