Announcements

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# Announcements - PowerPoint PPT Presentation

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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Presentation Transcript
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
• Amplifier impedance
• The operational amplifier
• Ideal op-amp
• Negative feedback
• Applications
• Amplifiers
• Summing/ subtracting circuits
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)
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
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
• 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.

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.
• Amplifiers
• Integrators and differentiators
• Clock generators
• Active Filters
• Digital-to-analog converters
Applications

Originally developed for use in analog computers:

Applications

Originally developed for use in analog computers:

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:

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:
• 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:
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 vIN!

1) No current flows into the op-amp

2) v+ ≈ v-

Op amp circuit 1: Voltage follower
• So vO=vIN
• or, using equations
• What\'s the gain of this circuit?
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
• 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

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)