Operational Amplifier OpAmp

1. Operational AmplifierOpAmp

2. Overview • Amplifier impedance • The operational amplifier • Ideal op-amp • Negative feedback • Applications • Amplifiers • Summing/ subtracting circuits

3. Impedances • Why do we care about the input and output impedance? • Simplest "black box" amplifier model: ROUT VOUT VIN RIN AVIN • The amplifier measures voltage across RIN, then generates a voltage which is larger by a factor A • This voltage generator, in series with the output resistance ROUT, is connected to the output port. • A should be a constant (i.e., gain is linear)

4. Impedances • Attach an input - a source voltage VS plus source impedance RS RS ROUT RIN VOUT AVIN VIN VS • Note the voltage divider RS + RIN. • VIN=VS(RIN/(RIN+RS) • We want VIN = VS regardless of source impedance • So want RIN to be large. • Q: What would be the input impedance of an ‘ideal amplifier’? •  The ideal amplifier has an infinite input impedance

5. Impedances • Attach a load - an output circuit with a resistance RL RS ROUT RL RIN AVIN VIN VOUT VS • Note the voltage divider ROUT + RL. • VOUT=AVIN(RL/(RL+ROUT)) • Want VOUT=AVIN regardless of load • We want ROUT to be small. • Q: What would be the output impedance of an ‘ideal amplifier’? •  The ideal amplifier has zero output impedance

6. Operational Amplifier • Integrated circuit containing ~20 transistors, multiple amplifier stages

7. Ideal Operational Amplifier • Operational amplifier (Op-amp) is made of many transistors, • diodes, resistors and capacitors in integrated circuit technology. • Ideal op-amp is characterized by: • Infinite input impedance • Infinite gain for differential input • Zero output impedance • Infinite frequency bandwidth

8. Operational Amplifier • An op amp is a high voltage gain, DC amplifier with high input impedance, low output impedance, and differential inputs. • Positive input at the non-inverting input produces positive output • Positive input at the inverting input produces negative output.

9. 741 Op Amp IC

10. A component-level diagram of the common 741 op-amp. Dotted lines outline: current mirrors (red); differential amplifier (blue); class A gain stage (magenta); voltage level shifter (green); output stage (cyan).

11. IC Product DIP-741 Dual op-amp 1458 device Operational Amplifier

12. A small-scale integrated circuit, the 741 op-amp shares with most op-amps an internal structure consisting of three gain stages: 1. Differential amplifier (outlined blue) — provides high differential amplification (gain), with rejection of common-mode signal, low noise, high input impedance

13. 2. Voltage amplifier (outlined magenta) — provides high voltage gain, a single-pole frequency roll-off, and in turn drives the 3. Output amplifier (outlined cyan and green) — provides high current gain (low output impedance), along with output current limiting, and output short-circuit protection. Additionally, it contains current mirror (outlined red) bias circuitry and a gain-stabilization capacitor (30 pF).

14. Op Amp Equivalent Circuit vd = v2 – v1 A is the open-loop voltage gain v2 v1 Voltage controlled voltage source

15. Operational Amplifier • Can model any amplifier as a "black-box" with a parallel input impedance Rin, and a voltage source with gain Av in series with an output impedance Rout.

16. RS + RL vout - Ideal op-amp • Place a source and a load on the model So the equivalent circuit of an ideal op-amp looks like this: • Infinite internal resistance Rin (so vin=vs). • Zero output resistance Rout (so vout=Avvin). • "A" very large • iin=0; no current flow into op-amp

17. Ideal vs. Real op-amps!

18. Symbols for Ideal and Real Op Amps

19. Ideal Vs Practical Op-Amp Operational Amplifier

20. Typical Op Amp Parameters

21. Almost Ideal Op Amp • Ri = ∞ W • Therefore, i1 = i2 = 0A • Ro = 0 W • Usually, vd = 0V so v1 = v2 • The op amp forces the voltage at the inverting input terminal to be equal to the voltage at the noninverting input terminal if there is some component connecting the output terminal to the inverting input terminal. • Rarely is the op amp limited to V- < vo < V+. • The output voltage is allowed to be as positive or as negative as needed to force vd = 0V.

22. Many Applications, e.g., • Amplifiers • Adders and subtractors • Integrators and differentiators • Clock generators • Active Filters • Digital-to-analog converters

23. Applications • Audio amplifiers • Speakers and microphone circuits in cell phones, computers, mpg players, boom boxes, etc. • Instrumentation amplifiers • Biomedical systems including heart monitors and oxygen sensors. • Power amplifiers • Analog computers • Combination of integrators, differentiators, summing amplifiers, and multipliers

24. Applications Originally developed for use in analog computers:

25. Using op-amps • Power the op-amp and apply a voltage • Works as an amplifier, but: • No flexibility (A~105-6) • Exact gain is unreliable (depends on chip, frequency and temp) • Saturates at very low input voltages (Max vout=power supply voltage) • To operate as an amp, v+-v-<VS/A=12/105 so v+≈v- • In the ideal case, when an op-amp is functioning properly in the active region, the voltage difference between the inverting and non-inverting inputs≈0

26. Voltage Transfer Characteristic Range where we operate the op amp as an amplifier. vd

38. Inverting Apmlifier

40. Non-inverting amplifier

43. Noninverting Amplifier

44. When A is very large: Take A=106, R1=9R, R2=R >>1 • Gain now determined only by resistance ratio • Doesn’t depend on A, (or temperature, frequency, variations in fabrication)

45. Negative feedback: • How did we get to stable operation in the linear amplification region??? • Feed a portion of the output signal back into the input (feeding it back into the inverting input = negative feedback) • This cancels most of the input • Maintains (very) small differential signal at input • Reduces the gain, but if the open loop gain is ~, who cares? • Good discussion of negative feedback here: • http://www.allaboutcircuits.com/vol_3/chpt_8/4.html

46. Why use Negative feedback?: • Helps to overcome distortion and non-linearity • Improves the frequency response • Makes properties predictable - independent of temperature, manufacturing differences or other properties of the opAmp • Circuit properties only depend upon the external feedback network and so can be easily controlled

47. Positive Feedback When we flip the polarization of the op-amp as shown on the figure we will get a positive feedback that saturates the amplifier output. This is not a good idea.

48. Negative vs. Positive Feedback Familiar examples of negative feedback: • Thermostat controlling room temperature • Driver controlling direction of automobile • Pupil diameter adjustment to light intensity Familiar examples of positive feedback: • Microphone “squawk” in sound system • Mechanical bi-stability in light switches Fundamentally pushes toward stability Fundamentally pushes toward instability or bi-stability Week 8, Prof. White

49. Noninverting amplifier Noninverting input with voltage divider Less than unity gain Voltage follower Operational Amplifier

50. Inverting Amplifier • Kirchhoff node equation at V+ yields, • Kirchhoff node equation at Vyields, • Setting V+ = V– yields Notice: The closed-loop gainVo/Vin is dependent upon the ratio of two resistors, and is independent of the open-loop gain. This is caused by the use of feedback output voltage to subtract from the input voltage. Operational Amplifier