# logaritmic scale

Discussion in 'General Electronics Chat' started by Thomas.R, Apr 17, 2008.

1. ### Thomas.R Thread Starter Member

Aug 16, 2007
20
0
hallo,
i have looked on the www but i didn't get any wiser.
can someone tell me how to read logarithmic scales?

Thomas

Apr 10, 2008
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3. ### Caveman Senior Member

Apr 15, 2008
471
1
Thomas,

Put up an example, and we should be able to help.

4. ### Mark44 Well-Known Member

Nov 26, 2007
626
1
On a uniform scale (for lack of a better term) the distance between two successive integer values is the same anywhere on the scale. For example, the distance between 1 and 2 is the same as that between 7 and 8.

On a logarithmic scale the distance between two successive integer values shrinks as the values get larger, something like this:
1 2 3 4 5 6 7 8 ...

The main reason for using a logarithmic (or log) scale is that it can more easily accommodate data of several orders of magnitude.

The numbers on a log scale are displayed at distances representing their logarithms. IOW, 1 is usually where 0 would be on an ordinary scale, 2 is about .30 units to the right of 1 , 3 is about .47 units to the right of 1, 4 is .60 to the right of 1, and so on, assuming logs base 10.

When you ask how to read a log scale, I assume you're talking about how to interpolate where a point is located. A point that looks to be halfway between, say, 3 and 4 would not be at 3.5. Instead it would be a bit larger than 3.3, considering what I've already said in the previous paragraph.

Does that help?
Mark

5. ### Thomas.R Thread Starter Member

Aug 16, 2007
20
0
the example i am looking at is: http://www.datasheetcatalog.com/datasheets_pdf/U/A/7/4/UA741.shtml
look at the one from T.I.
there is given a open-loop large signal differential voltage amplification vs frequency table
i want to know what is the -3db cut off
maybe i would be clear if somebody could give me the values of the x scale from 1 to 100
i hope this isn't asked to much
thanks Thomas

6. ### jpanhalt Expert

Jan 18, 2008
7,268
1,635
Some variables show a logarithmic relationship. Thus, a log-linear graph gives a straight line. That is the main reason I have used "semi-log" paper, not to span a greater range of values.

I have always thought of that the other way around. Zero on a linear scale cannot be plotted on a log scale, as log(0) is undefined. Log(1) = 0 It is that fact that seems to lead to the most confusion for students with whom I have worked. The reason is that so much empirical data is collected with a "zero" point and the students want to include the zero.

As already mentioned, perhaps the best way to explain it is for you to give a sample of the data you want to see graphed and we will try to show you how to graph it. John

7. ### Mark44 Well-Known Member

Nov 26, 2007
626
1
I think we're saying the same thing, but maybe I wasn't as clear as I should have been. When I wrote my response to the OP I was visualizing a slide rule scale (A, B, C, D scale), where the left-most number is 1. And this value corresponds to 0 on an ordinary scale.

8. ### jpanhalt Expert

Jan 18, 2008
7,268
1,635
Hey, anyone who knows what a slide rule is, much less how to use it, has my vote. I still have my old K&E mahogany. I thought we were saying the same thing, I just wasn't sure. John

9. ### Mark44 Well-Known Member

Nov 26, 2007
626
1
I have 3 or 4 of them around the house. One of them is an aluminum (aluminium for the Brits) Pickett I bought when I was an EE student (and not a very good one, I might add--but I was able to run the table playing pool!)

10. ### Caveman Senior Member

Apr 15, 2008
471
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The better term is "linear scale". Just FYI.

11. ### Caveman Senior Member

Apr 15, 2008
471
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Thomas,
In this graph, the horizontal (x) axis is logarithmic. The vertical axis is linear. I'm going to assume you know how a linear scale works, and move on to the vertical. The left most vertical line is 1Hz. I mean the one that is bold and defines the left side of the box. You will notice that as you move right, the numbers multiply by 10 each time. That is what this is all about. You can fit a huge range in a small space. However, it makes the numbers that are not multiples of 10 go all wonky. That is why there is a repeating squishing pattern of the vertical lines. They count as follows 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100, 200 ... Of course, only the 1,10,100,etc are numbered at the bottom.

Now, to understand further, look at where the graph is 90dB. It is just a hair right of one of the vertical lines. It is one vertical line right of the 10Hz line, so it is 20Hz.

The -3dB that you are looking for probably the 3dB below DC gain. Notice how it rolls off starting at about 3-4Hz. The -3dB from max is about 4-5Hz. Not enough detail there to estimate better than that.

Hope that helps

12. ### kubeek Expert

Sep 20, 2005
5,540
1,072
I don´t understand why logarithmic scale is called logarithmic, when it actually is exponential scale.
1,10,100,1000 semms to be exponential series, while 1, 1.3, 1.47, 1.6, 1.69 is logarithmic series.
If the scale was logarithmic, on the x axis wouldn´t be x but log(x).
So why are on logarithmic scale numers a^x?

13. ### jpanhalt Expert

Jan 18, 2008
7,268
1,635
Isn't that what a logarithm is? You plot (usually) log(Y) vs. X. You can do that on normal linear graph paper by converting your Y values to logs first, or you can use semi-log graph paper and just plot the values of Y. John

14. ### Caveman Senior Member

Apr 15, 2008
471
1
Or another way of thinking about it:

If you have 1,10,100,1000, and you want to put them on a scale, you put 1 at 0, 10 at 1, 100 at 2, 1000 at 3. Therefore, you are putting each of them at the log of their values.