Why Op Amps Have Low Bandwidth
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Transcript Why Op Amps Have Low Bandwidth
Why Op Amps Have Low
Bandwidth
Define gain of non-inverting amplifier
Open loop gain of op amp
(a simplification)
A O L (s)
A0
s
1
ω0
3
Let A0=105, ω0=106
Closed Loop Gain
vo
vi
A O L (s)
1 β A O L (s)
;
β
R1
R1 R 2
β =1 for follower.
Characteristic equation
1 β A O L (s) 1 β
A0
s
1
ω0
3
Note that for this circuit
β≤1.
0
Since denominator is
1+Aβ, the condition for
osicllation is Aβ=-1.
Gain of Op-Amp vs Frequency
Bode plot of A(s), A 0=1E5, three poles at w 0=1E6
100
Magnitude (dB)
80
60
40
20
0
-20
-40
0
Phase (deg)
-45
-90
-135
-180
Phase goes to 180⁰ here
-225
-270
0
10
1
10
2
10
3
10
4
10
Frequency (rad/sec)
5
10
6
10
7
10
8
10
Find closed loop gain (low freq)
Closed Loop Gain
vo
A C L (s)
vi
A O L (s)
A O L (s)
1 β A O L (s)
A0
s
1
ω0
3
(A0=105, ω0=106)
For large AOL(0)=A0; A0β>>1
A C L (0)
vo
vi
A0
βA 0
F o r th is c irc u it β
1
β
R1
R1 R 2
, s o A C L ( 0)
1
β
R1 R 2
R1
1
R2
R1
For resistive circuits, the extreme value is β→1 (R2 →0, Ri→∞); a follower.
Find where roots are on axis
Characteristic equation
1 β A O L (s) 1 β
1 β
A0
s
1
ω0
3
0
A0
s
1
ω0
3
A0
1 β
1 3
s
ω0
2
s
s
3
ω
ω
0
0
2
3
Find where roots are on jω axis
3
s
s
s
1 3
3
βA 0
ω0
ω
ω
0
0
2
3
jω
jω
jω
1 3
3
βA 0
ω0
ω
ω
0
0
Find conditions for oscillation
1 3
jω
ω0
1 j3
ω
ω0
2
3
jω
jω
3
βA 0
ω0
ω0
2
ω
ω
3
ω0
ω
0
ω
1 3
2
3
ω
ω0
R e al
3ω 0
3
2
βA 0
1 9 βA 0
8 βA 0
3
ω
0
ω0
0
3
ω
ω
3
j
βA 0
ω
ω
0
0
ω
1 3
βA 0
ω0
32
Im a g
Restrictions on closed loop gain
For oscillation
ω
This is obviously only useful if you
require large gain. It is certainly
not useable for a follower.
3ω 0
8 βA 0
(A0=105, ω0=106)
8 β 10
5
To make it useable we need to
decrease the loop gain. Since we
want to use a full range of β, our only
choice is to decrease the open loop
gain of the open loop gain.
For stability
β
8
10
5
82d B
or
A C L (0)
A0
1 A 0β
10
8
5
11, 000
Graphical explanation
Bode plot of A(s), A 0=1E5, three poles at w 0=1E6
100
Magnitude (dB)
80
60
40
• When phase is -180⁰, mag is 82dB.
•|Aβ|=1 at this frequency for stability
• So we need to make β=-82dB (this
is only marginally stable)
20
0
-20
-40
0
Phase (deg)
-45
-90
-135
-180
Phase goes to -180⁰ here
ω = √3·ω0 = 1.7E6
-225
-270
0
10
1
10
2
10
3
10
4
10
Frequency (rad/sec)
5
10
6
10
7
10
8
10
Increasing Stability (1)
To decrease the gain, redesign op amp so one of it’s open loop poles
is at a much lower frequency, to decrease gain at high frequencies
(where oscillations occur)
A O L (s)
A0
s
s
1
1
ωd
ω0
2
;
ωd ω 0
Characteristic equation
0 1 β A O L (s)
A0
s
s
s
1
1 2
ω
ω
ω
d
0
0
2
A0
1
2
2
1
1
2
3
s
s
1 s
2
2
ω
ω
ω
ω
ω
ω
ω
d
0
d
0
0
d
0
A O L (s)
A0
1
2
1
2
3
1
s
s
s
2
ωd
ω dω 0
ω dω 0
0 1 β
A0
1
2
1
2
3
1
s
s
s
2
ωd
ω dω 0
ω dω 0
1 β
A0
1
2
1
2
3
1
s
s
s
2
ω
ω
ω
ω
ω
d
d
0
d
0
1
2
1
2
3
βA 0 1 s
s
s
2
ω
ω
ω
ω
ω
d
d
0
d
0
Increasing Stability (2)
Let’s find the conditions for instability
βA 0 1 s
1
ωd
s
2
2
ω dω 0
s
1
3
ω dω
Let s=jω
0 ω
1
ωd
ω
ωd
ω
1
32
2
ωd ω0
ω ω0
β A 0 1 jω
βA 0 1 ω
1
0 ω
2
0
2
1
ωd
ω
2
ω dω 0
jω
3
βA 0 1 ω 0
1
2
2
2
ω dω 0
ωd ω0
ω d 1 β A 0 2ω 0
2
ω dω 0
3
2
1
2
ω dω 0
R e al
Im a g
ωd
2ω 0
1 β A 0
Let’s find the value of ωd that
creates marginal stability with β=1.
ωd
2 10
6
1 1 1 0
5
20
ra d
se c
This is
quite low…
Graphical explanation
Bode plot of A(s), A 0=1E5, two poles at w 0=1E6 and one at w d=20
100
Magnitude (dB)
50
0
• When phase is -180⁰, mag is 0 dB (i.e., 1).
• |Aβ|=1 at this frequency for stability
• So circuit is stable for β≤1
(marginally stable for β=1)
-50
-100
-150
0
Phase (deg)
-45
-90
-135
-180
Phase goes to -180⁰ here
ω = ω0 = 1E6
-225
-270
0
10
1
10
2
10
3
10
4
10
Frequency (rad/sec)
5
10
6
10
7
10
8
10