LECTURE DEMONSTRATION MANUAL | Instructional Research Lab : ucla physics | |
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E.7.5 RC - Integration and Differentiation A simple RC circuit will integrate or differentiate waveforms: (Of course, the derivative and integral of a sine wave is the leading and lagging cosine wave; these are just the normal 90° phase shifts.) The circuit below integrates. The resistance R is made large and the capacitative reactance Xc is made small by using a large C and/or a large W. Then the current into the circuit is set by R and proportional to Vin. The capacitor stores and integrates the charge. To differentiate the circuit is wired as below: We arrange for nearly all the input voltage to drop across the capacitor (Vc >> Vout ) by making R small and Xc large using a small C and/or w Thus the voltage drop across R measures i without disturbing Vc. The circuit looks essentially like a capacitor to the input. The current is set by C and the small R is placed in series to sense it. RL circuits will perform the same operations. |