# 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.

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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 Applications –Amplifiers –Summing/ subtracting circuits

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)

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

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

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

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.

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.

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:

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

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

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

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

Noninverting Amplifier

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

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

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.)

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 -

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 -

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

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

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

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

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)

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

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)

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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