An Op-Amp Differentiator Consider the op-amp differentiator in Example 6.9 . Assume that the parameter values are [latex]R=1[/latex] [latex]M \Omega[/latex] and [latex]C=1 \mu \mathrm{F}[/latex]. Build a Simscape model of the op-amp circuit and find the output voltage [latex]v_{o}(t)[/latex] when the input voltage is [latex]v_{\mathrm{i}}=-0.1 \mathrm{~V}[/latex].

The Simscape block diagram of the op-amp differentiator is shown in Figure 6.65, in which a Clock block and a Gain block are used to generate the input voltage [latex]v_{\mathrm{i}}=-0.1 \mathrm{t} \mathrm{V}[/latex]. The Simulink input signal is converted into an equivalent voltage source using a Controlled Voltage Source block. According to the result in Example 6.9 , the output voltage [latex]v_{o}[/latex] is proportional to the time derivative of the input voltage [latex]v_{\mathrm{i}}[/latex] via [latex]v_{\mathrm{o}}=-R C \dot{v}_{\mathrm{i}}[/latex]. Substitute the parameter values, and a constant value of 0.1 is expected to be the output voltage. The problem of building a Simulink block diagram based on the differential equation is left to the reader as an exercise.

Question 6.16: An Op-Amp Differentiator Consider the op-amp differentiator ...

Modeling and Analysis of Dynamic Systems

An Op-Amp Differentiator

Consider the op-amp differentiator in Example 6.9. Assume that the parameter values are $R=1$ $M \Omega$ and $C=1 \mu \mathrm{F}$ . Build a Simscape model of the op-amp circuit and find the output voltage $v_{o}(t)$ when the input voltage is $v_{\mathrm{i}}=-0.1 \mathrm{~V}$ .

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The Simscape block diagram of the op-amp differentiator is shown in Figure 6.65, in which a Clock block and a Gain block are used to generate the input voltage $v_{\mathrm{i}}=-0.1 \mathrm{t} \mathrm{V}$ . The Simulink input signal is converted into an equivalent voltage source using a Controlled Voltage Source block. According to the result in Example 6.9, the output voltage $v_{o}$ is proportional to the time derivative of the input voltage $v_{\mathrm{i}}$ via $v_{\mathrm{o}}=-R C \dot{v}_{\mathrm{i}}$ . Substitute the parameter values, and a constant value of 0.1 is expected to be the output voltage. The problem of building a Simulink block diagram based on the differential equation is left to the reader as an exercise.