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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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• 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

• 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:

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)

• 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

• 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

• Integrated circuit containing ~20 transistors, multiple amplifier stages

• 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.

• 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

• Amplifiers

• Integrators and differentiators

• Clock generators

• Active Filters

• Digital-to-analog converters

Originally developed for use in analog computers:

Originally developed for use in analog computers:

• 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

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)

• 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:

• 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.)

• 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-

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

1) No current flows into the op-amp

2) v+ ≈ v-

• So vO=vIN

• or, using equations

• What's the gain of this circuit?

• 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

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

• v+=v- connected to ground

v+ grounded, so:

• Same as previous, but add more voltage sources

• 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)

• Feedback resistor still to inverting input, but no voltage source on inverting input (note change of current flow)

• Input voltage to non-inverting input

• 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)

• 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)