To turn Differential Equation into algebra
Solving
differential equation by hand is insane – but we don’t want to use PC to solve
everything because still needs to get a feel of how circuit element behave to
do a proper job. And the best way to achieve this is by learning Laplace.
Example:
The simplest RC circuit is a
capacitor and a resistor in series. When a
circuit consists of only a charged capacitor and a resistor, the capacitor will
discharge its stored energy through the resistor (when Vin = 0V). The voltage across the
capacitor, which is time dependent, can be found by using Kirchhoff's current law, where
the current through the capacitor must equal the current through the resistor.
This results in the linear differential equation
Solve Using Differential Equation:
Solve Using Laplace transform:
And it is much more intuitive! To get the same result as the time domain method, just perform inverse Laplace transform.
To be able to apply
control theory – transfer function – frequency response…
Working
with Laplace transformed stuffs are actually working in frequency domain. And
in engineering (especially electronic and mechanical), there’s no escape in
dealing with the above mentioned skills.
If one can
think in frequency domain, then one is very well geared up for practical
engineering works. And has significant advantage over the peers who can’t.
It is easy
One just
needs to realize that the world is not just about time domain, lots of time it
is just being open minded enough for new concept. Yes, seeing is believing, but what you can’t
see not necessary is not true.
It is philosophy – it
actually teaches you something about life
It teaches
you that there are many perspectives that you can have on things.
Other than
looking at time response you can look at the frequency response
A cup of
water is half empty or half full
Links:
Nice blog… Thanks for sharing very useful information about electrical circuits.
ReplyDeleteLearn Electronic Circuits