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Add dB unit stuff

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squeaky otter 1 year ago
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Signed by: dashie GPG Key ID: C2D57B325840B755
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title = "Cerveau"
author = "Dashie the otter"
description = "My draft notebook"
[output.html]
mathjax-support = true

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# Summary
[Introduction](./structure/intro.md)
- [Ham](./ham/main.md)
- [dB/units...](./ham/dbs_units.md)

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# DBs Units
## Refs
- https://www.youtube.com/watch?v=1mulRI-EZ80
## dB
A logarithmic expression of the <ins>ratio</ins> of two <ins>power</ins> levels:
\\[ 10 \times \log_{10}\left(\frac{P1}{P2}\right) \\]
| P1 | P2 | \\( \frac{P1}{P2} \\) | dB |
|----|----|-----------------------|----|
| 1 | 1 | 1 | 0 |
| 2 | 1 | 2 | 3 |
| 10 | 1 | 10 | 10 |
| 0.5 | 1 | 0.5 | -3 |
| 7.2 | 1.6 | 4.5 | 6.5 |
| 100 | 1 | 100 | 20 |
| 1000 | 1 | 1000 | 30 |
Since a dB is a <ins>ratio</ins>, it is not an absolute quantity, like a watt, etc.
To make it an absolute quantity, we must specify a <ins>reference</ins>.
## dB suffix
- dBm -> reference is milliwatt (mW)
- dbµ -> reference is microwatt (µW)
- dBmV -> reference is millivolt (mV)
The suffix can turn <ins>dB</ins> into an absolute quantity <ins>dbM</ins>.
### Example
10 MHz sinewave at 950mVpp into \\( 50\Omega \\).
\\[
Vpp = 950mV
\\]
\\[
Vrms = \frac{Vpp}{2 \times \sqrt{2}} = \frac{950mV}{2 \times \sqrt{2}} = 336mV_{rms}
\\]
Therefore, the power in the \\( 50\Omega \\) load is:
\\[
P = \frac{\left(Vrms\right)^2}{R} = \frac{0.336^2}{50} = 2.256mW
\\]
To express this in dBm, the reference is 1mW:
\\[
dBm = 10\times\log_{10}\left(\frac{2.256mW}{1mW}\right) = 3.53dBm
\\]
In dBµ, the reference is 1µW:
\\[
dBµ = 10\times\log\left(\frac{2.256 \times 10^{-3}}{1 \times 10^{-6}}\right) = 33.53dBµ
\\]
## Voltage ratios
The dB relates to <ins>power</ins>, so we have to calculate power.
\\[
10\times\log\left[\frac{\frac{V1^2}{R}}{\frac{V2^2}{R}}\right]
\\]
\\[
10\times\log\left[\frac{V1^2}{R}\times\frac{R}{V2^2}\right]
\\]
\\[
10\times\log\left[\frac{V1^2}{V2^2}\right]
\\]
\\[
10\times\log\left[\left(\frac{V1}{V2}\right)^2\right]
\\]
\\[
2\times10\times\log\left[\frac{V1}{V2}\right]
\\]
\\[
20\times\log\left[\frac{V1}{V2}\right]
\\]
Thus, our 950mVpp can be expressed in dBmv
\\[
dBmv = 20\times\log\left(\frac{336mV}{1mV}\right) = 50.5dBmV
\\]
## What about dBc ?
- dBc means it is dB relative to some "<ins>carrier</ins>" power leev
- very common in RF applications

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# Ham

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# Introduction
## What ?
Brain is like a draft notebook. A place to store all my notes.
## Why ?
While browsering [dev.to](https://dev.to), I found this article :
- [Takes Notes On Everything](https://dev.to/maxwell_dev/takes-notes-on-everything-3io)
Then I decide to give this concept a shot.
## Licence
You can do whatever the fuck you want with this.
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
Version 2, December 2004
Copyright 2017 dashie
Everyone is permitted to copy and distribute verbatim or modified
copies of this license document, and changing it is allowed as long
as the name is changed.
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. You just DO WHAT THE FUCK YOU WANT TO.

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