1. Operational Amplifiers

2. What is an Op Amp? High voltage gain IC with differential inputs –Designed to have characteristics near ideal Inexpensive, widely used IC Available in wide range of packages Typically require a positive and a negative power supply Uses: amplifier, buffer, summer, differentiator, integrator, comparator, instrumentation amp, Schmitt trigger, negative impedance, super diode, logarithmic/exponential output, simulated inductor

3. History of Op Amps Originally designed for analog computers using vacuum tubes –Output voltage is a function of input voltage (addition, subtraction, integration, differentiation, exponential, logarithm…) K2-W: first mass produced op amp (1952) –Invented by George Philbrick –$22. Gain ≈ 20,000. Gain-bandwidth ≈ 1MHz. Input impedance ≈ 50kΩ –See picture (K2-W with and without shell)

4. History of Op Amps First transistor op amp (μA702) used 12 BJTs –Invented in 1964 by Bob Widlar –Sold for $300 –Prone to short circuits μA709 improved on μA702 (used 14 transistors) –Invented in 1965 also by Bob Widlar –Higher gain, more bandwidth, cheaper, more robust –Sold for $70 to start, then $2 within a few years

5. 741 Op Amp Introduced in 1968, and versions still available and in use today

6. μA741 Op Amp

7. Op Amp Flavours High output power High speed large bandwidth Low noise Low power Low voltage PrecisionRail-to-Rail Small package >1 Op Amp per package

8. Ideal Op Amp Input resistance is infinite Output resistance is zero Bandwidth is infinite Input current is zero Open loop gain is infinite Output voltage is zero when input voltages are zero

10. Ideal Op Amp Gain If open loop gain of ideal op amp → ∞, what’s the use? –Any input will result in + or – saturation Even non-ideal op amps not useful with open loop –Only small input voltages before + or - saturation Op amps almost never use open loop. –Use feedback to control the actual gain Feedback!

11. Feedback Positive Feedback –Output feeds back to input, and increase output leading to out of control system –E.g., microphone picks up speaker output, driving speaker output higher which is picked up by microphone… Negative Feedback –Output feeds back to input to allow system to adjust and keep output within a certain range –E.g., body controlling blood glucose levels

12. Feedback in Op Amps If output is fed back to non-inverting input – positive feedback occurs –Not useful If output is fed back to inverting input – negative feedback occurs –Widely used configuration

13. Golden Rules for Op-Amps 1. With negative feedback: The op amp drives the output so that the two inputs are at equal voltage 2. Assume that the input current is zero.

14. Buffer or Voltage Follower No voltage difference between the output and the input Buffer draws no current, so it puts no load on the source. Output current supplied by VCC. Used to isolate sources from loads

15. Non-Inverting Amplifier

16. A V = V o /V I V I = V 2 (i.e., V in+ = V in- ) … from “Golden Rules” No current flows into V in+ (Golden Rule) therefore: V I = V 2 = V o * R1/(R 1 + R 2 ) … voltage divider V I = V 2 = V o * R1/(R 1 + R 2 ) … voltage divider A V = V o /V I = (R 1 + R 2 )/R 1 = 1 + (R 2 / R 1 ) V2V2

17. Non-Inverting Amplifier Other Considerations R2 can’t be too low since the Op Amp has limited current capability R1 should be much smaller than the input impedance Circuit voltage gain should be much less than the open loop gain of the Op Amp The output voltage swing has to be less than the supply voltages

18. Non-Inverting Amplifier Examples (from course package)

19. Inverting Amplifier

20. Current through R 1 equals the current through R f No current into the inputs The voltage at both op amp inputs is zero

21. Inverting Amplifier Current through R 1 Current through R f

22. Inverting Amplifier Why the minus sign for the current through R f ? –The convention for Ohm’s Law is that the current flows from the high voltage to the low voltage for a resistor –Here the current flows from the low voltage (ground) to the high voltage (V O )

23. Inverting Amplifier The current through R 1 must equal the current through R 2 since there is no current in the inputs. Combining the two equations for the currents

24. Inverting Amplifier Examples (from course package)

25. Op Amp Applications Arithmetic –Summing, differencing Calculus –Integration, differentiation Level detectors –Comparators, Schmitt Triggers