# Why express gain in dB's??

#### MossyIRL

Joined Dec 29, 2011
3
Hi,

Been looking on the site awhile now and looks great..
Just registered today..

Quick question for my exams coming up..
Why would we express the gain of an op amp in dB's?

I think it is because it is non linear and this gives us a straight line graph which is easier to work with.. Could sombody please confirm this or point me in the right direction??

Thank you..

#### MrChips

Joined Oct 2, 2009
21,666
The effect we feel when things change is non-linear.

A man whose net worth $100 doubles to$200 feels the same effect as another man whose net worth doubles from one million to two million dollars. That is why the stock market is drawn on a ratio scale (log scale).

Our perception of increased level of sound when all is quiet compared to when it is very loud shows the same effect. It is not the absolute increase we perceive but the relative increase. That is why we use a logarithmic scale. Decibels (dB) is a log scale.

Joined Dec 26, 2010
2,148
Expressing things on a logarithmic scale also has a number of advantages when it comes to displaying data on a graph. It can also clarify certain mathematical relationships. A graph of gain against frequency could be plotted on a linear scale, but if this included regions where the gain dropped far below its maximum value, it would be very hard to see what was going on.

At a thousand times less power, or 30dB down, the curve would look to have dropped to zero on a linear scale. Decibel plots can be used to show detail over many tens of dB, useful whether dealing with the response of an amplifier, a loudspeaker, or even a medical test of someone's hearing.

Another advantage of a decibel graph is that if the frequency axis is also made logarithmic, some frequency-dependent effects appear as linear slopes, whereas they would appear curved on a linear plot. For instance, the simplest sort of frequency dependency presents as a slope of 6dB for every doubling in frequency. The slope of the graph may therefore be helpful in analysing circuit behaviour.

#### Papabravo

Joined Feb 24, 2006
14,244
Using a logarithmic scale allows you to cover many more orders of magnitude than would be convenient on a linear scale. In my estimation three orders of magnitude is about the limit for a linear scale. On a logarithmic scale 12 or 13 orders of magnitude can be accommodated.

#### steveb

Joined Jul 3, 2008
2,436
With dB scales, there is also the mathematical benefits inherent in any log scale. Multiplication/division on a linear scale converts to addition/subtraction on a log scale. Input and output signal levels can be represented in dBm (dB referenced to 1 mW), or dBV (dB referenced to 1 V), or dB referenced to any other absolute reference. Once this is done, the gain (or loss) of each stage (or component or transmission path etc.) can be expressed in dB, and the net effect is computed as additions (or subtractions) of dB values.

Once we are familiar with dB scales we can easily convert between linear numbers and corresponding dB values, and all calculations/conversions can be done in the head without need of a calculator nor, (ironically) a slide rule.

#### MossyIRL

Joined Dec 29, 2011
3
Expressing things on a logarithmic scale also has a number of advantages when it comes to displaying data on a graph. It can also clarify certain mathematical relationships. A graph of gain against frequency could be plotted on a linear scale, but if this included regions where the gain dropped far below its maximum value, it would be very hard to see what was going on.

At a thousand times less power, or 30dB down, the curve would look to have dropped to zero on a linear scale. Decibel plots can be used to show detail over many tens of dB, useful whether dealing with the response of an amplifier, a loudspeaker, or even a medical test of someone's hearing.

Another advantage of a decibel graph is that if the frequency axis is also made logarithmic, some frequency-dependent effects appear as linear slopes, whereas they would appear curved on a linear plot. For instance, the simplest sort of frequency dependency presents as a slope of 6dB for every doubling in frequency. The slope of the graph may therefore be helpful in analysing circuit behaviour.
Thank you everyone for the replies.

I think this may be the answer i seek (for the level of electronics i am at) as we plot the frequency on a log scale (0Hz-1MHz). So id be right in saying the magnitude must be in dB's to give a staight line graph which makes the circuit easier to analyse??

#### crutschow

Joined Mar 14, 2008
25,267
Thank you everyone for the replies.

I think this may be the answer i seek (for the level of electronics i am at) as we plot the frequency on a log scale (0Hz-1MHz). So id be right in saying the magnitude must be in dB's to give a staight line graph which makes the circuit easier to analyse??
You seem to hung up on straight lines.

The line is straight only if the gain does not change with frequency or is a constant rolloff with frequency such as caused by a simple filter. dB is used for the reasons stated by the other posters. It really has nothing to due with straight lines.

#### bountyhunter

Joined Sep 7, 2009
2,512
Hi,

Been looking on the site awhile now and looks great..
Just registered today..

Quick question for my exams coming up..
Why would we express the gain of an op amp in dB's?

I think it is because it is non linear and this gives us a straight line graph which is easier to work with.. Could sombody please confirm this or point me in the right direction??

Thank you..
The dB (decibel) was used to express sound levels. The human ear sensitivity is logarithmic, not linear.

A standard leaving cert physics exam question is “why do we have the decibel scale”?
The standard answer is that the range of sound intensities is so large that a second, much more compact scale is required to make the numbers more manageable, and for sound this scale is based on multiples of ten and is called the decibel scale (and what it measures is called sound intensity levels).