i was wondering why do engineers use Decibel (dB) to represent some signal / noise or even gain. what is the logic behind it?. why not just say the Signal/Noise ratio is 5, amplifier gain is 5 rather than say 20dB.
Well as you know the decibel is a logarithmic representation, there are several distict advantages to representing simple ratios in this fashion:
1. Much of the physical worlds behaviour is non-linear and therefore is conveniently represented using logarithimic scales similar to decibels. In fact the orgins of the use of decibels stem from work by Alexander Graham Bell who invented the telephone - human hearing perception is
logarithmic by nature.
2. Decibel representation alows for very large and very small ratios to be represented by a convenient value, that is manageable from an engineering perspective. I'm sure there are many others, but these are the two that spring to mind.
Another example that has sprung to mind that is loosely related to the above two is that of representing data (that is often logarithmic in form, or of lareg/small ratios).
An example for you to look at is a Bode Magnitude Plot which is widely used in Control Engineering or Signal Processing as a way of viewing the magnitude response of a system transfer function. If the magnitude data is plotted on a logarithmic scale, i.e. the magnitude or gain is ploted in decibels, against the log of the frequency, then the drop-off characteristics of the transfer function are easily deduced and understood. This information could not be (easily) deduced from purely linear data.