1 1 Op Amp Basics op amp = operational amplifier Prepared by Scott Robertson Fall 2007 Diefenderfer and Holton (D&H), Ch. 9 Horowitz and Hill (H&H), Ch. 4,5,6,7 2 What are they good for? • Amplifiers: sum and difference of voltages • Differentiators • Integrators • Buffers or follower (cable drivers) • Filters: high pass, low pass, bandpass, band reject, notch • Comparators • Limitations of op amps (nonideal behavior) • Oscillators (another lecture)
21
Embed
Op Amp Basics 8 - University of Colorado Boulder€¦ · 4 7 Characteristics of the ideal op amp 1. Input impedance is infinite inputs draw no current 2. Gain G is infinite in the
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
1
Op Amp Basics
op amp = operational amplifier
Prepared by Scott RobertsonFall 2007
Diefenderfer and Holton (D&H), Ch. 9
Horowitz and Hill (H&H), Ch. 4,5,6,7
2
What are they good for?• Amplifiers: sum and difference of voltages• Differentiators• Integrators• Buffers or follower (cable drivers)• Filters: high pass, low pass,
bandpass, band reject, notch• Comparators• Limitations of op amps (nonideal behavior)• Oscillators (another lecture)
2
3
Theorists view: 3 pins:
Experimentalists view:7 pins + ground:
+
−
VoutVB
VA
VoutVB
VA
V+
V−
Offset adjust
(optional)
Vout = Gain × (VB – VA) Vout from Golden Rules
Inverting input
Non-inverting input
+
−
Positive power supply
Negative power supply
Ground is sometimes not connected to the op amp.
4
Manufacturer’s views
Dual-in-line (DIP) PackageThe socket also has a notch at pin 1 so you don’t put the op amp in backwards.
Notch
3
5
What’s inside?
National’s LF356
6
“Bypass” the impedance of the power supply wires using small capacitors
VoutVB
VA
V+
V−
+
−
0.01 μF, >15 V
Failure to do this can cause oscillation and “cross talk”between circuits because the power supply voltage will otherwise vary when the load varies.
To power supply
To power supply
A screwdriver-adjust potentiometeris used for “one time” offset adjustment
Small disc ceramic capacitors are used for “bypass.” They MUST be located near (a few cm) to the chip and attached to a “good” ground.
4
7
Characteristics of the ideal op amp1. Input impedance is infinite
inputs draw no current2. Gain G is infinite
in the math, terms with 1/G → 03. Negative feedback determines the
function performed Negative feedback is a connection from the output to the inverting input
4. Output impedance is zero
From D & H ch 9-1
8
Inverting x1 amplifier (G not ∞)
+
− Vout
VB
VA
R
R
I1
I2Vin
BGAGV
AB
inGGV
inout
Ainout
outAAin
Aout
B
VVVV
VVV
VVVR
VVR
VV
VGVV
out
out
⎯⎯ →⎯=−
−⎯⎯ →⎯−−=
+−=
−=
−=
−×==
∞→
∞→
;
unknowns 2 equations, 22
(2)
II(1) )0(
thus0
2
21
Negativefeedback
5
9
Golden rules of ideal op amps
1. The output does what is necessary to make VB = VA.
2. The inputs draw no current.
With these rules, knowledge of G is not needed as long as G>>1.
Reference: H&H 4.03
10
Inverting amplifier from Golden Rules
+
−
Vout
VB
VA
R2
R1
I1
I2Vin
inout
outin
AB
VRRV
RV
RV
VVII
1
2
21
21
unknown 1 equation, 1
000 and
:rulesGolden
−=
−=
−===
X10 inverting amplifier if R2 = 100KΩ and R1 = 10 kΩ.
6
11
Summing amplifier
+
−
Vout
VB
VA
R
V1V2V3
VA = 0
Vout = -(V1 + V2 + V3)
R,R,R
“intuitively obvious”
12
Current to voltage converteror electrometer
+Vout
VB
VA
R
I1
-I1
Vout = −I1 R + Voffset
Used to measure small currents.
Offset error: Voffset = -Ileak R,
where Ileak is the nonideal input offset current
(also called Ibias).
→ Ileak-
7
13
Non-inverting amplifier with gain >1
+
−
Vout
VA
R2
R1
I1
I2
Vin
1
2
1
21
21
1
1
:divider voltagesimple isFeedback rule)(Golden
RR
VV
RRRVV
RRRVV
VV
in
out
inout
outA
Ain
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛ +=
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=
=
Answer is NOT R2/R1.
Can’t make a x1 or x0.5 amplifier this way!
VB
14
Non-inverting amplifier with gain = 1 or <1
+
−
Vout
VA
Vin
x1 amplifier is a buffer or followerIt is used to drive long lengths of cable, otherwise signal is decreased.
High current buffer amplifiers with no “-B”input are available.
VB
+
−
Vout
VA
Vin
VB
Volume control, gain <1
BUF634 can put out 250 mA !
8
15
Difference or “B-A” amplifier
+
−
Vout
V1
VA
R2
R1
V2
R1R2
VB
The mathematical analysis is in D&H, ch. 9-5, (3 eqns., 2 unknowns)
1
212 )(
RRVVVout −=
Gain can be 1, >1 or <1.
16
Differentiator from Golden Rules
inout
outin
outin
AB
VdtdRCV
RCVV
dtd
RVV
dtdC
VVII
−=
−=
−=
===
unknown 1 equation, 1
or
0 and :rulesGolden
21
+
−
Vout
VB
VA
R
C
I1
I2Vin
The derivative of a step fcn. is a delta fcn.
What determines the width of the delta fcn. in this case?What determines the height?
Vin
Vout
Here is what it will do to a square pulse:
oscilloscope
9
17
Simple integrator is “ruined” by nonideal Ibias
+
→ Ileak
Vout
VB
VA
C
R
I1
I2Vin
stops.n integratio andcurrent leakage by the voltagesupply the tocharged iscapacitor the,Eventually
)0(11
unknown 1 equation, 1
or
0 and :rulesGolden
nintegratioofconstant
00
21
4342143421
=+′−′−=
+−=−=−
===
∞→
∫∫ tVtdIC
tdVRC
V
CI
RCVV
dtdV
dtdCI
RV
VVII
out
t
leak
t
inout
leakinoutoutleak
in
AB
Ileak is the tiny input current to terminal VA, often ignored. Ileak is also called Ibias.
18
Practical op amp integrator with extra resistor
+Vout
VB
VA
C
R1
I1
I2Vin
22
2
02
merror ter
0201
2121
21
:is thisofcost The big. R make so
1or 1
1
if small is error term
11
or
0 and :rulesGolden
RIVCR
tV
tdVCR
tdVCR
tdVCR
V
CRV
CRVV
dtd
RVV
dtdC
RV
VVII
leakoffset
out
t
out
t
out
t
inout
outinout
outout
in
AB
−=
<<<<
′
′−′−=
−−=−−=
===
∫
∫∫4434421
Ileak is the tiny input current to terminal VA, often ignored.
R2
R2 tends to discharge C
→ Ileak
10
19
Error of practical integrator is “droop”Vin
t’ → t
Vout True integral
Output of practical integrator “droops” with time constant R2C
Not significant if R2C >> t
Input signal
oscilloscope
20
The comparator
a special kind of op amp
11
21
Comparatoroutput is either high (V+) or low (V-)
+
−
Vout
VA
V+
VB
Vref
Vtest
Vtest > Vref Vout is V+
Vtest < Vref Vout is V-
Op amps designed to be comparators are not damaged if VA ≠ VB.
22
Comparator as temperature controller
+
−
Vout
V+
Vref
Vtest
V+
Heater
RT
Thermistor RT is heated and gets more resistive, driving Vtest down below Vref, and the heater turns off until the comparator changes state again.
Buffer
R
R
R
Note that V- can be ground.
“Thermostat”
Colder
Hotter
12
23
Some comparators only “sink” currentthe output is an “open collector”
+
−
Vout
VA
V+
VB
Vref
Vtest
Rload
LF311
Wait a bit and we will talk about transistors and what this means.
V+
24
Schmitt triggerDefinition:
A comparator that goes high at a higher reference voltage than the reference voltage for going low.
If off, and then
Vtest > Vref - ΔV then output goes high (furnace turns on at 68 F)
If on, and then
Vtest < Vref + ΔV then output goes low (furnace turns off at 70 F)
Why do this?
So that your furnace (for example) will stay on until the house heats up a few degrees, then turn off. The furnace should run 5 minutes per hour rather than 5 seconds per minute. ΔV determines how much the parameter being controlled is allowed to vary.
13
25
Comparator made into Schmitt trigger
+
−
Vout
V+
Vref
“thermostat”
Vtest
V+
Heater
RT Buffer
Positive feedback (100RT) raises Vtest relative to Vref when the heater is on, which has the same effect as lowering Vref (by about 1% in this case). This circuit provides control to order 1%.
100 RT
R R
R
RT ≅ R
26
Schmitt trigger for digital logicprevents noise from changing the output
Vref+ΔVVref – ΔV
Vin
Noisy signal
Special symbol For Schmitt trigger
time →
Clean output
Noisy outputOrdinary
comparator
Vout
Vout
14
27
Comparator made into time delay
+
−
Vout
VA
V+
VB
Vref
time →
Vref
Vin
Vout
Input pulse (solid)
C voltage (dotted)
Delayed output pulseDelay is of order RC
R CVin
28
Filters
15
29
Filters are for1. removal of noise2. selecting a feature (radio station?)Low pass High pass Bandpass,
Band reject
f f f
Q ≅ f / Δf
Quality factor
in
out
VV
in
out
VV
in
out
VV
30
Unsophisticated low pass filter (3db per octave)
+
−
Vout
VB
VA
Z2 = [(R2)-1+jC2ω]−1
Z1= R1
Vin
ω
ω
ω
jRCVV
CjRRR
VV
RZjCR
Z
VZZVV
RRV
in
out
in
out
inoutinout
+=
+⎟⎟⎠
⎞⎜⎜⎝
⎛−=
=⎟⎟⎠
⎞⎜⎜⎝
⎛+=
−=−=
−
11
:RC simple toCompare
11
and 1 :Let
becomes
analysiscircuit amp opin by Z R Replace
21
2
11
1
22
2
1
2
1
2C2
R2
Vin Vout
Vout/Vin
f
16
31
Unsophisticated high pass filter
+
−
VB
VA
R2
C
I1
I2Vin R1
ωωω
ω
ωωω
ω
ω
jRCjRCjRC
jCRR
VV
CjRRR
CjRCjR
jCRR
VV
RZjCRZ
VZZV
in
out
in
out
inout
/111
1/1
:RC simple toCompare
/111
1/1
and /1 :Let
11
2
1
2
1
2
2212
1
2
+=
+=
+=
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−=+−
=⎟⎟⎠
⎞⎜⎜⎝
⎛+
−=
=+=
−=
Vin
Vout/Vin
f
32
Sophisticated filters• You can easily get 6 db per octave with 1 op amp, 2 Rs
and 2 Cs, so don’t settle for 3 db per octave (previous slides).
• It is standard practice to copy the filter design from a book.
• There are “too many” filter designsButterworth, Bessel, Chebyshev, etc.Some designs are flatter near the cutoff.
• See textbooks for examples
f
17
33
Typical 6 db per octave filter4 Rs, 2 Cs
+
−
C
R
C
See H&H, Fig. 5-16.
R
R
R
34
Twin – T notch reject filterVin
Vout
90 degreephase advance at f0
90 degreephase delay at f0
At frequency f0, currents from the two sides of the circuit are 180 degrees out of phase and cancel at location Vout .
f0 f
2C R/2
R,R C,C
Vout/Vin
18
35
Non ideal op amps
• There is a nonzero input current (20 pA?)• Op amp can’t put out more volts than V+ or V-
• The output current is limited (usually it can’t drive a long 50 ohm cable) 5 V / 50 ΩΩ = 100 mA = too much
• The frequency response is limited(pay more $ above 1 MHz)
36
Input current is not zero
And it increases with temperature strongly!
LF156 family
19
37
Output impedance
Output impedance is higher at higher frequencies and higher gains Av.
Don’t ask for more than about 15 mA from this chip. This chip cannot put 1 V onto 50 ohms!
LF156 family
38
Op amp frequency response
)(1)(1)(
0
0
0
0
ffjG
jGG
+=
+=
ωωω
000 )( ωωωωω >>≅× GG
Open loop gain G(ω) is less at high frequencies.
f0 and ω0 are 3 db points of op amp.
Open loop gain-bandwidth product (~5 MHz) is a constant at the higher frequencies.
An expression for the gain G valid at all frequencies is:
)/(1)(
0
0
ωωω
jGG
+=
20
39
Using gain bandwidth product
Suppose the gain-bandwidth product G(ω)ω = 5 MHz.
Then I can have a gain of 5 at 1 MHz.
Or a gain of 1 at 5 MHz.
Or a gain of 50 at 100 kHz, etc.
This helps you SELECT the proper op amp for the job.
40
Op amp frequency response with feedback
If the feedback sets the gain at 30 db, then the frequency response of the circuit is flat to 100 kHz for this chip.
Open loop response
Closed (feedback) loop response for
30 db gain
21
41
The op amp has internal noise
Ordinary noise(independent of f)
1/f (one-over-f) noisebelow ~100 Hz (varies)
Noise is covered later in PHYS3330. Please wait a while to find out what √Hz is all about.