Update Content - 2022-03-15

content/zettels/analog_to_digital_converters.md

@@ -1,20 +1,20 @@
 +++
 title = "Analog to Digital Converters"
-author = ["Thomas Dehaeze"]
+author = ["Dehaeze Thomas"]
 keywords = ["electronics"]
 draft = false
 category = "equipment"
 +++
 
 Tags
-: [Electronics]({{<relref "electronics.md#" >}})
+: [Electronics]({{< relref "electronics.md" >}})
 
 
 ## Types of Analog to Digital Converters {#types-of-analog-to-digital-converters}
 
 <https://dewesoft.com/daq/types-of-adc-converters>
 
--   Delta Sigma ([Baker 2011](#orgbdb61af))
+-   Delta Sigma <baker11_how_delta_sigma_adcs_work_part>
 -   Successive Approximation
 
 
@@ -33,11 +33,11 @@ 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](#org4bd731c)).
+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](#figure--fig:probability-density-function-adc)).
 
-<a id="org4bd731c"></a>
+<a id="figure--fig:probability-density-function-adc"></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="<span class=\"figure-number\">Figure 1: </span>Probability density function \\(p(e)\\) of the ADC error \\(e\\)" >}}
 
 Now, we can calculate the time average power of the quantization noise as
 
@@ -59,13 +59,12 @@ Thus, the two-sided PSD (from \\(\frac{-f\_s}{2}\\) to \\(\frac{f\_s}{2}\\)), we
 \end{equation}
 
 <div class="important">
-  <div></div>
 
 Finally, the Power Spectral Density of the quantization noise of an ADC is equal to:
 
 \begin{equation}
   \begin{aligned}
-    \Gamma &= \frac{q^2}{12 f\_s} \\\\\\
+    \Gamma &= \frac{q^2}{12 f\_s} \\\\
           &= \frac{\left(\frac{\Delta V}{2^n}\right)^2}{12 f\_s} \text{ in } \left[ \frac{V^2}{Hz} \right]
   \end{aligned}
 \end{equation}
@@ -73,7 +72,6 @@ Finally, the Power Spectral Density of the quantization noise of an ADC is equal
 </div>
 
 <div class="exampl">
-  <div></div>
 
 Let's take a 18bits ADC with a range of +/-10V and a sample frequency of 10kHz.
 
@@ -87,7 +85,4 @@ The quantization is:
 {{< youtube b9lxtOJj3yU >}}
 
 
-
-## Bibliography {#bibliography}
-
-<a id="orgbdb61af"></a>Baker, Bonnie. 2011. “How Delta-Sigma Adcs Work, Part.” _Analog Applications_ 7.
+## Oversampling {#oversampling}