GATE EC 2024 Set 1 — Question 49
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Analog Circuits → Op-Amp Circuits → Differentiator & Integrator
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Question
The opamps in the circuit shown are ideal, but have saturation voltages of . 
Assume that the initial inductor current is . The input voltage () is a triangular signal with peak voltages of and time period of . Which one of the following statements is true?
Correct answer
(D) V₀₁ is delayed by 1 μ s relative to Vᵢ, and V₀₂ is a trapezoidal waveform.
Solution
1.OPA1 Analysis (Schmitt Trigger): OPA1 is a non-inverting Schmitt trigger. The threshold voltages are and .
2.Input Signal: is a triangular wave with peak and . It takes to go from to . Thus, it reaches the threshold of at . This introduces a delay in the switching of relative to the zero-crossing of .
3.OPA2 Analysis (Integrator): OPA2 is an inverting integrator. The output is proportional to the integral of . Since is a square wave, would normally be a triangular wave. However, the time constant is . The slope of integration is . In a half-period of , the voltage would try to change by , but it saturates at . Therefore, the output is a trapezoidal waveform.
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