Transcript A-open loop gain.

lecture 2&3:
Amplifiers
The heart of EE
Lecture
outline
Ideal Op-Amp
Reading:
Negative Feedback
1)Hambley Ch 1,2, section 8.1
Application to Filters
2) Lab 2 handout
Linear systems
Bode plots
Op-amp nonidealities
Positive feedback
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)
http://www.youtube.com/watch?v=TQB1VlLBgJE
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
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
http://www.national.com/mpf/LM/LM324.html#Overview
Quad
LM324
Single
LM741
Output voltage determined by rails (power
supply)
Open loop gain not infinity
Inputs draw small amount of current-nA’s or less
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 systems
Any voltage signal can be represented by a sum of sinusoidal voltage signalsFourier/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
t
t
t
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
See Hambley section 8.1
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.
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
http://en.wikipedia.org/wiki/Schmitt_trigger
Amplifies differences, so output is always +/-Vcc
Schmitt trigger
Standard Schmitt
Inverting Schmitt
Switches between 2 output rails +/-M.
Switch when inputs equal each other
Use resistors to control this
Inverting and non-inverting Schmitt triggers
inverting schmitt trigger
Vtrigger=+/-VR2/(R1+R2)
Input into inverting input
Schmitt application
Does this represent
inverting or non-inverting
Schmitt?
To minimize switching too often in noisy
environment
e.g. Thermostat-switch only when T=+/-1degree
EE SHORT: Tubes vs. OpAmps
http://www.youtube.com/watch?v=PbJ1GZMi_ho
Old amplifiers used tubes-BIG!
New amplifiers use op-amps. Compact, high
performance
more transfer functions & Timer
circuits
frequency response cont.