1. Operational Amplifiers

The very short version of the analysis rules for an ideal op amp are:

  • Infinite input resistance.

  • Infinite gain.

  • Zero output resistance.

which then imply the following identities for circuit analysis:

  • zero input current into each pin

  • \(v_+ = v_-\) [1]

These properties are the result of taking the internal equivalent model and seeing what happens when \(A_{v0} \rightarrow \infty\).

2. Resources

The Google Drive docs folder has a dedicated folder opamps for information. This includes AN-7 and:

3. Tasks

3.1. From day24

  • Find V(out2) using symbolic (linear) circuit analysis. This was done in class.

  • Find V(out3) using symbolic (linear) circuit analysis.

  • Find V(out4) using symbolic (linear) circuit analysisk

Please use superposition to do this! The Figure 1. Op amp internal DC model has three independent sources, so set all but one source to zero and solve the circuit, then add the three results to get the full output voltage.

3.2. From day25

  • Finish your work for finding the DC solution.

  • Find the small-signal transfer function of the amplifier.

  • Match your numbers to the simulation version. Specifically the magnitude of the gain at "middle" frequencies.

1. Though the two pins are the same voltage, they are not the same node, and so there are two separate KCLs at the two input nodes.