The opamps in the circuit shown are ideal but have saturation voltages of \(\pm 10 \, {V}\). Assume that the initial inductor current is \(0 \, {A}\). The input voltage (\(V_i\)) is a triangular signal with peak voltages of \(\pm 2 \, {V}\) and a time period of \(8 \, \mu {s}\). Which one of the following statements is true?
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When analyzing circuits with operational amplifiers, determine the function of each opamp (e.g., integrator, amplifier), account for RC time constants, and include saturation effects in the output waveform analysis.
\(V_{01}\) is delayed by \(2 \, \mu {s}\) relative to \(V_i\), and \(V_{02}\) is a triangular waveform.
\(V_{01}\) is not delayed relative to \(V_i\), and \(V_{02}\) is a trapezoidal waveform.
\(V_{01}\) is not delayed relative to \(V_i\), and \(V_{02}\) is a triangular waveform.
\(V_{01}\) is delayed by \(1 \, \mu {s}\) relative to \(V_i\), and \(V_{02}\) is a trapezoidal waveform.
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The Correct Option isD
Solution and Explanation
Step 1: Behavior of \(V_{01}\).
The first operational amplifier (OPA1) functions as an integrator. When the input \(V_i\) is a triangular waveform, the output \(V_{01}\) becomes a sine wave-like signal, as the integral of a triangular waveform is sinusoidal. The phase delay in \(V_{01}\) is influenced by the RC time constant, and for this circuit, the delay is approximately \(1 \, \mu {s}\).
Step 2: Behavior of \(V_{02}\).
The second operational amplifier (OPA2) acts as an amplifier with saturation limits of \(\pm 10 \, {V}\). As the amplified output exceeds the saturation voltages, \(V_{02}\) transforms into a trapezoidal waveform.
Final Answer:
\[
\boxed{{(4) } V_{01} { is delayed by } 1 \, \mu {s} { relative to } V_i, { and } V_{02} { is a trapezoidal waveform.}}
\]
