(Solved): Figure 6: An active RC differentiator (C=1F) Implement the differentiator given in the schematic ...

Figure 6: An active $$\mathrm{RC}$$ differentiator $$(C=1?F)$$ Implement the differentiator given in the schematic. (Based on the results in Discussion). The $$10?$$ resistor between $$V_{IN}$$ and the capacitor is to avoid a potential oscillation and may be ignored in your calculations. You may need to increase the resistance slightly, until oscillation stops. Assuming $$v_{IN}(t)=1\mathrm{V}\times \sin (2?\times 100\mathrm{Hz}\times t)$$, look at the $$v_{OUT}(t)$$. Plot the $$v_{OUT}(t)$$ and $$v_{IN}(t)$$, and compare the magnitude and phase responses between the measured values and the ones calculated in discussion. Next, assuming $$v_{IN}(t)$$ is a triangular signal with an amplitude of $$1\mathrm{V}$$ peak-to-peak (toggling between $$?0.5\mathrm{V}$$ and $$+0.5\mathrm{V})$$ and $$100\mathrm{Hz}$$ input frequency, look at $$v_{OUT}(t)$$. Plot $$v_{OUT}(t)$$, and compare the measured and calculated values. Discussion: - Derive the transfer function, magnitude response, and phase response of the differentiator. - Determine $$R$$ that gives a magnitude gain of $$0.2?$$ at $$100\mathrm{Hz}$$. What is the phase? - Assuming $$v_{IN}(t)=u(t)$$ a step input, derive the transient response of $$v_{OUT}(t)$$.