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Appendix C: Data Plots

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Appendix C

Data Plots

It is often desirable to make a two-dimensional plot of data in order to examine relationships be-

tween variables, for example: voltage versus time, current versus time, output voltage versus in-

put voltage, output voltage versus frequency, etc. When the range of both variables used in the

plot is not large a linear vertical (or “y”) scale and a linear horizontal (or “x”) scale is often con-

venient, particularly if one or both of the variables can have negative values. In the cases where

one of the variables may have a relatively small range while the other covers several orders of

magnitude (i.e. over several powers of 10 in size) a linear versus logarithmic, or semi-log, plot is

convenient. When both variables can cover a large range a logarithmic versus logarithmic, or

log-log, plot is convenient.

The semi-log or log-log plots are also useful when trying to determine whether the data follows a

pattern that can be described by a mathematical function. For example, the decay voltage of a

capacitor discharging through a resistance follows the mathematical function









exp

V t V t



  (C.1)

where τ = RC. This function can be plotted on a semi-log plot. Taking the logarithm (base 10) of

both sides





















0 0

log log log( ) log 0.4343

V t V t e V t

 

    

 

(C.2)

which is a straight line (with a negative slope) when plotted on a log[V] versus linear t plot. Note

here that log[ ] is taken to be log

Another example of a semi-log plot is a (linear) phase angle versus (logarithmic) frequency Bode

plot. The amplitude versus (logarithmic) frequency Bode plot is a semi-log plot when the ampli-

tude has been converted to decibels, i.e. 20·log

(A). Otherwise, log(A) can be plotted versus

log(f).

You have become accustomed to making linear versus linear plots in the past, starting in algebra

and proceeding upward through various subsequent math courses. Even though taking a loga-

rithm might seem to be a “natural” operation (i.e. “no big deal”) now, the use of logarithmic

plots might seem strange at first. However, a great deal of engineering information is published

and exchanged in semi-log or log-log format, and even some in log(log)-log format. Thus it is

useful to learn how to make and interpret such plots. You can purchase semi-log or log-log paper

at a book store which deals with engineering supplies.

When you want to make a semi-log or log-log plot and you do not have any of the commercially

printed plotting paper at hand, you can make your own log scale. The procedure is as follows.

Refer to the scale in Figure C.1, which shows a linear scale at the top and a logarithmic scale at

the bottom. The latter is calculated on the basis of log(1) = 0, log(2) = 0.301 (30% of the spacing

from 1 to 10 on the bottom -log- scale), log(3) = 0.477 (47.7%), log(4) = 0.602 (about 60%), etc.

Using this procedure, you can quickly construct a log scale on linear plotting paper, or on a

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