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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)

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