Download Physics 160 Lecture 16

Physics 160
Lecture 16
R. Johnson
May 20, 2015
Behavior, Limitations of Real Op-amps
•
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•
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Input offset voltage
Input current, and input-current mismatch
– Design to minimize voltage offsets from this current
– Input offset current
See the data sheet for the
Temperature dependences
LF411 (posted on the course
Slew rate
web page)
page).
– e.g. correcting crossover distortion
Frequency range (gen. purpose op amps are not for high frequencies)
Voltage gain and phase shift
– Stability!
CMRR and Common-mode input range
Input impedance with negative feedback is extremely high
Output impedance with negative feedback is very low
– What is really relevant is the limitation on output current drive
Output range (how close can the output get to the supply rails?)
– Single-supply op amps; can the output slew all the way to zero?
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Offset Voltage and Input Current
•
Offset voltage
– 2 mV max. for the 411
• This is the effective mismatch at the input. At the output it gets
multiplied
lti li d b
by th
the gain!
i !
– Trimming
+
V+
U1
3
7
V1
15
OS2
2
-
V-
OUT
OS1
6
1
R2
4
LM741
5
V2
– Temperature and time drifts
•
10k
15
I
Input
t currents
t (esp.
(
for
f BJTs)
BJT )
– Balancing resistors on inputs
– Input offset current
•
A/C Amp: reduce DC gain to unity to minimize offset effects
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Slew Rate
•
411 can slew outputs up to 15 V/s with no capacitive load
– For a 1 V sine wave output, for example, this limits the frequency to
2.4 MHz to avoid “harmonic”
harmonic distortion.
– Recall the limits on using an op-amp to cure crossover distortion
2.4  10 6 Hz  2  1V  15  10 6 V/s
4
Q1
3
+
V+
V1
15Vdc
OUT
V3
1k
-
LM324
V
11
2
Q2N3904
1
V-
R1
VOFF = 0
VAMPL = .2
FREQ = 10000
U1A
Q2N3906
Q2
R2
10k
V2
15Vdc
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Physics 160
Above ~100 Hz the
op-amp cannot slew
fast enough to cure
the cross-over
di t ti
distortion.
4
OP-AMP
OP
AMP STABILITY
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Gain and Phase Shift
Open loop gain of 100,000
Gain (dB
B)
Dominant Pole
LM301A Op-Amp
(uncompensated)
Second Pole
Unity gain
Frequency
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Stability Criterion
•
If the loop gain is >1 when the phase shift around the negative
feedback loop hits 180 degrees, then the circuit will oscillate.
– Your negative feedback becomes positive feedback at high
frequency!
– You probably won’t see the oscillation in a PSpice transient
simulation without doing extra work to introduce real-life effects,
plus some stimulus to initiate the oscillation. Don’t be fooled by
trusting your computer simulation too much!
A
B
•
Remember, the loop gain is AB, where A is the open-loop gain,
and B is the gain of the negative feedback.
– The follower has B=1, so that is usually the worst-case scenario for
stability (inverting amp usually has B<1)
• (A loop with B>1 is even more dangerous, hence the caution
about
b t putting
tti a capacitor
it across th
the ttransistor
i t iin th
the log-amp
l
feedback.)
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Phase
LM301A Op-Amp
(uncompensated)
Gain ((dB)
The open-loop gain is >0 dB at 180
degrees phase shift, so this op-amp
will surely oscillate if used as a
follower without compensation.
p
This doesn’t include additional
phase shifts that might exist in the
feedback network!
Frequency
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Compensated Op-Amp
Deliberately
D
lib t l enhance
h
the Miller effect to move
the dominant pole to
lower frequency
R
C
Miller effect at this gain
stage produces the
dominant pole
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External Compensation
Advantage
Ad
t
off
external
compensation: you
don’t need to
compensate as
much if B<1, so you
can have higher
frequency
performance.
Cs=30 p
pF
According to this formula from the data sheet, to make a
follower with R1>>R2
follower,
R1>>R2, C1 needs to be at least equal to Cs.
Cs
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Simulation of Follower Instability
Insignificant load,
load
like a ×10 scope
probe.
+
V+
V
U5
V1
OUT
C1
VS
2
-
V-
15Vdc
5
6
1
V
8
LM301A
4
V1 = 0
V2 = 0.2
TD = 0.1u
TR = 10n
TF = 10n
PW = 10u
PER = 10m
B
C2
3
7
Square wave input
CL
0.1pF
RL
10Meg
CC
1p
V2
R2
15Vdc
10Meg
Should be 30pF for compensation at unity gain (B=1).
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Simulation of Follower Instability
This sortt off ringing
Thi
i i iin th
the
simulation should be a warning
that in real life it is probably
going
g
g to oscillate wildly!
y
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Simulation of Follower Instability
With capacitive load CL on output increased to 1nF!
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Gain (dB)
Phase
LM301a with 30pF Single-Pole Compensation
Rule of thumb: add enough capacitance
such that the loop gain drops to 0 dB at or
below the 3dB frequency of the 2nd pole.
I have p
plotted the forward g
gain,, but
remember that for a follower, the
loop gain equals the forward gain.
Frequency
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Finite Gain Effects and Bandwidth
D tto internal
Due
i t
l compensation.
ti
For a single pole, the gain falls as 1
over the frequency.
The bandwidth (f3dB) times
the gain (G) will always equal
a constant gain-bandwidthproduct (fT).
)
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Pure Differentiator
R1
100k
V2
+
V+
U1
3
7
15Vdc
OUT
2
V4
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B1
5
6
1
V
LF411
4
1Vac
1V
0Vdc
Rises 6dB/octave!
Remember that this
circuit is unstable at
high frequency. 15Vdc
.01uF
-
V-
C2
Voltage gain = jRC
B2
This is a good example of
instability that occurs when
negative feedback becomes
positive feedback at high
frequency.
V1
0
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Spice AC-sim: gain rising at 6dB/octave
(20 dB/decade)
dB/d
d )
90 phase shift from principal pole
411 open-loop gain
Gain
n (dB)
The curves would cross
at about 35kHz. At that
point the gain must turn
over, but also, there will
then be an additional
90 p
phase shift from the
feedback network.
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Frequency
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Phase Shifts Around the Loop
This low-pass filter gives a
90 degree phase shift!
= 270 at low f
= 360 at high f (>35 kHz) R1
100k
Break the loop here.
C2
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B1
3
+
V+
OUT
0
U1
B2
1
6
5
= 180 at low f
= 270
270 at high f (>35 kHz)
7
The source
looks like a low
impedance to
ground.
V-
=0
LF411
2
-
4
.01uF
0
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Phase (d
(deg)
Spice AC-sim up to high frequency:
Gain
n (dB)
Resonance at
about 35 kHz!
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Frequency
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Transient Simulation with Square-Wave Input
R1
100k
V2
+
V+
U1
3
7
15Vdc
OUT
2
V5
B1
5
6
1
V
LF411
4
V1 = 0
V2 = 0.1
TD = 50n
TR = 1n
TF = 1n
PW = 0.5m
PER = 1m
-
V-
C2
.01uF
B2
V1
15Vdc
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Physics 160
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Transient Simulation with Square-Wave Input
Input
34 kHz oscillation
O tp t
Output
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Add a 1k Resistor in Series with the Cap
R1
100k
V2
2
V5
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B1
6
1
V
LF411
This resistor
keeps
p the cap
p
from shifting the
phase by a full
90 when going
around the loop.
V1
15Vdc
-
5
4
V1 = 0
V2 = 0.1
TD = 50n
TR = 1n
TF = 1n
PW = 0.5m
PER = 1m
.01uF 1k
B2
OUT
R2
V-
C2
+
V+
V
U1
3
7
15Vdc
0
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Phase (deg)
Low-Pass Filter with Extra Resistor
Gain (dB)
G
Never gets
g
all the way
to a 90
phase shift.
in
out
R3
100k
V
V1
1Vac
0Vdc
R2
1k
Frequency
C1
0.01uF
Looks like a simple voltage
divider at high frequency
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With 1k Resistor in Series with Cap
Spice simulation of the
differentiator with a
square wave input.
i
t
Now we see just the derivative of
the square wave (no oscillation).
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No more
resonance
Gain
n (dB)
Phase (d
deg)
With 1k Resistor in Series with Cap
Frequency
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Lab Differentiator Circuit
C1
0.1n
Added cap here
gives even a little
more phase margin
R1
100k
V2
2
V3
.01uF
V
-
B1
5
6
1
V
LF411
4
V1 = 0
V2 = .1
1
TD = 0
TR = .5m
TF = .5m
PW = 0.5m
PER = 2m
1k
B2
OUT
C2
V-
R2
+
V+
+
U1
3
7
15Vdc
Ordering of R2 and C2
doesn’t matter.
V1
15Vdc
May 20, 2015
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Physics 160
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Differentiator without feedback capacitor
The g
gain turns over at
about 35 kHz, as
expected.
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Differentiator with feedback capacitor
Turn-over lowered from
35 kHz to 14 kHz
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Input and Output Impedance
•
Differential input impedance
– For a non-inverting amp, it is boosted by a factor of (1+AB) to near
infinity due to negative voltage feedback. Thus it becomes an
insignificant parameter. (Remember: AB=“loop gain”.)
•
Output impedance: 40 ohms for the 411 without feedback
– For a real application the output impedance depends on the
feedback network (low for V source; high for I source)
– With negative voltage feedback the output impedance drops by a
factor of 1/(1+AB) to such a low value as to become insignificant.
The maximum current drive of the output stage is then the
much more relevant parameter.
•
Maximum output current and output swing
– 411
11 can go ffrom VEE+2V
2 to VCC2V
2 with a 1 kohm load
– Single-supply op-amps (e.g. LM358) can swing from ground to
close to the positive rail (but typically they can only reach ground if
they don
don’tt have to sink too much current
current, e
e.g.
g <50 A).
A)
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Op-Amp Example (Single Supply)
Details of the current references and mirrors are not shown.
High Gain
DC-coupled
diff
differential
ti l
amp.
IIncreases Miller
Mill effect
ff t
to kill gain at high
frequency (for stability)
Short-circuit protection
Pushpull
output
t t
LM324
Darlington
2nd stage amp
(common
(commonemitter)
2 emitter
f ll
followers
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Physics 160
Helps to pull
the output all
the way to
ground.
30
Input and Output Impedance
•
Input
impedance
without
feedback.
Non-inverting amplifier (voltage, or series, feedback)
– Zin gets increased by (1+AB)
– Zout gets decreased by 1/(1+AB)
V
A
G  out 
Vin 1  AB
Vin  BVout
Vin
I in 

Ri
Ri  (1  AB)
Zin
Differential
gain = A
Output
impedance
without
feedback.
Suppose Vin  0 and apply V at output.
Amp sees 0  BV across its 2 inputs.
V  ( ABV )
1  AB
I out 
V 
R0
R0 1/Z
out
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Input and Output Impedance
•
Inverting amp (shunt feedback)
Zin reduced by 1/(1+A)
Iin
R1
2
V-
In
4
R2
-
Out
8
+
1
V+
OUT
3
V V
V  (1  A)
I in  in out  in
R2
R2
Impedance into the amp input itself is
so high that we can ignore it here. It is
in parallel with R2/(1+A), which is tiny.
T
Transresistance
it
Amp
A
0
2
-
+
1
Out
V+
OUT
3
Z in  R1 
V-
R1
R2
 R1
1 A
8
In
4
R2
0
May 20, 2015
The output impedance of the inverting
amp is the same as for the noninverting amp. In both cases the
voltage is sampled at the output and
fed back.
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Output Impedance
•
Current source (current sampling)
The feedback is
using R3 to
sample the output
current.
15.00V
1.020mA
R1
R3
470
2.7k
3
V1
12 25V
12.25V
-28.05pA
28 05pA
+
7
12.25V
V+
V
U6
B2
OUT
2
-28.05pA
-
B1
M1
6
8.629V
VP1310
1
LF411
Vout
4
9.064mA
V-
15Vdc
5
R2
8.793V
5.862mA
RL
12k
1.5k
0V
The op-amp output
uses the MOSFET
gm to control the
current.
V2
15Vdc
2.170mA
-15.00V
When Vout changes from 0 to 11.5V, the current
changes from 5.86209625 mA to 5.86209775 mA.
Z out 
May 20, 2015
11.5
1.5  10
Physics 160
9
 7.7 G !!
33
Some additional circuits studied in the lab:
ACTIVE RECTIFIERS
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Active ½ Wave Rectifier
U1
3
+
7
Negative feedback exists
here only when the op-amp
output swings positive!
V+
V2
15Vdc
The input does not
need to exceed a
diode drop
p to g
get a
non-zero output.
B2
2
-
VV
OUT
B1
5
6
1
V
LF411
V3
4
VOFF = 0
VAMPL = 0.5
FREQ = 100
D1
D1N914
V
R2
10k
This is very similar to how
we removed
d th
the di
diode
d
drops of the push-pull
output stage by using
g
feedback.
negative
V1
15Vdc
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Active Rectifier Transient Simulation
Op-Amp Output
100 Hz
Negative
feedback
No feedback
Rectifier Output
Glitch
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Active Rectifier Transient Simulation
Op-Amp Output
10 kHz
Rectifier Output
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Improved Active ½ Wave Rectifier
R1
10k
V2
V
15Vdc
3
+
7
B1
5
D1N914
6
1
LF411
4
V3
-
V-
2
VOFF = 0
VAMPL = .5
FREQ = 10k
B2
OUT
R2
10k
D1
V+
V
U2
D2
D1N914
V1
15Vdc
15Vd
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Physics 160
D2 provides a feedback path
when the op-amp output
swings negative, keeping
the op amp from trying to
swing all the way to VEE.
38
Improved Active Rectifier
Op-Amp Output
10 kHz
Note how the op
amp no longer
has to swing
g
down to 15V, so
the requirements
on slew rate are
much relaxed.
relaxed
Rectifier Output
Note the
inversion with
respect to the
previous circuit.
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