Circuit Response Related to Unit Impulse
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Unit impulse (see Laplace transforms) has the dimens ions of time1. For example, suppose a capacitor of 1 microfarad is suddenly connected to a battery of 100 volts, with the circuit inductance and resistance negligib ly small. Then the current is iO coulomb multiplied by unit impulse. The general transformed equation of a circuit or system may be writte.
Now apply unit impulse S0(t) (multiplied by 1 volt-second), and designate the circuit current in this case by B(t) and its transform by [B]. The Laplace transform of S0(t) is 1, so.
To this there must be added the current i0 due to any initial conditions that exist. From (8) S [i0] = çb(p) (Eq. 13) Then i0 is the inverse transform of ,(p).
Here [ii is the transform of the required current (or (Eq. 5) other quantity) and .E [e] is the transform of the applied voltage or driving force eQ). The transform of the initial
conditions, at t = 0, is included in q’(p). First considering the case when the system is initially at rest, b(p) = 0. Writing a for the current in this case
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