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

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

Example 4.5: Determine vo

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

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.

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

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 !

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

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.

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

Example 5.4: Use superpositon to find Vo

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.