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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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Announcements
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


Lecture 11 overview
Lecture 11 Overview

  • Amplifier impedance

  • The operational amplifier

  • Ideal op-amp

  • Negative feedback

  • Applications

    • Amplifiers

    • Summing/ subtracting circuits


Impedances
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)


Impedances1
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


Impedances2
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


Operational amplifier
Operational Amplifier

  • Integrated circuit containing ~20 transistors, multiple amplifier stages


Operational amplifier1
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 amplifier2
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.


Ideal op amp

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


Many applications e g
Many Applications e.g.

  • Amplifiers

  • Adders and subtractors

  • Integrators and differentiators

  • Clock generators

  • Active Filters

  • Digital-to-analog converters


Applications
Applications

Originally developed for use in analog computers:

http://www.youtube.com/watch?v=PBILL8UypHA


Applications1
Applications

Originally developed for use in analog computers:

http://www.youtube.com/watch?v=PBILL8UypHA


Using op amps
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



When a is very large
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)


Negative feedback
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
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
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 insight1
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-


Op amp circuit 1 voltage follower
Op amp circuit 1: Voltage follower

  • So vO=vIN

  • or, using equations

  • What's the gain of this circuit?


Op amp circuit 1 voltage follower1
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


Op amp circuit 2 inverting amplifier
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
Op amp circuit 3: Summing Amplifier

  • Same as previous, but add more voltage sources


Summing amplifier applications
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
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
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
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)