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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

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Lecture 11 Overview Amplifier impedance The operational amplifier Ideal op-amp Negative feedback Applications –Amplifiers –Summing/ subtracting circuits

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

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Attach an input - a source voltage V S plus source impedance R S Impedances R IN R OUT V IN AV IN V OUT Note the voltage divider R S + R IN. V IN =V S (R IN /(R IN +R S ) We want V IN = V S regardless of source impedance So want R IN to be large. The ideal amplifier has an infinite input impedance VSVS RSRS

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Attach a load - an output circuit with a resistance R L Impedances Note the voltage divider R OUT + R L. V OUT =AV IN (R L /(R L +R OUT )) Want V OUT =AV IN regardless of load We want R OUT to be small. The ideal amplifier has zero output impedance R IN R OUT V IN AV IN V OUT VSVS RSRS RLRL

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

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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.

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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 R in, and a voltage source with gain A v in series with an output impedance R out.

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Ideal op-amp Place a source and a load on the model Infinite internal resistance R in (so v in =v s ). Zero output resistance R out (so v out =A v v in ). "A" very large i in =0; no current flow into op-amp - + v out RLRL RSRS So the equivalent circuit of an ideal op-amp looks like this:

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

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

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

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Using op-amps Power the op-amp and apply a voltage Works as an amplifier, but: No flexibility (A~10 5-6 ) Exact gain is unreliable (depends on chip, frequency and temp) Saturates at very low input voltages (Max v out =power supply voltage) To operate as an amp, v + -v - <V S /A=12/10 5 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

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Noninverting Amplifier

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When A is very large: Take A=10 6, R 1 =9R, R 2 =R Gain now determined only by resistance ratio Doesn’t depend on A, (or temperature, frequency, variations in fabrication) >>1

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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

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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.)

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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 -

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

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Op amp circuit 1: Voltage follower So v O =v IN or, using equations What's the gain of this circuit?

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Op amp circuit 1: Voltage follower So v O =v IN 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 R IN R OUT V IN AV IN V OUT VSVS RSRS RLRL

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

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

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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)

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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

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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)

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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 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) http://www.picotech.com/applications/ecg.html

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