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Class Exercise 4 (March 22 - 27, 2004)

4. Passive Integrators and Differentiators    Op-amp Integrator Builder

 KINDS integrators differentiators capacitive C integrator I > V RC integrator V > V C differentiator V > I CR differentiator V > V inductive L integrator V > I L differentiator I > V RL differentiator V > V

4.1. Elementary capacitive circuits. Deriving a functional notion of an element storing potential energy from many everyday situations (analogies).
4.1.1. Capacitive integrator with current input and voltage output (C current-to-voltage integrator). Application - an elementary building block for
assembling more complicated integrators. Discussion: Is the circuit an ideal integrator? Imperfections caused by a real current source. Looking for a remedy.

 Capacitor as an ideal current integrator.

4.1.2. Capacitive differentiator with voltage input and current output (C voltage-to-current differentiator). Application - an elementary building block for assembling more complicated capacitive differentiators. Discussions: Is the circuit correct? What does a voltage source "like"? What does it "hate"? Is it an ideal differentiator? Imperfections caused by a real current load. Looking for a remedy.

4.2. Building compound resistive-capacitive converters with voltage inputs and outputs.
4.2.1. RC integrator. Building the circuit by using the more elementary voltage-to-current converter and C current-to-voltage integrator. Applications: imperfect ramp generator (assembling from an external square generator and RC integrator); filtering circuits etc. Imperfections and remedies.

 RC integrator = voltage-to-current converter + C current-to-voltage integrator. Imperfections. Remedy.

4.2.2. CR differentiator. Building the circuit by using the more elementary C differentiator and current-to-voltage converter. Applications: pulse "shortening" circuits; dynamic potential "shifting" circuits (ideas for future applications in transistor bias circuits). Imperfections and remedies.

4.3. Elementary inductive circuits. Deriving a functional notion of an element storing kinetic energy from many everyday situations (analogies).
4.1.1. Inductive integrator with voltage input and current output (L voltage-to-current integrator). Application - an elementary building block for
assembling more complicated inductive integrators. Imperfections caused by a real current load. Looking for a remedy.
4.1.2. Inductive differentiator with current input and voltage output (L voltage-to-current differentiator). Application - an elementary building block for
assembling more complicated inductive differentiator. Discussions: Is the circuit correct? What does a current source "like"? What does it "hate"? Is it an ideal differentiator? Imperfections caused by a real current source. Looking for a remedy.

4.4. Building compound resistive-inductive converters with voltage inputs and outputs.
4.4.1. LR integrator. Building the circuit by using the more elementary L integrator and current-to-voltage converter. Imperfections and remedies.
4.4.2. RL differentiator. Building the circuit by using the more elementary voltage-to-current converter and C differentiator and L differentiator. Visualizing the operation by means of potential bars. Imperfections and remedies.

Last updated October 22, 2004

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