Tab Electronics Guide to Understanding Electricity ... - Sciences Club

Linear Electronic Circuits
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“apples with apples”; an amplifier rated at 100 watts rms into an 8-ohm
load is more powerful than an amplifier rated at 120 watts rms into a
4-ohm load.
The human ear does not respond in a linear fashion to differing
amplitudes of sound. It is very fortunate for you that you are made this
way, because the nonlinear ear response allows you to hear a full range
of sounds; from the soft rustling of leaves to a jackhammer pounding
on the pavement. For example, a loud sound that is right on the threshold
of causing pain to a normal ear is about 1,000,000,000,000 times louder
than the softest sound that can be heard. Our ears tend to “compress”
louder sounds, and amplify smaller ones. In this way, we are able to hear
the extremely broad spectrum of audible sound levels.
When one tries to express differing sound levels, power ratios, noise
content, and various other audio parameters, the nonlinear characteristic
of human hearing presents a problem. It was necessary to develop a
term to relate linear mathematical ratios with nonlinear hearing
response. That term is the decibel. The prefix deci means 1 10
, so the term
decibel actually means “one-tenth of a bel.”
The bel is based on a logarithmic scale. Although I can’t thoroughly
explain the concepts of logarithms within this context, I can give a basic
feel for how they operate. Logarithms are trigonometric functions, and
are based on the number of decimal “columns” contained within a
number, rather than the decimal values themselves. Another way of
putting this is to say that a logarithmic scale is linearized according to
powers of ten. For example, the log of 10 is 1; the log of 100 is 2; the log of
1000 is 3. Notice, in each case, that the log of a number is actually the
number of weighted columns within the number minus the “units” column.
The bel is a ratio of a “reference” value, to an “expressed” value, stated
logarithmically. A decibel is simply the bel value multiplied by 10
(bels are a little too large to conveniently work with).
In this case, I believe a good example is worth a thousand words.
Assume you have a small radio with a power output of 100 mW rms.
During a party, you connect the speaker output of this radio into a
power amplifier which boosts the output to 100 watts rms. You would
like to express, in decibels, the power increase. The power level that you
started with, 100 mW (0.1 watt), is your reference value. Dividing this
number into 100 watts gives you your ratio, which is 1000. The log of
1000 is 3 (bel value). Finally, multiply 3 by 10 (to convert bels to decibels),
and the answer is 30 decibels.
Each 3-dB increase means a doubling of power: 6 dB gives 4 times the
power [3 dB 3 dB equates to 2x power times 2x power; 2x(2x) 4x]. A