Page 26 - Numerical Analysis Using MATLAB and Excel

Using MATLAB to Make Plots

The ratio of any two values of the same quantity (power, voltage, or current) can be expressed in
decibels (dB). Thus, we say that an amplifier has 10 dB power gain, or a transmission line has a
power loss of 7 dB (or gain 7– dB ). If the gain (or loss) is 0 dB the output is equal to the input.
By definition,
P
out
dB = 10log ---------- (1.10)
P in
Therefore,

10 dB represents a power ratio of 10
10n dB represents a power ratio of 10 n

It is very useful to remember that:

20 dB represents a power ratio of 100

30 dB represents a power ratio of 1 000,

60 dB represents a power ratio of 1 000 000, ,

Also,
1 dB represents a power ratio of approximately 1.25

3 dB represents a power ratio of approximately 2
7 dB represents a power ratio of approximately 5

From these, we can estimate other values. For instance,

4 dB = 3 dB + 1 dB and since 3 dB power ratio of 2 and 1 dB power ratio of 1.25
≅
≅
then, 4 dB ratio of 2 1.25×(≅ ) = ratio of 2.5

Likewise, 27 dB = 20 dB + 7 dB and this is equivalent to a power ratio of approximately
100 5 = 500
×
Using the relations
2
y = log x = 2log x
and

2
P = V 2 I Z
------- =
Z
if we let Z = 1 , the dB values for voltage and current ratios become

Numerical Analysis Using MATLAB® and Excel®, Third Edition 1−13
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