![Page 1: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/1.jpg)
Op amp output
ElectronicsNegative Feedback in Operational Amplifiers
Terry Sturtevant
Wilfrid Laurier University
July 29, 2013
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 2: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/2.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The equation for the output of an op amp is always true as long asthe output is not saturated
V+
V−
Vo
Vo = A (V+ − V−)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 3: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/3.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The equation for the output of an op amp is always true as long asthe output is not saturated
V+
V−
Vo
Vo = A (V+ − V−)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 4: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/4.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The equation for the output of an op amp is always true as long asthe output is not saturated
V+
V−
Vo
Vo = A (V+ − V−)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 5: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/5.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For negative feedback, make the voltage at V− be someportion of Vo.
This ratio of V− to Vo is called the feedback factor, β.
β
V+
V−Vo
�
6
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 6: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/6.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For negative feedback, make the voltage at V− be someportion of Vo.This ratio of V− to Vo is called the feedback factor, β.
β
V+
V−Vo
�
6
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 7: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/7.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For negative feedback, make the voltage at V− be someportion of Vo.This ratio of V− to Vo is called the feedback factor, β.
β
V+
V−Vo
�
6
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 8: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/8.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For instance, with just a wire from V− to Vo, the feedabckfactor is 1.
This is the case for a voltage follower.
β = 1
V+
V−Vo
� �
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 9: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/9.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For instance, with just a wire from V− to Vo, the feedabckfactor is 1.This is the case for a voltage follower.
β = 1
V+
V−Vo
� �
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 10: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/10.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For instance, with just a wire from V− to Vo, the feedabckfactor is 1.This is the case for a voltage follower.
β = 1
V+
V−Vo
� �
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 11: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/11.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedback
V− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 12: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/12.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 13: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/13.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
where
β ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 14: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/14.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 15: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/15.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 16: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/16.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomes
Vo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 17: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/17.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 18: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/18.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
For feedbackV− = βVo
whereβ ∈ [0, 1]
So the op amp equation
Vo = A (V+ − V−)
becomesVo = A (V+ − βVo)
Vo = AV + − βAVo
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 19: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/19.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo + βAVo = AV+
Vo (1 + βA) = AV+
Vo (1 + βA) = AV+
Vo = V+
( A1 + βA
)
Vo = V+
(1
1A + β
)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 20: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/20.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo + βAVo = AV+
Vo (1 + βA) = AV+
Vo (1 + βA) = AV+
Vo = V+
( A1 + βA
)
Vo = V+
(1
1A + β
)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 21: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/21.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo + βAVo = AV+
Vo (1 + βA) = AV+
Vo (1 + βA) = AV+
Vo = V+
( A1 + βA
)
Vo = V+
(1
1A + β
)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 22: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/22.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo + βAVo = AV+
Vo (1 + βA) = AV+
Vo (1 + βA) = AV+
Vo = V+
( A1 + βA
)
Vo = V+
(1
1A + β
)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 23: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/23.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo + βAVo = AV+
Vo (1 + βA) = AV+
Vo (1 + βA) = AV+
Vo = V+
( A1 + βA
)
Vo = V+
(1
1A + β
)
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 24: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/24.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)thus
Vo ≈ V+
( 1β
)so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 25: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/25.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)thus
Vo ≈ V+
( 1β
)so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 26: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/26.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)thus
Vo ≈ V+
( 1β
)so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 27: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/27.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)
thusVo ≈ V+
( 1β
)so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 28: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/28.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)thus
Vo ≈ V+
( 1β
)
so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 29: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/29.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If the gain, A, is much greater than 1, then
A� β
and so1A � β
Vo = V+
(1
��1A + β
)thus
Vo ≈ V+
( 1β
)so Vo only depends on β.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 30: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/30.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo ≈ V+
( 1β
)
So for a voltage follower, where β = 1,
Vo ≈ V+
as expected.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 31: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/31.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo ≈ V+
( 1β
)So for a voltage follower, where β = 1,
Vo ≈ V+
as expected.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 32: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/32.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo ≈ V+
( 1β
)So for a voltage follower, where β = 1,
Vo ≈ V+
as expected.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 33: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/33.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Vo ≈ V+
( 1β
)So for a voltage follower, where β = 1,
Vo ≈ V+
as expected.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 34: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/34.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Non-inverting amplifier
V+-
V−-
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 35: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/35.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Non-inverting amplifier
V+-
V−-
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 36: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/36.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
V+
V−
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 37: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/37.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
V+
V−
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 38: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/38.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
V+
V−
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 39: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/39.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
V+
V−
Vo
Rf
Ri
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 40: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/40.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thusβ = Ri
Rf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 41: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/41.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.
Thusβ = Ri
Rf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 42: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/42.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thus
β = RiRf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 43: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/43.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thusβ = Ri
Rf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 44: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/44.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thusβ = Ri
Rf +Ri
so
gain = 1β = Rf +Ri
Ri
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 45: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/45.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thusβ = Ri
Rf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 46: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/46.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Rf and Ri form a voltage divider, so the voltage at V− is afraction of Vo
By definition, this is the feedback factor, β.Thusβ = Ri
Rf +Ri
sogain = 1
β = Rf +RiRi
as expected
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 47: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/47.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
VB
Vi��
@R
Vo
VA���
��
Rf
Ri
VoVi
= VAVB
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 48: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/48.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
VB
Vi��
@R
Vo
VA���
��
Rf
Ri
VoVi
= VAVB
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 49: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/49.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
This can be redrawn
VB
Vi��
@R
Vo
VA���
��
Rf
Ri
VoVi
= VAVB
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 50: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/50.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If Ri is not grounded, then it looks like this.
VB
Vi��
@R
VAVo
���
��VC
Rf
Ri
V0 is VA - VC
Vi is VB - VC
so VoVi
= VA−VCVB−VC
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 51: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/51.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If Ri is not grounded, then it looks like this.
VB
Vi��
@R
VAVo���
��VC
Rf
Ri
V0 is VA - VC
Vi is VB - VC
so VoVi
= VA−VCVB−VC
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 52: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/52.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If Ri is not grounded, then it looks like this.
VB
Vi��
@R
VAVo���
��VC
Rf
Ri
V0 is VA - VC
Vi is VB - VC
so VoVi
= VA−VCVB−VC
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 53: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/53.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If Ri is not grounded, then it looks like this.
VB
Vi��
@R
VAVo���
��VC
Rf
Ri
V0 is VA - VC
Vi is VB - VC
so VoVi
= VA−VCVB−VC
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 54: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/54.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
If Ri is not grounded, then it looks like this.
VB
Vi��
@R
VAVo���
��VC
Rf
Ri
V0 is VA - VC
Vi is VB - VC
so VoVi
= VA−VCVB−VC
= 1 + RfRi
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 55: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/55.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
We can redraw the circuit slightly differently.
VB VA
VC
Rf
Ri
Since VA−VCVB−VC
= 1 + RfRi
This can be rewritten VA −(
1 + RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 56: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/56.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
We can redraw the circuit slightly differently.
VB VA
VC
Rf
Ri
Since VA−VCVB−VC
= 1 + RfRi
This can be rewritten VA −(
1 + RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 57: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/57.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
We can redraw the circuit slightly differently.
VB VA
VC
Rf
Ri
Since VA−VCVB−VC
= 1 + RfRi
This can be rewritten VA −(
1 + RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 58: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/58.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
We can redraw the circuit slightly differently.
VB VA
VC
Rf
Ri
Since VA−VCVB−VC
= 1 + RfRi
This can be rewritten VA −(
1 + RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 59: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/59.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The derivation goes like this:
VA − VCVB − VC
= 1 +RfRi
VA − VC =
(1 +
RfRi
)(VB − VC )
VA −��VC =
(1 +
RfRi
)VB −��VC −
RfRi
VC
VA −(
1 +RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 60: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/60.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The derivation goes like this:
VA − VCVB − VC
= 1 +RfRi
VA − VC =
(1 +
RfRi
)(VB − VC )
VA −��VC =
(1 +
RfRi
)VB −��VC −
RfRi
VC
VA −(
1 +RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 61: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/61.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The derivation goes like this:
VA − VCVB − VC
= 1 +RfRi
VA − VC =
(1 +
RfRi
)(VB − VC )
VA −��VC =
(1 +
RfRi
)VB −��VC −
RfRi
VC
VA −(
1 +RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 62: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/62.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The derivation goes like this:
VA − VCVB − VC
= 1 +RfRi
VA − VC =
(1 +
RfRi
)(VB − VC )
VA −��VC =
(1 +
RfRi
)VB −��VC −
RfRi
VC
VA −(
1 +RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 63: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/63.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
The derivation goes like this:
VA − VCVB − VC
= 1 +RfRi
VA − VC =
(1 +
RfRi
)(VB − VC )
VA −��VC =
(1 +
RfRi
)VB −��VC −
RfRi
VC
VA −(
1 +RfRi
)VB = −Rf
RiVC
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 64: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/64.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC which is an inverting amplifier!
So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 65: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/65.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC which is an inverting amplifier!
So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 66: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/66.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC which is an inverting amplifier!
So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 67: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/67.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0
Then VA = −RfRi
VC which is an inverting amplifier!So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 68: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/68.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC
which is an inverting amplifier!So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 69: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/69.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC which is an inverting amplifier!
So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers
![Page 70: Electronics- Negative Feedback in Operational Amplifiersdenethor.wlu.ca/pc300/lectures/feedback.pdf · Op amp output Op amp output with negative feedback Example: non-inverting amplifier](https://reader030.vdocuments.net/reader030/viewer/2022021808/5bf2d9b309d3f2cb7d8cbbc7/html5/thumbnails/70.jpg)
Op amp output Op amp output with negative feedbackExample: non-inverting amplifier
Finally, we can set VB to ground.
VB = 0
VA
VC
Rf
Ri
So if VA −(
1 + RfRi
)VB = −Rf
RiVC
and VB = 0Then VA = −Rf
RiVC which is an inverting amplifier!
So the feedback factor, β, is the same as for a non-invertingamplifier.
Terry Sturtevant Electronics Negative Feedback in Operational Amplifiers