What The Heck Is A Decibel?

Maybe "decibel" is not part of your normal vocabulary but it is a term we all occasionally read or hear used. Typically it has to do with noise levels - we use decibels to describe loud or soft sounds. US government research even suggests a safe exposure sound limit of 85 decibels for eight hours a day. We frequently hear the term but - have you ever wondered what a "decibel" really is? Let's take a look.

Decibel (abbreviated dB) measurement is a logarithmic measurement typically of a output/input ratio of power or voltage. According to Wikipedia, the decibel originates from methods used to quantify reductions in audio levels in telephone circuits. Over distance any type of transmission media (copper wire, fiber optic lines, wireless) signal gets lost. The simplest way to think of a transmission system is as a box with signal going in and signal coming out the other end. In the diagram below we'll use P_in for our input signal and P_out for our output signal.
P_loss in the diagram is the power lost as the signal moves from the input to the output of the system. Any communications system signal is going to lose strength as it moves from one point to another due to things like resistance, capacitance and inductance that are all integral parts of any transmission system. Heat (as in hot days) can be a major problem for cable and telephone companies because wire resistance increases with heat causing more power to be lost in the delivery system. Sometimes signal loss is so significant amplifiers have to be added to a communications links to clean up and boost signal strength. Let's take a look at how decibels are calculated.

Power loss in dB is calculated by multiplying 10 times the base-10 log of the output power (P_out) divided by the input power (P_in). Let's look at an example where P_in is 20 Watts (or 20W) and a P_out is 15W.

P_loss in dB = 10 x log₁₀(P_out/P_in)

P_loss in dB = 10 x log₁₀(15W/20W)

P_loss in dB = 10 x log₁₀(.75)

Using a calculator to take the base-10 log of .75 we get -.125 Don't miss the negative sign - it is important here - it indicates power is being lost in the transmission system. Continuing with our equation.

P_loss in dB = 10 x (-.125)

P_loss in dB = -1.25dB

So, in this transmission system example, our output signal is said to be down (referencing the negative sign) 1.25 dB.

Let's work one more calculation, this time using a P_in of 16W and a P_out of 8W. Not a very efficient transmission system if we are losing half the power we put in. Let's see what we get for decibel loss working through the equation.

P_loss in dB = 10 x log₁₀(P_out/P_in)

P_loss in dB = 10 x log₁₀(8W/16W)

P_loss in dB = 10 x log₁₀(.5)

Using a calculator to take the base-10 log of .5 we get -.3 Again - don't forget the negative sign. Continuing with our equation.

P_loss in dB = 10 x (-.3)

P_loss in dB = -3dB

In this example, the system is losing half the input power and our output signal is said to be 3dB down. This is important to remember - for every 3 dB power decreases or increases by 50%. How do we know if it is increases or decreases? By that very important positve or negative sign!

In a future post we'll take power calculations a little further and discuss something called the dBm Scale.

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Update 01/25/10

Homework: If P_in is 7W and P_out is 5W what is the P_loss in dB?


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