---
aliases:
- /2008/03/decibels-db-and-dbm-in-terms-of-power
categories:
- astrophysics
date: 2008-03-29 02:13
layout: post
slug: decibels-db-and-dbm-in-terms-of-power
title: Decibels, dB and dBm, in terms of Power and Amplitude

---

<p>
 It's not difficult, just always having some doubts...
 <br/>
</p>
<h4>
 Power
</h4>
<br/>
$latex L_{dB} = 10 log_{10} \left( \dfrac{P_1}{P_0} \right) $
<br/>
<br/>
10 dB increase for a factor 10 increase in the ratio
<br/>
<br/>
3 dB = doubling
<br/>
<br/>
40 dB = 10000 times
<br/>
<h4>
 Amplitude
</h4>
<br/>
$latex L_{dB} = 10 log_{10} \left( \dfrac{A_1^2}{A_0^2} \right) = 20 log_{10} \left( \dfrac{A_1}{A_0} \right)  $
<br/>
<h4>
 dBm
</h4>
<br/>
dBm is an absolute value obtained by a ratio with 1 mW:
<br/>
<br/>
$latex L_{dBm} = 10 log_{10} \left( \dfrac{P_1}{1 mW} \right) $
<br/>
<ul>
 <br/>
 <li>
  0 dBm = 1 mW
 </li>
 <br/>
 <li>
  3 dBm ≈ 2 mW
 </li>
 <br/>
</ul>