The Laws of Circuit - you can learn and practice by just
Copyright. Charles Kim 2006
- Why Transient Analysis?
- Then why are we interested in the
transient (or transition) period after switching? It's because there are
a lot of such demands in real world. Think about a
defibrillator which applies shock voltage (or current) to
unbeating heart. You need very high level energy but at
the same time you do not want to apply that high level of
energy for a long time. You do only a few milliseconds.
Of course after that period, your energy level must be
zero. Now we are interested in the level of energy and
the time period in terms of circuit analysis. Then what
is t<0 event in the defibilitator example? During
t<0 , it is charging a capacitor. For t>0 analysis,
the voltage source is removed by a switching action at
t=0 (remember that they press the switch in ER), but the
charged energy in the capacitor will flow through the
heart until it is fully discharged. Since there is no
source connected in the circuit, after the discharge,
there is no voltage applied to the heart.
example. Ignition in automobile. To start your car, you turn
your ignition switch, then your hear the beautiful sound
of starter motor then the gasoline engine picks up.
Optimum starting operation requires, for example, a
current reaching at least 1 A within 100ms and remains
above 1A for 1 - 1.5s. So how do you design your
ignition circuit? Simply put, R(modeled from ignition
coil resistance), C, and L (modeled from the ignition
coil) and the 12V battery are serially connected and C
and L are charged for t<0 period. Then when you turn on the
ignition switch you actually disconnect your battery from
the circuit. And the charged energy in C and L are
driving the transient current to the ignition coil. And
as you read above, you have to have your current at a
certain value for a limited amount of time (transient).
Then your current flow should stop (steady-state). Any
system which needs very high energy for a very short period
(like pulsed power) needs such transient analysis.
Missile launch is just one of many such applications.