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Thomas Dehaeze
2022-03-15 16:40:48 +01:00
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content/zettels/signal_to_noise_ratio.md
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title = "Signal to Noise Ratio"
author = ["Thomas Dehaeze"]
author = ["Dehaeze Thomas"]
draft = false
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Tags
: [Electronics]({{< relref "electronics" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
: [Electronics]({{< relref "electronics.md" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting.md" >}})
## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#org55bd4a6)) (Section 3.3.2):
From (<a href="#citeproc_bib_item_2">Jabben 2007</a>) (Section 3.3.2):
> Electronic equipment does most often not come with detailed electric schemes, in which case the PSD should be determined from measurements.
> In the design phase however, one has to rely on information provided by specification sheets from the manufacturer.
@@ -23,7 +23,6 @@ From ([Jabben 2007](#org55bd4a6)) (Section 3.3.2):
> with \\(x\_{fr}\\) the full range of \\(x\\), and \\(C\_{snr}\\) the SNR.
<div class="exampl">
<div></div>
Let's take an example.
@@ -50,7 +49,6 @@ If the full range is \\(\Delta V\\), then:
\\[ S\_\text{rms} = \frac{\Delta V/2}{\sqrt{2}} \\]
<div class="exampl">
<div></div>
As an example, let's take a voltage amplifier with a full range of \\(\Delta V = 20V\\) and a SNR of 85dB.
The RMS value of the noise is then:
@@ -67,7 +65,6 @@ If the wanted full range and RMS value of the noise are defined, the required SN
\\[ S\_{snr} = 20 \log \frac{\text{Signal, rms}}{\text{Noise, rms}} \\]
<div class="exampl">
<div></div>
Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V\\), the corresponding SNR is:
@@ -78,14 +75,13 @@ Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V
## Noise Density to RMS noise {#noise-density-to-rms-noise}
From ([Fleming 2010](#org65ccddc)):
From (<a href="#citeproc_bib_item_1">Fleming 2010</a>):
\\[ \text{RMS noise} = \sqrt{2 \times \text{bandwidth}} \times \text{noise density} \\]
If the noise is normally distributed, the RMS value is also the standard deviation \\(\sigma\\).
The peak to peak amplitude is then approximately \\(6 \sigma\\).
<div class="exampl">
<div></div>
- noise density = \\(20 pm/\sqrt{Hz}\\)
- bandwidth = 100Hz
@@ -96,9 +92,9 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
</div>
## Bibliography {#bibliography}
<a id="org65ccddc"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org55bd4a6"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” <i>Ieee/Asme Transactions on Mechatronics</i> 15 (3): 433–47. doi:<a href="https://doi.org/10.1109/tmech.2009.2028422">10.1109/tmech.2009.2028422</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_2"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.</div>
</div>