designing for predictable amplifier gain gain is hard to control varies with operating point...
TRANSCRIPT
![Page 1: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/1.jpg)
Designing for Predictable Amplifier Gain
• Gain is hard to control• Varies with operating point• Non-constant gain causes distortion• Gain varies from one transistor to the next• Sensitive to temperature
1EEE 3308
![Page 2: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/2.jpg)
Amplifier Gain Varies a Lot
2EEE 3308
• Gain varies with operating point• Non-constant gain causes distortion
![Page 3: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/3.jpg)
Input, Output, Source & LoadImpedance Variations Affect
Gain
3EEE 3308
A
v=
Vout
Vs
=Zin
Zin + ZS
Avo
ZL
Zout + ZL
Zin
Zout
Avovivi
vs
Zs
ZL vout
![Page 4: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/4.jpg)
Input, Output, Source & LoadImpedance Variations Affect
Gain
4EEE 3308
A
v=
Vout
Vs
=Zin
Zin + ZS
Avo
ZL
Zout + ZL
Zin
Zout
Avovivi
vs
Zs
ZL vout
• Impedances vary with frequency, too.
![Page 5: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/5.jpg)
So How Can We Possibly Design Amps That Just Work?
5EEE 3308
• How to get gain that is stable, predictable, temperature-independent?• How to get stable biasing?• How to get desired input and output impedances?
![Page 6: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/6.jpg)
So How Can We Possibly Design Amps That Just Work?
6EEE 3308
• How to get gain that is stable, predictable, temperature-independent?• How to get stable biasing?• How to get desired input and output impedances?
FEEDBACK!
![Page 7: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/7.jpg)
Classic Feedback Example:The Non-Inverting Feedback Amplifier
7EEE 3308
R2R1
vs vo
![Page 8: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/8.jpg)
Non-Inverting Feedback Amplifier
8EEE 3308
vo=A ⋅(vi)
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 9: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/9.jpg)
Non-Inverting Feedback Amplifier
9EEE 3308
vo=A ⋅ vs −vf( )
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 10: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/10.jpg)
Non-Inverting Feedback Amplifier
10EEE 3308
v
o=A ⋅ vs −vf( ) =A ⋅ vs −
R1
R1 +R2
vo
⎛
⎝⎜⎞
⎠⎟
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 11: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/11.jpg)
Non-Inverting Feedback Amplifier
11EEE 3308
v
o=A ⋅ vs −vf( ) =A ⋅ vs −
R1
R1 +R2
vo
⎛
⎝⎜⎞
⎠⎟=A ⋅vs −A ⋅
R1
R1 +R2
vo
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 12: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/12.jpg)
Non-Inverting Feedback Amplifier
12EEE 3308
v
o=A ⋅ vs −vf( ) =A ⋅ vs −
R1
R1 +R2
vo
⎛
⎝⎜⎞
⎠⎟=A ⋅vs −A ⋅
R1
R1 +R2
vo
v
o1+ A ⋅
R1
R1 +R2
⎛
⎝⎜⎞
⎠⎟=Avs
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 13: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/13.jpg)
Non-Inverting Feedback Amplifier
13EEE 3308
v
o=A ⋅ vs −vf( ) =A ⋅ vs −
R1
R1 +R2
vo
⎛
⎝⎜⎞
⎠⎟=A ⋅vs −A ⋅
R1
R1 +R2
vo
v
o1+ A ⋅
R1
R1 +R2
⎛
⎝⎜⎞
⎠⎟=Avs
vo=
Avs
1+ A ⋅R1
R1 +R2
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 14: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/14.jpg)
Non-Inverting Feedback Amplifier
14EEE 3308
v
o=A ⋅ vs −vf( ) =A ⋅ vs −
R1
R1 +R2
vo
⎛
⎝⎜⎞
⎠⎟=A ⋅vs −A ⋅
R1
R1 +R2
vo
v
o1+ A ⋅
R1
R1 +R2
⎛
⎝⎜⎞
⎠⎟=Avs
ACL
=vo
vs
=A
1+ A ⋅R1
R1 +R2
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 15: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/15.jpg)
Non-Inverting Feedback Amplifier
15EEE 3308
β =
R1
R1 +R2
A is the “open-loop gain”
is the “feedback factor”
ACL is the “closed-loop gain”
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 16: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/16.jpg)
Non-Inverting Feedback Amplifier
16EEE 3308
A∞ @ACL A→ ∞
=1 / β =1+R2 / R1
T = Aβ is the “loop gain”
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 17: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/17.jpg)
Non-Inverting Feedback Amplifier
17EEE 3308
A∞ @ACL A→ ∞
=1 / β =1+R2 / R1
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 18: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/18.jpg)
Non-Inverting Feedback Amplifier
18EEE 3308
A∞ @ACL A→ ∞
=1 / β =1+R2 / R1
If T is big enough, the closed-loop gain is independent of the amplifier gain A.
R2R1
Avi
vivs
vfR2R1
vs vo
vo
![Page 19: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/19.jpg)
Feedback Analysis UsingLoop Gain and A∞
19EEE 3308
• The A-β approach works OK for the non-inverting amp example, but it doesn’t generalize well:
- Many circuits don’t split cleanly into β and A parts- Results depend on arbitrary assumptions about amp- Some of the results are significantly wrong- Not all feedback circuits are amplifiers
![Page 20: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/20.jpg)
Feedback Analysis UsingLoop Gain and A∞
20EEE 3308
• The A-β approach works OK for the non-inverting amp example, but it doesn’t generalize well:
- Many circuits don’t split cleanly into β and A parts- Results depend on arbitrary assumptions about amp- Some of the results are significantly wrong- Not all feedback circuits are amplifiers
• Loop gain (T) is the key parameter for feedback analysis• A∞ generalizes the ideal op amp• Combining separate analyses is design-oriented
![Page 21: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/21.jpg)
Finding Loop Gain
21EEE 3308
![Page 22: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/22.jpg)
Finding Loop Gain
22EEE 3308
Represent the amplifier by its linearized small-signal equivalent circuit.
![Page 23: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/23.jpg)
Finding Loop Gain
23EEE 3308
Turn off independent voltage and current sources, replacing themby their internal resistances (short for voltage sources, open for current sources).
![Page 24: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/24.jpg)
Finding Loop Gain
24EEE 3308
R2
R1
Ri
Ro
Avovi
vi
![Page 25: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/25.jpg)
Finding Loop Gain
25EEE 3308
Choose a branch through which the feedback signal flows...
R2
R1
Ri
Ro
Avovi
vi
![Page 26: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/26.jpg)
Finding Loop Gain
26EEE 3308
Choose a branch through which the feedback signal flows...
R2
R1
Ri
Ro
Avovi
vi
![Page 27: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/27.jpg)
Finding Loop Gain
27EEE 3308
Choose a branch through which the feedback signal flows...
R2
R1
Ri
Ro
Avovi
vi
![Page 28: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/28.jpg)
Finding Loop Gain
28EEE 3308
Break the branch.
R2
R1
Ri
Ro
Avovi
vi
![Page 29: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/29.jpg)
Finding Loop Gain
29EEE 3308
Call the input side the x port, and the output side the y port.
x y
R2
R1
Ri
Ro
Avovi
vi
Feedback signal flow
![Page 30: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/30.jpg)
Finding Loop Gain
30EEE 3308
Find the resistance, call it Rix, looking into the x port with port y shorted.
y
vx
y
R2
R1
Ri
Ro
Avovi
vi
Rix
![Page 31: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/31.jpg)
Finding Loop Gain
31EEE 3308
Find the resistance, call it Rix, looking into the x port with port y shorted.
y
vx
y
R2
R1
Ri
Ro
Avovi
vi
(R1||Ri)
![Page 32: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/32.jpg)
Finding Loop Gain
32EEE 3308
R1
Ri
Ro
Avovi
vi
Rix = R1 PRi( ) +R2
vx
R2
Find the resistance, call it Rix, looking into the x port with port y shorted.
![Page 33: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/33.jpg)
Finding Loop Gain
33EEE 3308
vy
R1
Ri
Ro
Avovi
vi
vx
R2
Place a copy of Rix across the y port.
Rix = R1 PRi( ) +R2
![Page 34: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/34.jpg)
Finding Loop Gain
34EEE 3308
Find the loop gain T = -vy/vx using standard amplifier analysis.
vy
R1
Ri
Ro
Avovi
vi
Rix = R1 PRi( ) +R2vx
R2
![Page 35: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/35.jpg)
Finding Loop Gain
35EEE 3308
In this case,
vy
vx
R2
R1
Ri
Ro
Avovi
vi
T =
R1 PRi
R1 PRi( ) +R2
Avo
Rix
Rix +R0
=R1 PRi
Rix
Avo
Rix
Rix +R0
=R1 PRi
Rix +R0
Avo
Rix = R1 PRi( ) +R2
![Page 36: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/36.jpg)
Finding Loop Gain
36EEE 3308
You get the same thing for T if you break the loop in other places.
R2
R1
Ri
Ro
Avovi
vi
![Page 37: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/37.jpg)
Finding Loop Gain
37EEE 3308
R2
R1
Ri
Ro
Avovi
vi
You get the same thing for T if you break the loop in other places.
![Page 38: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/38.jpg)
Finding Loop Gain
38EEE 3308
R2
R1
Ri
Ro
Avovi
vi
You get the same thing for T if you break the loop in other places.
![Page 39: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/39.jpg)
Finding Loop Gain
39EEE 3308
R2
R1
Ri
Ro
Avovi
vi
T is a key property of any feedback circuit. T is independent of how youfind it. It’s independent of where any inputs may be applied or any outputsare defined.
![Page 40: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/40.jpg)
40EEE 3308
Finding Loop Gain: Summary
![Page 41: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/41.jpg)
41EEE 3308
Finding Loop Gain: Summary
Represent the amplifier by its linearized small-signal equivalent circuit.
![Page 42: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/42.jpg)
42EEE 3308
Turn off independent voltage and current sources, replacing themby their internal resistances (short for voltage sources, open for current sources).
Finding Loop Gain: Summary
![Page 43: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/43.jpg)
43EEE 3308
Choose a branch through which the feedback signal flows.
R2
R1
Ri
Ro
Avovi
vi
Finding Loop Gain: Summary
![Page 44: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/44.jpg)
44EEE 3308
Break the branch.
R2
R1
Ri
Ro
Avovi
vi
Finding Loop Gain: Summary
x y
![Page 45: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/45.jpg)
45EEE 3308
Find the resistance, call it Rix, looking into the x port with port y shorted.
y
vx
y
R2
R1
Ri
Ro
Avovi
vi
Rix
Finding Loop Gain: Summary
![Page 46: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/46.jpg)
46EEE 3308
vy
R1
Ri
Ro
Avovi
vi
vx
R2
Place a copy of Rix across the y port.
Rix = R1 PRi( ) +R2
Finding Loop Gain: Summary
![Page 47: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/47.jpg)
47EEE 3308
Find the loop gain T = -vy/vx.
vy
R1
Ri
Ro
Avovi
vi
Rixvx
R2
Finding Loop Gain: Summary
![Page 48: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/48.jpg)
48EEE 3308
Finding A∞
R2R1
Avi
vs
vf
voRi vi
ii+
ii-
A∞ is the source-to-output gain when the controlled source gain A goes to infinity.
R2R1
vs vo
ii-
vi
![Page 49: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/49.jpg)
49EEE 3308
Finding A∞
R2R1
Avi
vs
vf
voRi vi
ii+
ii-
A∞ is the source-to-output gain when the controlled source gain A goes to infinity.
If v
o=Avi is finite, then A → ∞⇒ vi =
v0
A→ 0 .
R2R1
vs vo
ii-
vi
![Page 50: Designing for Predictable Amplifier Gain Gain is hard to control Varies with operating point Non-constant gain causes distortion Gain varies from one transistor](https://reader035.vdocuments.net/reader035/viewer/2022062322/5697bf8a1a28abf838c8aa8f/html5/thumbnails/50.jpg)
50EEE 3308
Finding A∞
R2R1
Avi
vs
vf
voRi vi
ii+
ii-
A∞ is the source-to-output gain when the controlled source gain A goes to infinity.
Also, zero voltage across Ri ⇒ ii+ → 0 and ii− → 0 .
R2R1
vs vo
ii-
vi
If v
o=Avi is finite, then A → ∞⇒ vi =
v0
A→ 0 .
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51EEE 3308
Finding A∞
R2R1
Avi
vs
vf
voRi vi
ii+
ii-
A∞ is the source-to-output gain when the controlled source gain A goes to infinity.
v i=0 ii+ =0 ii− =0
These are equivalent to the ideal op assumptions:
R2R1
vs vo
ii-
vi
Also, zero voltage across Ri ⇒ ii+ → 0 and ii− → 0 .
If v
o=Avi is finite, then A → ∞⇒ vi =
v0
A→ 0 .
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EEE 3308 52
Finding A∞: The Ideal Op Amp Assumptions
R2R1
Avi
vs
vfR2R1
vs vovoRi vi
ii+
ii-
Ideal Op Amp Assumptions: v i=0 ii+ =0 ii− =0
vi=0 ⇒ vf =vs
ii− =0 ⇒ vf =R1
R1 +R2
vo by voltage division;
Combining, A∞ =ACL A→ ∞=
vo
Vs A→ ∞
=R1 +R2
R1
ii+
ii-
vi
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53EEE 3308
Finding A∞
The A∞ approach can be applied to any feedback circuit, even when there is no op amp as such.
In general, A∞ is the overall source-to-output gain when the signal controlling the controlled source is forced to be zero because of infinite controlled-source gain.
As with the ideal op amp, assuming infinite gain leads to simpler circuit analysis.
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54EEE 3308
Putting It All Together
Once you know T and A∞ you can find the overall gain using
A
CL=
A∞
1+1 / T.
The loop gain is a measure of how close the circuit is to ideal.