lecture 2&3:Amplifiers

The heart of EE

Lecture outline

Ideal Op-Amp

Negative Feedback

Application to Filters

Linear systems

Bode plots

Op-amp nonidealities

Positive feedback

Reading:1)Hambley Ch 1,2, section 8.1

2) Lab 2 handout

Amplifiers

They are everywhere: Music, Computers, Sensors

Used to turn a small voltage into a bigger voltage that can be manipulated easily.

Some filtering is used as well.

amplifiers give gain

Simple amp-1 input and 1 output

Gain, A=Vout/Vin

Example

If the amplifier above gives an output voltage of 1000V with an input voltage of 50V, what is the gain?

ideal operational-amplifier(op-amp)

Inputs draw no current-infinite input impedace

Vout=A(Vplus-Vminus) A-open loop gain.

A is ideally infinity-How is this useful?

Output can provide as much voltage/current as needed-zero output impedance

http://www.youtube.com/watch?v=TQB1VlLBgJE

negative feedback

Negative feedback (NF) tries to reduce the difference

with NF, Vplus=Vminus ALWAYS

summing point constraints

virtual ground.

Inverting amplifier

Input goes into Vminus input-INVERTING input

Gain, Ainv=-R2/R1, gain is negative because inverting

inverting amplifier

Vplus=Vminus

Inputs draw no current

Non-inverting amplifier

Input goes into Vplus input-NON-INVERTING input

Gain, Ainv=1+R2/R1, gain is positive

unity gain buffer

Gain is 1 i.e. Vin=Vout

Used to isolate one side from the other

Real op-amps

Output voltage determined by rails (power supply)

Open loop gain not infinity

Inputs draw small amount of current-nA’s or less

Quad LM324Single LM741

http://www.national.com/mpf/LM/LM324.html#Overview

bandpass Filter amplifier

f1=0.3Hz, f2=10Hz

High freq., cap is short, low freq., cap is open

frequency<f1

all caps are open.

What is the gain?

F1<Frequency<F2

C1 is short. C2 is open.

What is the gain?-midband gain.

frequency>f2

All caps are shorts

What is the gain?

linear systems

T(s) has zeros when T(s)=0

T(s) has poles when T(s)=infinity

linear systemsAny voltage signal can be represented by a sum of sinusoidal voltage signals-Fourier/Laplace theorems

If s=jω, the input voltage is represented by:

V0exp(jωt)= V0exp(st)

Allows us to use algebra instead of differential eqns.

RLC circuit, for example.

t

ttt

filter op-amp

What is T(s)?

filter op-amp

zero at s=0

poles at 1/R1C1 and 1/R2C2

What happens at the zero? At the poles?

bode plots

Frequency response on log/log axes

x-axis frequency on log scale

y-axis gain in decibels (dB)

gain in dB=20log|Vo/Vi|

20dB/decade will appear often.

Can sketch quickly without doing too much math

bode plot rules

Zeros of transfer function

+20dB/decade increase in gain starting at zero

phase contribution at zero frequency is +45°

Total phase change is 90° attained at 10 times zero freq.

Poles of transfer function

-20dB/decade decrease in gain starting at zero

phase contribution at pole frequency -45°

Total phase change is -90° attained at 10 times pole freq.

See Hambley section 8.1

bode plot errors

Bode magnitude plot only has straight lines

not true near break frequencies ~3dB error

Bode phase plot only has straight lines

not true for phase near break frequencies ~5° error

Bode plot of filter

Zero at s=0, poles at s=1/R1C1 and 1/R2C2

Gain at midband =R2/R1or 20log(R2/R1) dB

midband, inverted output so phase=180°

bode plot of filter

180

135

90

op-amp non-idealities

Slew rate -maximum rate of change of voltage at output-arises from compensating capacitor

i.e. dv/dt|max

If input voltage changes too quickly, op-amp can’t keep up-leads to distortion of output.

Gain-bandwith product-high frequency, lower gain.

AOLfOL=ACLfCL HINT for prelab! Eqn 2.39

Unity gain frequency

Positive feedback

Amplifies differences, so output is always +/-Vcc

http://en.wikipedia.org/wiki/Schmitt_trigger

Schmitt trigger

Switches between 2 output rails +/-M.

Switch when inputs equal each other

Use resistors to control this

Inverting and non-inverting Schmitt triggers

Inverting SchmittStandard Schmitt

inverting schmitt trigger

Vtrigger=+/-VR2/(R1+R2)

Input into inverting input

Schmitt application

To minimize switching too often in noisy environment

e.g. Thermostat-switch only when T=+/-1degree

Does this represent inverting or non-inverting Schmitt?

EE SHORT: Tubes vs. Op-Amps

Old amplifiers used tubes-BIG!

New amplifiers use op-amps. Compact, high performance

http://www.youtube.com/watch?v=PbJ1GZMi_ho

more transfer functions & Timer circuitsfrequency response cont.