From 38a870aa2a389812e01f9bac999586dc8871393c Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 24 Sep 2020 16:00:15 +0200 Subject: [PATCH] Update Content - 2020-09-24 --- content/zettels/signal_to_noise_ratio.md | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/content/zettels/signal_to_noise_ratio.md b/content/zettels/signal_to_noise_ratio.md index 1169529..92c6eb5 100644 --- a/content/zettels/signal_to_noise_ratio.md +++ b/content/zettels/signal_to_noise_ratio.md @@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"] draft = false +++ -### 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. -
+
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}} \\] -
+
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}} \\] -
+
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\\). -
+
- 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} -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. . +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. . -Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University. +Jabben, Leon. 2007. “Mechatronic Design of a Magnetically Suspended Rotating Platform.” Delft University.