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# What is Decibel Representation for Wireless Communications?

## 1. What is dB Representation?

‘**Decibel**’ is a very common representation used across several disciplines of STEM *(Science, Technology, Engineering and Mathematics)*. An electronic engineering student might have never missed coming across the terms‘**amplifier gain**’, **signal-tonoise ratio**’, ‘**antenna gain**’, ‘**return loss**’, ‘**path loss**,and so on. One thing common in all of them is that they are all expressed in ‘decibels’(dB). The decibel representation (dB) is to express magnitudes that vary over large range of levels, in a single plot.

## 2. What is the Definition of decibel (dB)?

The dB representation maps the ratio of two comparable quantities in the linear scale onto the logarithmic scale. Out of the two quantities expressed as a ratio, one is usually a reference quantity like reference power, voltage, and current and so on.

$$\frac{Y}{X}=\frac{10}{1}=10(linear\:scale)\longleftrightarrow10 dB(logarithmic\:base\:10\:scale )$$

The logarithm (base 10) of a number is actually the

*“number of times ‘10’ must be multiplied by itself so that we arrive at the number”*.

The decibel value represents the ratio of two comparable quantities on the logarithm base 10 scale.

Logarithms are expressed in many bases but some of the commonly used bases are

*base-10*and*base-2*. Natural logarithm follows base-e where ‘e’ equals 2.718. The following equation explains the conversion from linear value to logarithmic value.

**45(in linear scale)=log _{10}(45)=1.653(in logarithmic scale)**

**10 multiplied by itself 1.653 times gives 45. Thus, 1.653 is the logarithmof 45**

Thus, in this way, ‘1000’ just comes down to ‘3’ in logarithmic base-10 scale and we know that 10 multiplied by itself 3 times gives 1000.

### Some Common Examples

**Microbiology**A microbiologist examining the growth of a bacterial population is most likely to use ‘logarithms’ to interpret the laboratory results. To plot an exponentially growing analytic function, a logarithmic scale is used. ‘dB’ is based on logarithms.

**Sales figures**The yearly sales figures of automobilesare represented using logarithmic plots.

**Number of users on the internet**Increase in the number of users of the Internet over the years, growth of subscriptions to Amazon Prime over the years and the daily cases of recent COVID 19 are some of the remarkable examples where logarithmic scale is used for representation of data.

**Received power levels in mobile communications**In mobile communications, the received power levels vary over several orders of magnitude and in order to plot those values and study them conveniently, we expressed the received power levels in the dB scale. We use a reference value to express the received power levels.

If 1 milli-watt is used as the reference, we represent the power level in **dBm**, which means, received power level with respect to 1 milli-watt.

**A positive dBm indicates that the received power level is greater than 1 milli-watt while a negative dBm indicates that the received power level is less than 1 milliwatt.**

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