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Thomas Dehaeze 2020-09-04 15:44:12 +02:00
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content/zettels/analog_to_digital_converters.md
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@ -14,7 +14,7 @@ This analysis is taken from [here](https://www.allaboutcircuits.com/technical-ar
Let's note: Let's note:
- \\(q = \frac{\Delta V}{2^n}\\) the quantization in [V] (the corresponding value in [V] of the least significant bit) - \\(q = \frac{\Delta V}{2^n}\\) the quantization in [V], which is the corresponding value in [V] of the least significant bit
- \\(\Delta V\\) is the full range of the ADC in [V] - \\(\Delta V\\) is the full range of the ADC in [V]
- \\(n\\) is the number of ADC's bits - \\(n\\) is the number of ADC's bits
- \\(f\_s\\) is the sample frequency in [Hz] - \\(f\_s\\) is the sample frequency in [Hz]
@ -23,9 +23,9 @@ 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](#org5158d30)). 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](#orgf06d261)).
<a id="org5158d30"></a> <a id="orgf06d261"></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\\)" >}}

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