1. EENG 2610: Circuits Analysis Class 6: Operational Amplifiers (Op-Amp), 1/2 Oluwayomi Adamo Department of Electrical Engineering College of Engineering, University of North Texas

2. Operational Amplifier (Op-Amp) Op-amp is the single most important integrated circuit (IC) for analog circuit design; it has been extensively used in circuit design at all levels. Op-amp is consisted of individual transistors and resistors interconnected on a printed circuit board (PCB) Op-amp was originally designed to perform mathematical operations such as addition, subtraction, differentiation, and integration. We have learned tools to analyze practical circuits using op-amps !

3. Op-Amp Models Op-amp is just a really good voltage amplifier! Example: LM324 from National Semiconductor  General purpose quad (four in a pack) op-amp. unit: inch Dual Inline Pack (DIP) style package Four identical op-amps in the package IN +: noninverting input IN -: inverting input OUT : output V CC : positive voltage V EE : negative voltage or ground Typically, A 0 is between 10,000 and 1,000,000 ! In-Out Voltage Relation:

4. Op-amp is modeled using a dependent voltage source and resistors Power Supply and Ground A simple model of op-amp In-Out Voltage Relation: voltage source

5. Effects of Power Supply Each op-amp has minimum and maximum supply ranges over which the op-amp is guaranteed to function  For proper operation, the input and output voltages are limited to no more than the supply voltages ( V CC, V EE). Inputs and output are called rail-to-rail, if the inputs and output can reach within a few dozen millivolts of the supplies. An op-amp is said to be in saturation,  If an increase in the input voltage may not yield a corresponding increase in the output voltage

6. Saturation and Rail-to-Rail In-Out Voltage Relation: Rail-to-rail output voltage PA03

7. Unity Gain Buffer Circuit That’s why it’s called Unity Gain Buffer, or Voltage Follower. PERFORMANCE OF REAL OP-AMPS Voltage Gain:

8. What should be the values for Voltage Gain: To achieve large overall gain independent of ideally (Commercial op-amps do have this tendency !) Equivalent resistance of voltage source Equivalent load resistance Op-amp Model

9. Ideal Op-Amp Model

10. Analyze unity gain buffer using ideal model Where does the current come from?

11. Why use unity gain buffer? Unity gain buffer is buffer amplifier  Unity gain buffer isolates driving circuits from load circuits, which is called buffering  The load current (or energy) comes from op-amp power supply, which have plenty of current (or energy) output capacity, rather than the driving circuit. CONNECTION WITHOUT BUFFER CONNECTION WITH BUFFER consume source energy does not consume source energy driving circuit load

12. 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

13. Example 4.2: Basic inverting op-amp configuration Determine gain using both non-ideal model and ideal model Note: the ground can all be connected to a single node. Equivalent

14. 1.Identify op-amp nodes 2. Redraw the circuit cutting out the op-amp 4. Redraw as needed 3.Draw components of linear op-amp Using non-ideal op-amp model:

15. Typical values:

16. Using ideal op-amp model: Ideal op-amp model: From now on, unless otherwise stated, we will use the ideal op-amp model to analyze circuits containing op-amp. General rule for op-amp circuit analysis  Use the ideal op-amp model conditions  Write nodal equations at the op-amp input terminals