{"id":2080,"date":"2018-09-28T18:10:06","date_gmt":"2018-09-28T22:10:06","guid":{"rendered":"http:\/\/www.circuitcrush.com\/?p=2080"},"modified":"2021-06-30T16:49:36","modified_gmt":"2021-06-30T20:49:36","slug":"the-decibel","status":"publish","type":"post","link":"https:\/\/www.circuitcrush.com\/the-decibel\/","title":{"rendered":"All About the Decibel"},"content":{"rendered":"<p>There are some things in the world of electronics that are just confusing to people, though they are actually simple underneath. The decibel is one of them.<\/p>\n<p>If you\u2019re into electronics you probably have heard the term decibel or dB thrown around.<\/p>\n<p>Even if you\u2019re not an electronics enthusiast at all, you may have heard the term used in situations dealing with sound.<\/p>\n<p>Understanding the decibel (or dB) is important for any aspiring electronics geek.<\/p>\n<p>Decibels show up in amplifier design, filter design, Bode plots, antenna specs and more.<\/p>\n<p>Fortunately, the concept of the decibel is relatively simple once you understand it. In fact, this post will probably be shorter than most of the others due to the simplistic nature of this unit.<\/p>\n<p><!--more--><\/p>\n<p>Now, let\u2019s talk about decibels.<\/p>\n<h1><strong>The Decibel<br \/>\n<\/strong><\/h1>\n<h2><strong>Quick History of the Decibel<br \/>\n<\/strong><\/h2>\n<p>Historically, the bel was used to measure the ratio of two levels of power or power gain.<\/p>\n<p>This unit is named after the famous inventor of the telephone &#8212; Alexander Graham Bell.<\/p>\n<p>The problem is that the bel is a big, clunky unit that is mostly impractical to work with because it represents a rather large change in levels. Most of the time you need something smaller with better resolution. Because of this, few people use the bel these days.<\/p>\n<p>Enter the decibel.<\/p>\n<p>As you may know, the prefix <em>deci<\/em> means one-tenth. Therefore, a decibel is one-tenth of a bel and is also a way easier unit to work with.<\/p>\n<h2><strong>So, What is a Decibel?<br \/>\n<\/strong><\/h2>\n<p>In electronics, you\u2019ll often encounter situations where you\u2019ll need to compare the power or amplitude of two signals.<\/p>\n<p>The basis for the decibel stems from the logarithmic response of the human ear to the intensity of sound. There is genius in nature and as we\u2019ll soon see this type of response allows us to perceive a huge range of sound levels.<\/p>\n<p>Perhaps you\u2019re familiar with logarithms. Or maybe not.<\/p>\n<p>This isn\u2019t a math blog, but just so we\u2019re all on the same page I\u2019ll give a quick example of what a logarithm is for those who are new to them.<\/p>\n<p>Consider equation 1.<\/p>\n<p><em>log<sub>10<\/sub>(100) = ?<\/em> (eq. 1)<\/p>\n<p>If I wanted to state equation 1 in words, I would say something like <em>10 raised to what power equals 100?<\/em><\/p>\n<p>Logarithms can be in different bases, but for the purpose of the decibel they are in base 10. When writing logarithms in base 10, we usually infer the 10 rather than writing it out, so equation 1 normally appears as equation 2.<\/p>\n<p><em>log(100) = ? <\/em>(eq. 2) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[the fact that there\u2019s no subscript after <em>log<\/em> means it\u2019s in base 10]<\/p>\n<p>When writing logarithms is other bases, like base 2, the subscript is included so we know what base it\u2019s in.<\/p>\n<p>In case you didn\u2019t know, the answer to the equation above is 2, because 10<sup>2<\/sup> equals 100.<\/p>\n<p>Logarithms can sound intimidating if you\u2019re new to them, but the concept is simple. If you\u2019re unfamiliar with them the Internet or an algebra book can help. Understanding the basics of logarithms will be helpful in understanding the decibel.<\/p>\n<p>So, let\u2019s answer the question <em>what is a decibel?<\/em><\/p>\n<h3 style=\"text-align: center;\">Become the Maker you were born to be. Try <a href=\"https:\/\/learnarduinonow.com\">Arduino Academy<\/a> for FREE!<\/h3>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter  wp-image-4238\" src=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2.png\" alt=\"\" width=\"407\" height=\"155\" srcset=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2.png 828w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-300x114.png 300w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-150x57.png 150w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-768x292.png 768w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>The decibel is simply a ratio of two power levels, as we can see in equation 3.<\/p>\n<p>dB = 10 log (P<sub>2<\/sub>\/P<sub>1<\/sub>) (eq. 3)<\/p>\n<p>Often in electronics, one may deal with ratios that can approach several million or more. For example, the ratio of an input power of 1 mW \u00a0to an output power of 1,000 W is 1,000,000.<\/p>\n<p>Graphing something like this would be unwieldy, so that\u2019s where the logarithm comes in. The logarithm \u201csquishes\u201d it down so it will fit. For example, consider a graph of a ratio of powers that\u2019s 10\u2019 long. By using logarithms, we can fit the same graph on a much smaller sheet of paper.<\/p>\n<p>Anyway, the dB has no unit as it is simply a ratio. It\u2019s just a number that describes how much bigger or smaller a quantity is than some other quantity.<\/p>\n<p>In equation 3, if P<sub>2<\/sub> is larger than P<sub>1<\/sub> the decibel value is positive, such as in the gain of an amplifier. If P<sub>2<\/sub> is less than P<sub>1<\/sub> the dB value is negative and represents loss or attenuation, such as the roll-off of a filter.<\/p>\n<h2><strong>Decibels Can Also Compare Voltages &amp; Currents<br \/>\n<\/strong><\/h2>\n<p>The decibel unit can also be used to compare voltage or current levels.<\/p>\n<p>However, remember that the relationships between power and voltage and power and current are not linear. A doubling of voltage or current results in a quadrupling of power.<\/p>\n<p>Fortunately, the logarithmic nature of the dB makes this easy to deal with. Equations 4 and 5 show the dB relationship for voltage and current.<\/p>\n<p>dB = 20 log(V<sub>2<\/sub>\/V<sub>1<\/sub>) (eq. 4)<\/p>\n<p>dB = 20 log(I<sub>2<\/sub>\/I<sub>1<\/sub>) (eq. 5)<\/p>\n<p>Notice the only difference (besides using voltage or current instead of power) is that we\u2019re now multiplying the logarithm by 20 instead of 10. This is due to one of the logarithm laws, which makes the exponent in the I<sup>2<\/sup> or V<sup>2<\/sup> terms \u201cpop out\u201d of the logarithm. For more on logarithm laws <a href=\"https:\/\/www.chilimath.com\/lessons\/advanced-algebra\/logarithm-rules\/\" target=\"_blank\" rel=\"noopener\">check this out<\/a>.<\/p>\n<h2><strong>Alternate Representations of the Decibel<br \/>\n<\/strong><\/h2>\n<p>In certain situations, it is often convenient to compare a power level with some other reference.<\/p>\n<p>Whenever you see another letter following dB, you know that some reference power is being used.<\/p>\n<p>What do I mean?<\/p>\n<p>For example, a unit that is often used in measuring power is the dBm. The terms dBm means decibels referenced to 1 mW of power.<\/p>\n<p>So, if you use 1 mW as the reference level you will calculate your decibel values with respect to one milliwatt. In this case, a power level of 10 dBm is 10 times 1 mW or 10 mW while 3 dBm is 2 mW and so on.<\/p>\n<p>Other common representations of the decibel are the dBW (reference level of 1 watt), the dBV (reference level of one volt), and the dB\u00b5V (reference level of 1 \u00b5V).<\/p>\n<h2><strong>Recognizing Decibel Power Ratios<br \/>\n<\/strong><\/h2>\n<p>You may be wondering how I knew that 3 dBm was equal to 2 mW or how we can come up with the dB value \u201con the fly\u201d without a calculator.<\/p>\n<p>There are several common power ratios you should learn to recognize and associate with the corresponding number of decibels. It\u2019s easier than you may think.<\/p>\n<p>Doubling power is one common scenario. In decibels, doubling power is the same as increasing it by 3 dB. It doesn\u2019t matter what power you start with, doubling power always results in a gain of 3 dB.<\/p>\n<p>Another common scenario is halving the power. Those familiar with filters may have heard about something called the half-power point (also called the cut off frequency and other things). This is the -3 dB point on the frequency response graph of the filter. A loss of 3 dB cuts the power in half. The negative sign in front of the 3 simply indicates loss rather than gain.<\/p>\n<p>Need to increase the power by 4? No sweat. Just double the decibel (from 3 dB) to get a gain of 6 dB. If you\u2019re instead cutting it into fourths it would be -6 dB. Similarly, increasing power by 8 (which is 4 times 2) will give you 12 dB, which is 6 dB doubled. These all rely on doubling. Easy enough.<\/p>\n<p>Another trick involves exponents of 10. For example, a change of 100 (which is 10<sup>2<\/sup>) is the same as a change of 20 dB (2 x 10 dB) because of the logarithm laws. Likewise, a change of 1,000 (10<sup>3<\/sup>) corresponds to 30 dB (3 x 10).<\/p>\n<p>Even with these handy tricks there are times when you\u2019ll either need a calculator or a chart. Toward that end, the chart below summarizes the relationship between many decibel values and the power change.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-2087\" src=\"http:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1.jpg\" alt=\"Decibel Chart\" width=\"1280\" height=\"720\" srcset=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1.jpg 1280w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1-600x338.jpg 600w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1-150x84.jpg 150w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1-300x169.jpg 300w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1-768x432.jpg 768w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-Chart-1-1024x576.jpg 1024w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/p>\n<p><strong><em>Figure 1: common power ratios and their decibel equivalents. The chart is for POWER, the dB values for voltage or current ratios are different.<\/em><\/strong><\/p>\n<p>As an extra bonus, the nifty chart below shows decibel values as they relate to sound.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-2082\" src=\"http:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-levels-of-common-sounds.png\" alt=\"Decibels and Sound\" width=\"363\" height=\"403\" srcset=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-levels-of-common-sounds.png 363w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-levels-of-common-sounds-135x150.png 135w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/Decibel-levels-of-common-sounds-270x300.png 270w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p><strong><em>Figure 2: decibels pertaining to sound. Note that 0 dB (the hearing threshold) is the reference.<\/em><\/strong><\/p>\n<h1><strong>Does That Ring a Decibel?<br \/>\n<\/strong><\/h1>\n<p>I told you this post would be shorter than usual.<\/p>\n<p>If you\u2019re still a bit shaky on logarithms, I suggest doing more research on the topic as it will be a good aid in understanding why decibel values are what they are and why people even use this unit in the first place.<\/p>\n<p>Hopefully the term decibel is no longer foreign to you after reading this. Next time someone talks about the decibel, it\u2019ll ring a bell!<\/p>\n<p>Leave a comment and tell us about your dream project. What does it do? How does it work? We\u2019d love to know. Or you can just talk about decibels.<\/p>\n<h2 style=\"text-align: center;\">Become the Maker you were born to be. Try <a href=\"https:\/\/learnarduinonow.com\">Arduino Academy<\/a> for FREE!<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-4238\" src=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2.png\" alt=\"\" width=\"828\" height=\"315\" srcset=\"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2.png 828w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-300x114.png 300w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-150x57.png 150w, https:\/\/www.circuitcrush.com\/wp-content\/uploads\/FB_Cover2-768x292.png 768w\" sizes=\"(max-width: 828px) 100vw, 828px\" \/><\/p>\n<a target=\"_blank\" href=\"https:\/\/www.drpeterscode.com\/index.php\"><img src=\"https:\/\/www.circuitcrush.com\/wp-content\/plugins\/dpabottomofpostpage\/apixel1x1.jpg\" ><\/a><table><\/table>","protected":false},"excerpt":{"rendered":"<p>There are some things in the world of electronics that are just confusing to people, though they are actually simple underneath. The decibel is one of them. If you\u2019re into electronics you probably have heard the term decibel or dB thrown around. Even if you\u2019re not an electronics enthusiast at all, you may have heard [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2084,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9,67],"tags":[119],"class_list":{"0":"post-2080","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-electronics","8":"category-theory","9":"tag-decibel","10":"entry"},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.circuitcrush.com\/wp-content\/uploads\/The-decibel.jpg","_links":{"self":[{"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/posts\/2080","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/comments?post=2080"}],"version-history":[{"count":4,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/posts\/2080\/revisions"}],"predecessor-version":[{"id":4290,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/posts\/2080\/revisions\/4290"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/media\/2084"}],"wp:attachment":[{"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/media?parent=2080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/categories?post=2080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.circuitcrush.com\/wp-json\/wp\/v2\/tags?post=2080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}