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• Assignment 4 posted, due next week– Thursday in class, or Friday 5pm in my

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• mid-term: Thursday, October 27th

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

RIN

ROUT

VIN AVINVOUT

• 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)

• Attach an input - a source voltage VS plus source impedance RS

Impedances

RIN

ROUT

VINAVIN

VOUT

• 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

VS

RS

• Attach a load - an output circuit with a resistance RL

Impedances

• 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

RIN

ROUT

VINAVIN VOUTVS

RS

RL

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 Rin, and a voltage source with gain Av in series with an output impedance Rout.

Ideal op-amp• Place a source and a load on the model

• 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

-

+

voutRL

RS

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

ApplicationsOriginally developed for use in analog computers:

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

ApplicationsOriginally 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~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

Noninverting Amplifier

21

2

)(

RR

RvvAv

vvAv

OINO

O

INO AvRR

ARv

21

21

21

21 RRARAv

v INO

When A is very large:

Take A=106, R1=9R, R2=R

10101

101

10

9101

10

6

6

6

6

INO

INO

INO

vv

vv

RRR

vv

2

21

21

2

21

21

R

RRvv

RRR

A

Avv

RRARAv

v

INO

INO

INO

• 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:

vv

A

vRRR

A

vvv

IN

O 01

21

• We also know• i+ ≈ 0• i- ≈ 0

• Helpful for analysis (under negative feedback)• Two "Golden Rules"

1) No current flows into the op-amp2) v+ ≈ v-

More insight

• Allows us to label almost every point in circuit terms of vIN!

1) No current flows into the op-amp2) v+ ≈ v-

Op amp circuit 1: Voltage follower

• So vO=vIN

•or, using equations

2

21

R

RRvv INO

2

1 0

R

R

• What's the gain of this circuit?

Op amp circuit 1: Voltage follower

• So vO=vIN

•or, using equations

2

21

R

RRvv INO

2

1 0

R

R

• What's the application of this circuit?•Buffer

voltage gain = 1input impedance=∞output impedance=0

Useful interface between different circuits: Has minimum effect on previous and next circuit in signal chain

RIN

ROUT

VINAVIN VOUTVS

RS

RL

Op amp circuit 2: Inverting Amplifier

SS

Fout

F

out

S

S

F

out

S

S

FS

inFS

vR

Rv

R

v

R

v

R

vv

R

vv

ii

iii

00

0

• Signal and feedback resistor, connected to inverting (-) input.

• v+=v- connected to ground

S

F

S

out

R

R

v

vGain

0 vvv+ grounded, so:

Op amp circuit 3: Summing Amplifier

SNSN

FS

S

FS

S

Fout

F

out

SN

SN

S

S

S

S

FN

vR

Rv

R

Rv

R

Rv

R

v

R

v

R

v

R

v

iiii

.....

.....

.....

22

11

2

2

1

1

21

• Same as previous, but add more voltage sources

)...( 21 SNSSS

Fout vvv

R

Rv

SSNSS RRRR ... If 21

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

vv FS ii

S

in

vvv

i

and

0 sinceF

out

S R

vv

R

v

0

S

F

S

out

SS

Fout

S

Fout

R

R

v

v

vR

Rv

vR

Rv

1Gain

1

1

Op amp circuit 5: Differential Amplifier (subtractor)

021 ii

)( 121

2

221

2

21

1

vvR

Rv

vvRR

Rv

vv

R

vv

R

vv

out

out

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