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Announcements. Assignment 3 due now, or by tomorrow 5pm in my mailbox Assignment 4 posted, due next week Thursday in class, or Friday 5pm in my mailbox mid-term: Thursday, October 27 th. Lecture 11 Overview. Amplifier impedance The operational amplifier Ideal op-amp Negative feedback

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  1. Announcements • Assignment 3 due now, or by tomorrow 5pm in my mailbox • Assignment 4 posted, due next week • Thursday in class, or Friday 5pm in my mailbox • mid-term: Thursday, October 27th

  2. Lecture 11 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. • 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. • The ideal amplifier has zero output impedance

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

  7. 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.

  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. • 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.

  9. 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

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

  11. Applications Originally developed for use in analog computers: http://www.youtube.com/watch?v=PBILL8UypHA

  12. Applications Originally developed for use in analog computers: http://www.youtube.com/watch?v=PBILL8UypHA

  13. 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

  14. Noninverting Amplifier

  15. 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)

  16. 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

  17. 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 • Simplifies circuit design - can concentrate on circuit function (as opposed to details of operating points, biasing etc.)

  18. More insight • Under negative feedback: • We also know • i+ ≈ 0 • i- ≈ 0 • Helpful for analysis (under negative feedback) • Two "Golden Rules" • 1) No current flows into the op-amp • 2) v+ ≈ v-

  19. More insight • Allows us to label almost every point in circuit terms of vIN! 1) No current flows into the op-amp 2) v+ ≈ v-

  20. Op amp circuit 1: Voltage follower • So vO=vIN • or, using equations • What's the gain of this circuit?

  21. Op amp circuit 1: Voltage follower • So vO=vIN • or, using equations • What's the application of this circuit? • Buffer • voltage gain = 1 • input impedance=∞ • output impedance=0 Useful interface between different circuits: Has minimum effect on previous and next circuit in signal chain RS ROUT RL RIN AVIN VIN VOUT VS

  22. Op amp circuit 2: Inverting Amplifier • Signal and feedback resistor, connected to inverting (-) input. • v+=v- connected to ground v+ grounded, so:

  23. Op amp circuit 3: Summing Amplifier • Same as previous, but add more voltage sources

  24. Summing Amplifier Applications • Applications - audio mixer • Adds signals from a number of waveforms • http://wiredworld.tripod.com/tronics/mixer.html • Can use unequal resistors to get a weighted sum • For example - could make a 4 bit binary - decimal converter • 4 inputs, each of which is +1V or zero • Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

  25. Op amp circuit 4: Another non-inverting amplifier • Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow) • Input voltage to non-inverting input

  26. Op amp circuit 5: Differential Amplifier (subtractor) • Useful terms: • if both inputs change together, this is a common-mode input change • if they change independently, this is a normal-mode change • A good differential amp has a high common-mode rejection ratio (CMMR)

  27. Differential Amplifier applications • Very useful if you have two inputs corrupted with the same noise • Subtract one from the other to remove noise, remainder is signal • Many Applications : e.g. an electrocardiagram measures the potential difference between two points on the body http://www.picotech.com/applications/ecg.html The AD624AD is an instrumentation amplifier - this is a high gain, dc coupled differential amplifier with a high input impedance and high CMRR (the chip actually contains a few opamps)

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