Question

The opamps in the circuit shown are ideal but have saturation voltages of \(\pm 10 \, {V}\). \begin{center} \includegraphics[width=10cm]{49.png} \end{center} 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?

• A. \(V_{01}\) is delayed by \(2 \, \mu {s}\) relative to \(V_i\), and \(V_{02}\) is a triangular waveform.
• B. \(V_{01}\) is not delayed relative to \(V_i\), and \(V_{02}\) is a trapezoidal waveform.
• C. \(V_{01}\) is not delayed relative to \(V_i\), and \(V_{02}\) is a triangular waveform.
• D. \(V_{01}\) is delayed by \(1 \, \mu {s}\) relative to \(V_i\), and \(V_{02}\) is a trapezoidal waveform.

Hint:

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.

Answer 1

The Correct Option is D

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: \[ \boxed{{(4) } V_{01} { is delayed by } 1 \, \mu {s} { relative to } V_i, { and } V_{02} { is a trapezoidal waveform.}} \]