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# STEP RESPONSE OF AN RC CIRCUIT

الكلية كلية الهندسة     القسم  الهندسة الكهربائية     المرحلة 1
أستاذ المادة أواب قاسم جمعة الذهب       06/10/2018 16:01:58
5.5 STEP RESPONSE OF AN RC CIRCUIT
When the dc source of an RC circuit is suddenly applied, the voltage or current source can be modeled as a step function, and the response is known as a step response.
The step response of a circuit is its behavior when the excitation is the step function, which may be a voltage or a current source.
The step response is the response of the circuit due to a sudden application of a dc voltage or current source.

Figure 5.10 An RC circuit with voltage step input.
Consider the RC circuit in Fig. 5.10(a) which can be replaced by the circuit in Fig. 5.10(b), where Vs is a constant, dc voltage source. Again, we select the capacitor voltage as the circuit response to be determined.
We assume an initial voltage V0 on the capacitor, although this is not necessary for the step response. Since the voltage of a capacitor cannot change instantaneously,
v(0?) = v(0+) = V0 (7.22)
where v(0?) is the voltage across the capacitor just before switching and v(0+) is its voltage immediately after switching. Applying KCL, we have
C dv/dt +(v – Vs.u(t))/R = 0 (7.23)
where v is the voltage across the capacitor.
Thus,
v(t) ={?(V0 ,t< 0@Vs + (V0 - Vs)e^(-t/?) ,t>0)? (5.24)
This is known as the complete response of the RC circuit to a sudden application of a dc voltage source, assuming the capacitor is initially charged. The reason for the term “complete” will become evident a little later. Assuming that Vs > V0, a plot of v(t) is shown in Fig. 5.11.

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