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Lecture 12

Lecture 12. Review: Source transformations Maximum power transfer Derivation of maximum power transfer Thévenin theorem examples Operational Amplifiers Related educational modules: Sections 1.7.5, 1.8.0, 1.8.1. Using Source Transformations in Circuit Analysis.

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Lecture 12

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  1. Lecture 12 Review: Source transformations Maximum power transfer Derivation of maximum power transfer Thévenin theorem examples Operational Amplifiers Related educational modules: Sections 1.7.5, 1.8.0, 1.8.1

  2. Using Source Transformations in Circuit Analysis • Any voltage source in series with a resistance can be modeled as a current source in parallel with the same resistance and vice-versa

  3. Maximum Power Transfer • The load receives the maximum amount of power if RL = RTH • Why?

  4. Maximum Power Transfer – Derivation • Load voltage: • Delivered power:

  5. Maximizing power • Set derivative of power to zero: • Chain rule: • Set numerator to zero:

  6. Maximum Power Delivered • Delivered power: • Letting RL = RTH:

  7. Example 1: Maximum power transfer (a) Determine the load resistance, R, which absorbs the maximum power from the circuit. (b) What is the maximum power delivered to the load?

  8. Example 1(a): Load Design

  9. Example 1(b): Power delivered

  10. Example 2 • Determine the Norton equivalent of the circuit of example 1

  11. Operational Amplifiers • So far, with the exception of our ideal power sources, all the circuit elements we have examined have been passive • Total energy delivered by the circuit to the element is non-negative • We now introduce another class of active devices • Operational Amplifiers (op-amps) • Note: These require an external power supply!

  12. Operational Amplifiers – overview • We will analyze op-amps as a “device” or “black box”, without worrying about their internal circuitry • This may make it appear as if KVL, KCL do not apply to the operational amplifier • Our analysis is based on “rules” for the overall op-amp operation, and not performing a detailed analysis of the internal circuitry • We want to use op-amps to perform operations, not design and build the op-amps themselves

  13. uA741 op-amp schematic • Source: RFIC Technologies web site

  14. Ideal Operational Amplifiers • Typical circuit schematic symbol: • Three-terminal device (2 inputs, 1 output) • Operation characterized by: • Voltage difference between input terminals (vin) • Currents into the input terminals (ip and in)

  15. Ideal Operational Amplifier “Rules” • More complete circuit symbol • (Power supplies shown) • Assumptions: • ip = 0, in = 0 • vin = 0 • V - < vout < V +

  16. Notes on op-amp operation • Output current is generally not known (it is provided by external power supplies) • KCL at input nodes is generally a good starting point in op-amp circuit analysis • vinis multiplied by a large number to get vout • vout is limited by the external power supplies

  17. Op-amp circuit – example 1 • Find Vout

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

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