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content/zettels/signal_to_noise_ratio.md
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@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"]
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### Backlinks {#backlinks}
Backlinks:
- [Power Spectral Density]({{< relref "power_spectral_density" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
@ -17,7 +17,7 @@ Tags
## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#org620f0ec)) (Section 3.3.2):
From ([Jabben 2007](#org87840a5)) (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.
@ -29,7 +29,7 @@ From ([Jabben 2007](#org620f0ec)) (Section 3.3.2):
> \\[ S\_{snr} = \frac{x\_{fr}^2}{8 f\_c C\_{snr}^2} \\]
> with \\(x\_{fr}\\) the full range of \\(x\\), and \\(C\_{snr}\\) the SNR.
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Let's take an example.
@ -56,7 +56,7 @@ where \\(S\_{snr}\\) is the SNR in dB and \\(S\_\text{rms}\\) is the RMS value o
If the full range is \\(\Delta V\\), then:
\\[ S\_\text{rms} = \frac{\Delta V/2}{\sqrt{2}} \\]
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As an example, let's take a voltage amplifier with a full range of \\(\Delta V = 20V\\) and a SNR of 85dB.
@ -73,7 +73,7 @@ The RMS value of the noise is then:
If the wanted full range and RMS value of the noise are defined, the required SNR can be computed from:
\\[ S\_{snr} = 20 \log \frac{\text{Signal, rms}}{\text{Noise, rms}} \\]
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Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V\\), the corresponding SNR is:
@ -84,13 +84,13 @@ 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](#org094853a)):
From ([Fleming 2010](#orgc255675)):
\\[ \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 approximatively \\(6 \sigma\\).
The peak to peak amplitude is then approximately \\(6 \sigma\\).
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- noise density = \\(20 pm/\sqrt{Hz}\\)
@ -104,6 +104,6 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
## Bibliography {#bibliography}
<a id="org094853a"></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="orgc255675"></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="org620f0ec"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<a id="org87840a5"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.