1. EMLAB 1 Chapter 4. Operational amplifiers 2014. 9. 24.

2. EMLAB 2 Contents 1. Introduction 2. Op-Amp Models 3. Fundamental Op-Amp Circuits 4. Comparators 5. Application Examples 6. Design Examples

3. EMLAB 3 Why operational amplifiers ? 1.Originally, the op-amp was designed to perform mathematical operations such as addition, subtraction, differentiation, and integration. 2.By adding simple networks to the op-amp, we can create these “building blocks” as well as voltage scaling, current-to-voltage conversion, and myriad more complex applications.

4. EMLAB 4 2. Op-amp model Ideal op-amp :

5. EMLAB 5 Example

6. EMLAB 6 Example : unity gain buffer

7. EMLAB 7 Example 4.2 Let us determine the gain of the basic inverting op-amp configuration shown in the figure using both the non-ideal and ideal op-amp models

8. EMLAB 8 Ideal model Virtual short Step 1. Use the ideal op-amp model: A o = ∞, R i = ∞, R o = 0. i + = i - =0, v + = v - Step 2. Apply nodal analysis to the resulting circuit. Step 3. Solve nodal equations to express the output voltage in terms of the op-amp input signals.

9. EMLAB 9 Let us now determine the gain of the basic non-inverting op-amp configuration shown in the figure. Example 4.3

10. EMLAB 10 Consider the op-amp circuit shown in the figure. Let us determine an expression for the output voltage. Example 4.5

11. EMLAB 11 Example 4.6 The circuit shown in the figure is a precision differential voltage-gain device. It is used to provide a single-ended input for an analog-to-digital converter. We wish to derive an expression for the output of the circuit in terms of the two inputs.

12. EMLAB 12 Example 4.7

13. EMLAB 13 4.4 Comparators (a) A zero-crossing detector and (b) the corresponding input/output waveforms. (a) An ideal comparator and (b) its transfer curve.

14. EMLAB 14 Application example 4.11 An instrumentation amplifier of the form shown in Fig. 4.26 has been suggested. This amplifier should have high-input resistance, achieve a voltage gain V o /(V 1 -V 2 ) of 10, employ the MAX4240 op-amp listed in Table 4.1, and operate from two 1.5 V AA cell batteries in series. Let us analyze this circuit, select the resistor values, and explore the validity of this configuration.

15. EMLAB 15

16. EMLAB 16