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. Slope = A Cont’d

7. Example

8.    Ideal OP AMP • Infinite open-loop voltage gain: A  • Infinite input resistance: Ri  • Zero output resistance: Ro 0 • v1 = v2 (virtual short) assumed for analysis

9. (feedback resistor) Inverting AMP The equivalent circuit

10. i1 i2 a i3 Example: I-to-V Converters

11. Noninverting AMP

12. Voltage Follower • Conditions: Rf= 0 or R1=  or both • Unity gain: Av= 1 • Useful as a buffer amp due to its very high Ri and very low Ro

13. Summing AMP

14. Difference AMP

15. Cascaded OP AMP Circuits

16. Applications: DAC Digital-to-Analog Converter (DAC) MSB: most significant bit LSB: least significant bit

17. Applications:Instrumentation Amplifier (IA)

18. Cont’d • Characteristics of IA • Voltage gain adjustable by RG • Very high Ri and very low Ro • The differential voltage is amplified and the common-mode voltage is rejected