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Update Content - 2020-10-15

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Thomas Dehaeze
2020-10-15 21:36:53 +02:00
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content/zettels/analog_to_digital_converters.md
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@@ -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.
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](#orgf06d261)).
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](#org5848c2b)).
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{{< figure src="/ox-hugo/probability_density_function_adc.png" caption="Figure 1: Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
@@ -48,7 +48,7 @@ Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we
\int\_{-f\_s/2}^{f\_s/2} \Gamma(f) d f = f\_s \Gamma = \frac{q^2}{12}
\end{equation}
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Finally, the Power Spectral Density of the quantization noise of an ADC is equal to:
@@ -62,7 +62,7 @@ Finally, the Power Spectral Density of the quantization noise of an ADC is equal
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Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz.