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Understanding OP-AMP Circuits: Integrators, Differentiators, and Difference Amplifiers

This guide covers the fundamental principles of operational amplifier (OP-AMP) circuits, focusing on integrator, differentiator, and voltage subtractor configurations. By applying Kirchhoff's Current Law (KCL) at critical nodes, we derive relationships between input and output voltages. Key equations are provided, along with example problems to illustrate the application of these concepts in various circuits. The guide aims to enhance your understanding of OP-AMP behavior and its practical applications in electronic circuit design.

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Understanding OP-AMP Circuits: Integrators, Differentiators, and Difference Amplifiers

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  1. Practical OP-AMP Circuits

  2. Integrator i i

  3. Differentiator i i

  4. Voltage Subtractor or Difference Amplifier Applying KCL at node ‘a’, (V1 – V3)/R1 = (V3 – V0)/R2 (1) Applying KCL at node ‘b’, (V2 – V3)/R1 = V3/R2 (2) Rearranging (1), we get, (1/R1 + 1/R2)V3 – V1/R1 = V0/R2 (3) Rearranging (2), we get, (1/R1 + 1/R2)V3 – V2/R1 = 0 (4) (3) – (4), we get, (V2 – V1)/R1 = Vo/R2 or, Vo = R2(V2 – V1) /R1

  5. Ex.1) For the amplifier circuit find vo/v1

  6. Solution : io = i – i1 = vi/R1 – v/R= vi/R1 – (- iR)/R = vi/R1 + i = vi/R1 + vi/R1 = 2vi/R1 vo = v – ioR2 = - iR – 2viR2/R1 = - viR/R1 – 2viR2/R1 or, vo = - vi(R + 2R2)/R1 Hence, vo/vi = -(R + 2R2)/R1

  7. Ex.2) Find Vo in the following circuit.

  8. Solution V2 = V1 = 4/3 V Or, Vo – 4/3 = 2(4/3 +3) Or, Vo = 4/3 + 8/3 + 6 = 10 V

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