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Thomas Dehaeze 2021-05-02 16:28:46 +02:00
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content/zettels/analog_to_digital_converters.md
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@ -8,6 +8,11 @@ Tags
: [Electronics]({{< relref "electronics" >}}) : [Electronics]({{< relref "electronics" >}})
## Types of Analog to Digital Converters {#types-of-analog-to-digital-converters}
- Delta Sigma ([Baker 2011](#org1a9e622))
## Power Spectral Density of the Quantization Noise {#power-spectral-density-of-the-quantization-noise} ## Power Spectral Density of the Quantization Noise {#power-spectral-density-of-the-quantization-noise}
This analysis is taken from [here](https://www.allaboutcircuits.com/technical-articles/quantization-nois-amplitude-quantization-error-analog-to-digital-converters/). This analysis is taken from [here](https://www.allaboutcircuits.com/technical-articles/quantization-nois-amplitude-quantization-error-analog-to-digital-converters/).
@ -23,9 +28,9 @@ Let's suppose that the ADC is ideal and the only noise comes from the quantizati
Interestingly, the noise amplitude is uniformly distributed. Interestingly, the noise amplitude is uniformly distributed.
The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution). The quantization noise can take a value between \\(\pm q/2\\), and the probability density function is constant in this range (i.e., it’s a uniform distribution).
Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#org2f8924a)). Since the integral of the probability density function is equal to one, its value will be \\(1/q\\) for \\(-q/2 < e < q/2\\) (Fig. [1](#orga9627b6)).
<a id="org2f8924a"></a> <a id="orga9627b6"></a>
{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}} {{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@ -76,4 +81,7 @@ The quantization is:
{{< youtube b9lxtOJj3yU >}} {{< youtube b9lxtOJj3yU >}}
<./biblio/references.bib>
## Bibliography {#bibliography}
<a id="org1a9e622"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.