1. EENG 2610: Circuits Analysis Class 7: Operational Amplifiers (Op-Amp), 2/2
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas

2. Op-Amp Circuit Analysis
General rule for op-amp circuit analysis
Use the ideal op-amp model conditions
Write nodal equations at the op-amp input terminals

3. Example 4.5: Determine vo

4. Example 4.6: Determine vo
This is a precision differential voltage gain device 1 2

5. Comparator Comparator is a variant of op-amp
Ideal comparator and its transfer curve
Comparator is designed to operate with the outputs saturated
Op-amp is not.
Comparator is fast and less expensive than op-amp.

6. Zero-Crossing Detector - A Common Comparator Application
pull-up resistor

7. Equivalence Important:
A series connection of current sources or a parallel connection of voltage sources is forbidden unless the sources are pointing to the same direction and have exactly the same value !

8. Example 5.1: Determine Vout using linearity
Linear circuits are described by a set of linear algebraic equations
Linearity requires both additivity and homogeneity (scaling)
Example 5.1: Determine Vout using linearity

9. Superposition Principle of Superposition
In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contribution of each source acting alone.
When determining the contribution due to an independent source, any remaining voltage sources are made zero by replacing them with short circuits, and any remaining current sources are made to zero by replacing them with open circuits
Dependent sources are never made zero when using superposition.
This principle can be used to reduce a complicated problem to several easier problems – each containing only a single independent source.

10. Example 5.3: Use superpositon to find Vo
We set to zero the voltage source
Now we set to zero the current source

11. Example 5.4: Use superpositon to find Vo

13. Applying Superposition
Step 1: In a network containing multiple independent sources, each source can be applied independently with the remaining sources turned off.
Step 2: To turn off a voltage source, replace it with a short circuit, and to turn off a current source, replace it with an open circuit.
Step 3: When the individual sources are applied to the circuit, all the circuit laws and techniques we have learned or will soon be learned, can be applied to obtain a solution.
Step 4: The results obtained by applying each source independently are then added together algebraically to obtain a solution.
Important:
Superposition cannot be used to determine power because power is a nonlinear function.
Dependent sources are never turned off when applying superposition technique.