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Lecture 13

Lecture 13. Review: Operational Amplifiers Operational amplifier examples Dependent Sources Related educational modules: Sections 1.8.0, 1.8.1, 1.8.2. Operational Amplifiers. Circuit Symbol: Assume: i p = 0, i n = 0; v in = 0; V - < v out < V +. Lecture 12, example 1.

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Lecture 13

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  1. Lecture 13 Review: Operational Amplifiers Operational amplifier examples Dependent Sources Related educational modules: Sections 1.8.0, 1.8.1, 1.8.2

  2. Operational Amplifiers • Circuit Symbol: • Assume: ip = 0, in = 0; vin = 0; V - < vout < V +

  3. Lecture 12, example 1

  4. Op-amp circuit applications • Operational-amplifier based circuits are often used to implement mathematical operations • Example: • The circuit of Lecture 12, example 1 performs multiplication by a negative constant • Inverting voltage amplifier

  5. Saturation • The op-amp output is limited by V+ and V- • The operational amplifier output is not purely linear • If the output reaches the supply “rails”, the output “saturates” • Lecture 12, Example 1:

  6. Op-amp circuit – Example 1 • Find Vout

  7. Op-amp circuit – example 2 • Find Vout

  8. Op-amp circuit applications • Operational-amplifier can be used to isolate sections of a circuit from one another • The operational amplifier has a very high input resistance • Example: • The circuit example 2 draws no power from Vin

  9. Example 2 – revisited • We have a 3k load which requires 6V, but we only have access to a 12V supply.

  10. Dependent Sources • Operational amplifier based circuits are often modeled as dependent sources • Review: Four types of dependent sources: • Voltage controlled voltage source (VCVS) • Current controlled voltage source (CCVS) • Voltage controlled current source (VCCS) • Current controlled current source (CCCS)

  11. Dependent Sources – circuit symbols • VCVS: • VCCS: • CCVS: • CCCS:

  12. Op-amp circuit as dependent source -- example • Inverting voltage amplifier:

  13. Analysis of circuits with dependent sources • Can still use: • KVL • KCL • Ohm’s Law • Nodal analysis • Mesh analysis

  14. Dependent source analysis – example 1 • Find the current, i

  15. Dependent source analysis – example 2 • Find the voltage, v

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