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Thomas Dehaeze 2020-11-05 16:00:40 +01:00
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content/zettels/signal_to_noise_ratio.md
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@ -4,20 +4,13 @@ author = ["Thomas Dehaeze"]
draft = false
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Backlinks:
- [Power Spectral Density]({{< relref "power_spectral_density" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
- [Piezoelectric Actuators]({{< relref "piezoelectric_actuators" >}})
- [Position Sensors]({{< relref "position_sensors" >}})
Tags
: [Electronics]({{< relref "electronics" >}}), [Dynamic Error Budgeting]({{< relref "dynamic_error_budgeting" >}})
## SNR to Noise PSD {#snr-to-noise-psd}
From ([Jabben 2007](#orgae2d3e0)) (Section 3.3.2):
From ([Jabben 2007](#org4650879)) (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.
@ -77,6 +70,7 @@ If the wanted full range and RMS value of the noise are defined, the required SN
<div></div>
Let's say the wanted noise is \\(1 mV, \text{rms}\\) for a full range of \\(20 V\\), the corresponding SNR is:
\\[ S\_{snr} = 20 \log \frac{\frac{20/2}{\sqrt{2}}}{10^{-3}} \approx 77dB \\]
</div>
@ -84,7 +78,7 @@ 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](#org1022284)):
From ([Fleming 2010](#orgf1518db)):
\\[ \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\\).
@ -104,6 +98,6 @@ The peak-to-peak noise will be approximately \\(6 \sigma = 1.7 nm\\)
## Bibliography {#bibliography}
<a id="org1022284"></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="orgf1518db"></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="orgae2d3e0"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.
<a id="org4650879"></a>Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.