It is the way nature works
Just like planets evolve around sun, in nature’s world, log or exponential relationship is a common place.
For example:
1. Radioactive material has a half cycle of x amount of years
2. House mortgage or anything with compounded interest. If you principle is x0 amount of $$, with annual interest rate of i%, then without any payment, the balance at the end of each year will be x0 * (1+ i/100)^n, with n = the amount of years
To be able to look at wide dynamic range
x
|
y
|
1
|
1.00
|
2
|
2.00
|
3
|
4.00
|
4
|
8.00
|
5
|
16.00
|
6
|
32.00
|
7
|
64.00
|
8
|
128.00
|
9
|
256.00
|
10
|
512.00
|
Table 1
By representing gain/freq/attenuation in dB we are able to have a clue on how information of interest behaves over a wide range.
Let’s look at the perspective when we keep the linear scale at x-axis and do a linear (Graph 1) and a log scale y-axis plot (Graph 2) on a set of logarithmic data (which is very common in engineering life) and have a feel of the details of visual info available.
To be able to perform simulation with minimum resource
Figure 1: log scale from 1 to 10Meg
Consider the case of a simple low pass filter, if we were to calculate the response from 1Hz to 1MHz in one 1Hz step, then we need 1 million data points, which takes time. Instead of doing it the bull-dozer way, in log scale we only have to take 10 data points (it can be more) for each decade (x10), on in this case we have 6 decade * 10 points – just 60 points of calculation. Looking at Figure 1 gives you a sense of the look in logarithmic scale.
To be able to read specification
In engineering world, lots of specification being stated in dB, so by learning it, you are in tune with the industrial. If you want to be in engineering world, you must speak engineering terms, or your life will be miserable. It is as simple as not speaking English in UK or Japanese in Japan.
For example, we state filter attenuation, RF amplifier gain in dB
To turn multiplication/division into algebra
Let’s acknowledge this, hand calculation of multiplication is too much a pain in the ass.
By learning how to “log” a number, and how to “antilog” a number, all multiplication and divide WILL becomes simple algebra (addition or substract). If you have forgotten how to do it – refer to http://obsoleteskills.wikispot.org/Reading_a_log_table
Let’s say we want to know the following by hand calculation (use table attached)
23445 * 0.923 / 24543 = ?
To solve the problem using algebra, there’s only a few steps (simple steps)
1. Find out (for this you need to learn to use the log table, see the reference).
a. Log10 (23445) = 4.3701
b. Log10 (0.923) =-0.0348
c. Log10 (23543) =4.3900
2. Perform algebra operation according to * or / : 4.3701 + (-0.0348) – 4.3900 = - 0.0547
3. Then perform antilog operation: 10^(-0.0547) = 0.8817
Look at how AMAZING this is, this is so simple and do-able. In engineering works, do don’t need all the precision in the digit, for the following reason:
1. Real measurement circuit is only accurate up to certain level, 5digit is pretty good – which correspond to 0.001% accuracy and this is already very very good.
2. Practical environment does not allow precision data, even if your equipment is able to do it. for example, maybe you only have 1ms to perform your measurement, but to reach 0.01% accuracy you would typical needs 10’s of ms to get a stable result (actual time depend on your equipment).
3. To get intuition, 90% accuracy level is more than enough, struggle to get too much precision is futile, let the PC do the job, we human is not computer, the moment you lost this perception you are deem for a frustration.
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