Suppose the integrator of Fig. 1.20 has R = 100 k2 and C = 10 nF,...

    

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Suppose the integrator of Fig. 1.20 has R = 100 k2 and C = 10 nF, and includes also a 300-k resistance in parallel with C. (a) Assuming C is initially discharged, sketch and label vo(t) if v is changed from 0 V to +1 V at t = 0. Hint: The voltage across the capacitor can be expressed as v(t > 0) = vo + (vovo)exp[-t/(RegC)], where vo is the initial voltage, vo is the steady-state value to which v tends in the limit t → ∞ (when C acts as an open circuit), and Req is the equivalent resistance seen by C during the transient (to find Req, use the test method). (b) Sketch and label vo(t) if vI is changed to -0.5 V at the instant in which vo reaches -2 V. Suppose the integrator of Fig. 1.20 has R = 100 k2 and C = 10 nF, and includes also a 300-k resistance in parallel with C. (a) Assuming C is initially discharged, sketch and label vo(t) if v is changed from 0 V to +1 V at t = 0. Hint: The voltage across the capacitor can be expressed as v(t > 0) = vo + (vovo)exp[-t/(RegC)], where vo is the initial voltage, vo is the steady-state value to which v tends in the limit t → ∞ (when C acts as an open circuit), and Req is the equivalent resistance seen by C during the transient (to find Req, use the test method). (b) Sketch and label vo(t) if vI is changed to -0.5 V at the instant in which vo reaches -2 V.

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