1. Operational Amplifiers Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

2. Contents Introduction Operational Amplifiers (OP AMPs) Ideal OP AMP Inverting AMP Noninverting AMP Summing AMP Difference AMP Cascaded OP AMP Circuits Applications

3. Introduction The op amp is a basic building block for performing mathematical operations such as summation, amplification, integration, and differentiation The concept of virtual short between the differential inputs of the op amp is extremely important for circuit analysis

4. OP AMPs Complex circuit networks consisting of transistors, resistors, capacitors, and diodes

5. Cont’d Equivalent circuit of an op amp + _

6. Cont’d ParameterTypical range Ideal value Open-loop gain, A 10 5 to 10 8  Input resistance, R i 10 5 to 10 13     Output resistance, R o 10 to 100  0  Supply voltage, V CC 5 to 24 V Slope = A

7. Example

8. Ideal OP AMP Infinite open-loop voltage gain: A   Infinite input resistance: R i   Zero output resistance: R o  0 v 1 = v 2 (virtual short) assumed for analysis   

9. Inverting AMP The equivalent circuit (feedback resistor)

10. Example: I-to-V Converters i1i1 i2i2 i3i3 a

11. Noninverting AMP

12. Voltage Follower Conditions: R f = 0 or R 1 =  or both Unity gain: A v = 1 Useful as a buffer amp due to its very high R i and very low R o

13. Summing AMP

14. Difference AMP

15. Cascaded OP AMP Circuits

16. Applications: DAC [S 1 S 2 S 3 S 4 ]Decimal- V o 000000 000110.125 001020.25 001130.375 010040.5 010150.625 011060.75 011170.875 100081.0 100191.125 1010101.25 1011111.375 1100121.5 1101131.625 1110141.75 1111151.875 Digital-to-Analog Converter (DAC)

17. Applications: Instrumentation Amplifier (IA)

18. Cont’d Characteristics of IA –Voltage gain adjustable by R G –Very high R i and very low R o –The differential voltage is amplified and the common-mode voltage is rejected