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Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
4. Introduction to Feedback Amplifiers
S. S. Dan and S. R. Zinka
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
March 2, 2016
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Feedback
• The theory of negative feedback has been developed by electronicsengineers
• Harold Black, an electronics engineer with the Western ElectricCompany, invented the feedback amplifier in 1928
• The concept of feedback and its associated theory are currently used inareas other than engineering, such as in the modeling of biologicalsystems
• In this course, we will concentrate mainly on negative feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Feedback
• The theory of negative feedback has been developed by electronicsengineers
• Harold Black, an electronics engineer with the Western ElectricCompany, invented the feedback amplifier in 1928
• The concept of feedback and its associated theory are currently used inareas other than engineering, such as in the modeling of biologicalsystems
• In this course, we will concentrate mainly on negative feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Feedback
• The theory of negative feedback has been developed by electronicsengineers
• Harold Black, an electronics engineer with the Western ElectricCompany, invented the feedback amplifier in 1928
• The concept of feedback and its associated theory are currently used inareas other than engineering, such as in the modeling of biologicalsystems
• In this course, we will concentrate mainly on negative feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Feedback
• The theory of negative feedback has been developed by electronicsengineers
• Harold Black, an electronics engineer with the Western ElectricCompany, invented the feedback amplifier in 1928
• The concept of feedback and its associated theory are currently used inareas other than engineering, such as in the modeling of biologicalsystems
• In this course, we will concentrate mainly on negative feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Feedback
• The theory of negative feedback has been developed by electronicsengineers
• Harold Black, an electronics engineer with the Western ElectricCompany, invented the feedback amplifier in 1928
• The concept of feedback and its associated theory are currently used inareas other than engineering, such as in the modeling of biologicalsystems
• In this course, we will concentrate mainly on negative feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadAxs xo
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadAxs xo
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xo
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xixs
=1A
xo
xs=
1A
A1 + Aβ
=1
1 + Aβ
xf
xs=
βxo
xs=
Aβ
1 + Aβ
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xixs
=1A
xo
xs=
1A
A1 + Aβ
=1
1 + Aβ
xf
xs=
βxo
xs=
Aβ
1 + Aβ
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xixs
=1A
xo
xs=
1A
A1 + Aβ
=1
1 + Aβ
xf
xs=
βxo
xs=
Aβ
1 + Aβ
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xixs
=1A
xo
xs=
1A
A1 + Aβ
=1
1 + Aβ
xf
xs=
βxo
xs=
Aβ
1 + Aβ
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Nomenclature
Source LoadA
β
xs xi
xf
xo
+−
A : Open-loop gain
β : Feedback factor
Aβ : loop gain
1 + Aβ : Amount of Feedback
Af : gain with feedback or Closed-loop gain
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
1. Gain Desensitivity
Source LoadA
β
xs xi
xf
xo
+−
Af =A
1 + Aβ
⇒dAf
dA=
1
(1 + Aβ)2
⇒dAf
Af=
1
(1 + Aβ)2dAAf
=1
(1 + Aβ)
dAA
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Lowpass Filter)
Consider a lowpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A11
1 + s/ω1,
where A1 denotes the gain at ω = 0 and ω1 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A11+s/ω1
1 + β A11+s/ω1
=A1
1 + s/ω1 + βA1=
A11+A1 β
1 + s/ω1 (1 + A1β).
Thus the feedback lowpass amplifier will have a maximum gain of A11+A1 β and
a 3-dB frequency ω1f given by ω1 (1 + A1β).
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Lowpass Filter)
Consider a lowpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A11
1 + s/ω1,
where A1 denotes the gain at ω = 0 and ω1 is the 3-dB frequency.
Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A11+s/ω1
1 + β A11+s/ω1
=A1
1 + s/ω1 + βA1=
A11+A1 β
1 + s/ω1 (1 + A1β).
Thus the feedback lowpass amplifier will have a maximum gain of A11+A1 β and
a 3-dB frequency ω1f given by ω1 (1 + A1β).
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Lowpass Filter)
Consider a lowpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A11
1 + s/ω1,
where A1 denotes the gain at ω = 0 and ω1 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A11+s/ω1
1 + β A11+s/ω1
=A1
1 + s/ω1 + βA1=
A11+A1 β
1 + s/ω1 (1 + A1β).
Thus the feedback lowpass amplifier will have a maximum gain of A11+A1 β and
a 3-dB frequency ω1f given by ω1 (1 + A1β).
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Lowpass Filter)
Consider a lowpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A11
1 + s/ω1,
where A1 denotes the gain at ω = 0 and ω1 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A11+s/ω1
1 + β A11+s/ω1
=A1
1 + s/ω1 + βA1=
A11+A1 β
1 + s/ω1 (1 + A1β).
Thus the feedback lowpass amplifier will have a maximum gain of A11+A1 β and
a 3-dB frequency ω1f given by ω1 (1 + A1β).
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Highpass Filter)
Consider a highpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A2s/ω2
1 + s/ω2,
where A2 denotes the gain at ω → ∞ and ω2 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A2s/ω21+s/ω2
1 + β A2s/ω21+s/ω2
=A2
1 + βA2
sω2
(1 + βA2)
1 + sω2
(1 + βA2).
Thus the feedback highpass amplifier will have a maximum gain of A21+A2 β and
a 3-dB frequency ω2f given by ω21+A2 β .
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Highpass Filter)
Consider a highpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A2s/ω2
1 + s/ω2,
where A2 denotes the gain at ω → ∞ and ω2 is the 3-dB frequency.
Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A2s/ω21+s/ω2
1 + β A2s/ω21+s/ω2
=A2
1 + βA2
sω2
(1 + βA2)
1 + sω2
(1 + βA2).
Thus the feedback highpass amplifier will have a maximum gain of A21+A2 β and
a 3-dB frequency ω2f given by ω21+A2 β .
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Highpass Filter)
Consider a highpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A2s/ω2
1 + s/ω2,
where A2 denotes the gain at ω → ∞ and ω2 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A2s/ω21+s/ω2
1 + β A2s/ω21+s/ω2
=A2
1 + βA2
sω2
(1 + βA2)
1 + sω2
(1 + βA2).
Thus the feedback highpass amplifier will have a maximum gain of A21+A2 β and
a 3-dB frequency ω2f given by ω21+A2 β .
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Highpass Filter)
Consider a highpass amplifier (active filter) whose frequency response is char-acterized by a single pole. Its gain can be expressed as
A (s) = A2s/ω2
1 + s/ω2,
where A2 denotes the gain at ω → ∞ and ω2 is the 3-dB frequency. Applica-tion of negative feedback, with a frequency-independent factor β, around thisamplifier results in
Af =A (s)
1 + βA (s)=
A2s/ω21+s/ω2
1 + β A2s/ω21+s/ω2
=A2
1 + βA2
sω2
(1 + βA2)
1 + sω2
(1 + βA2).
Thus the feedback highpass amplifier will have a maximum gain of A21+A2 β and
a 3-dB frequency ω2f given by ω21+A2 β .
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Bandpass Filter)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Bandpass Filter)
A
20 log (AM)
-20 dB/decade+20 dB/decade
fL fH f (log scale)
Gain(dB)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Bandpass Filter)
Af
A
20 log (AM)
-20 dB/decade+20 dB/decade
20 log (AMf)
fLf fL fH fHf f (log scale)
Gain(dB)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
2. Bandwidth Extension (Bandpass Filter)
Af
A
20 log (AM)
-20 dB/decade+20 dB/decade
20 log (AMf)
fLf fL fH fHf f (log scale)
Gain(dB)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction
+−
Poweroutputstage(A1)
+
−
VoRLVS
Vn
SN
=Vs
Vn
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction
+−
Poweroutputstage(A1)
+
−
VoRLVS
Vn
SN
=Vs
Vn
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction
+−
Poweroutputstage(A1)
+
−
VoRLVS
Vn
SN
=Vs
Vn
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction ... Cont’d
+−
Feedbacknetwork
(β)
+
−
+−VfVoRLVS
Vn
Poweroutputstage(A1)
Preamplifier
(A2)
Vo = VsA1A2
1 + A1A2β︸ ︷︷ ︸+VnA1
1 + A1A2β︸ ︷︷ ︸SN
=Vs
VnA2
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction ... Cont’d
+−
Feedbacknetwork
(β)
+
−
+−VfVoRLVS
Vn
Poweroutputstage(A1)
Preamplifier
(A2)
Vo = VsA1A2
1 + A1A2β︸ ︷︷ ︸+VnA1
1 + A1A2β︸ ︷︷ ︸SN
=Vs
VnA2
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction ... Cont’d
+−
Feedbacknetwork
(β)
+
−
+−VfVoRLVS
Vn
Poweroutputstage(A1)
Preamplifier
(A2)
Vo = VsA1A2
1 + A1A2β︸ ︷︷ ︸+VnA1
1 + A1A2β︸ ︷︷ ︸
SN
=Vs
VnA2
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
3. Noise Reduction ... Cont’d
+−
Feedbacknetwork
(β)
+
−
+−VfVoRLVS
Vn
Poweroutputstage(A1)
Preamplifier
(A2)
Vo = VsA1A2
1 + A1A2β︸ ︷︷ ︸+VnA1
1 + A1A2β︸ ︷︷ ︸SN
=Vs
VnA2
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
4. Reduction in Nonlinear Distortion
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
4. Reduction in Nonlinear Distortion
(a)
vO (V)
vI, vS (V)
1
2
3
4
-1
-2
-3
-4
0.02 0.04 0.06 0.08-0.02-0.04-0.06-0.08
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
4. Reduction in Nonlinear Distortion
(a) (b)
vO (V)
vI, vS (V)
1
2
3
4
-1
-2
-3
-4
0.02 0.04 0.06 0.08-0.02-0.04-0.06-0.08
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Voltage Amplifiers
+−
Basicvoltage
amplifier
Feedbacknetwork
+
−
+−VfVoRL
RS
VS
Voltagesampling
Voltagemixing
Why are we using series-shunt (i.e., voltage sampling-voltage mixing)configuration for voltage amplifiers?
Because, series-shunt configuration increases the input impedance anddecreases the output impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Voltage Amplifiers
+−
Basicvoltage
amplifier
Feedbacknetwork
+
−
+−VfVoRL
RS
VS
Voltagesampling
Voltagemixing
Why are we using series-shunt (i.e., voltage sampling-voltage mixing)configuration for voltage amplifiers?
Because, series-shunt configuration increases the input impedance anddecreases the output impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Voltage Amplifiers
+−
Basicvoltage
amplifier
Feedbacknetwork
+
−
+−VfVoRL
RS
VS
Voltagesampling
Voltagemixing
Why are we using series-shunt (i.e., voltage sampling-voltage mixing)configuration for voltage amplifiers?
Because, series-shunt configuration increases the input impedance anddecreases the output impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Voltage Amplifiers
+−
Basicvoltage
amplifier
Feedbacknetwork
+
−
+−VfVoRL
RS
VS
Voltagesampling
Voltagemixing
Why are we using series-shunt (i.e., voltage sampling-voltage mixing)configuration for voltage amplifiers?
Because, series-shunt configuration increases the input impedance anddecreases the output impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Current Amplifiers
Io
Io
If If
RL
2
Is Rs
1
Basiccurrent
amplifier
Feedbacknetwork
Shunt-series configuration decreases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Current Amplifiers
Io
Io
If If
RL
2
Is Rs
1
Basiccurrent
amplifier
Feedbacknetwork
Shunt-series configuration decreases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Current Amplifiers
Io
Io
If If
RL
2
Is Rs
1
Basiccurrent
amplifier
Feedbacknetwork
Shunt-series configuration decreases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transconductance Amplifiers
Vf
RL
Rs
2
Vs
1
Basictransconductance
amplifier
Feedbacknetwork
Io
Io
Series-series configuration increases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transconductance Amplifiers
Vf
RL
Rs
2
Vs
1
Basictransconductance
amplifier
Feedbacknetwork
Io
Io
Series-series configuration increases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transconductance Amplifiers
Vf
RL
Rs
2
Vs
1
Basictransconductance
amplifier
Feedbacknetwork
Io
Io
Series-series configuration increases the input impedance and increases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transresistance Amplifiers
RL
2
Is
1
Basictransresistance
amplifier
Feedbacknetwork
Io
Rs
If If
Vo
Shunt-shunt configuration decreases the input impedance and decreases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transresistance Amplifiers
RL
2
Is
1
Basictransresistance
amplifier
Feedbacknetwork
Io
Rs
If If
Vo
Shunt-shunt configuration decreases the input impedance and decreases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Transresistance Amplifiers
RL
2
Is
1
Basictransresistance
amplifier
Feedbacknetwork
Io
Rs
If If
Vo
Shunt-shunt configuration decreases the input impedance and decreases theoutput impedance.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Non-Inverting Op-amp Configuration
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Non-Inverting Op-amp Configuration
_
+
_+vI
R1
+vO
R2
vf = voR1
R1 + R2︸ ︷︷ ︸β
Therefore, close-loop gain Af is given as
Af = limA→∞
A1 + Aβ
=1β=
R1 + R2R1
= 1 +R2R1
.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Non-Inverting Op-amp Configuration
_
+
_+vI
R1
+vO
R2
vf = voR1
R1 + R2︸ ︷︷ ︸β
Therefore, close-loop gain Af is given as
Af = limA→∞
A1 + Aβ
=1β=
R1 + R2R1
= 1 +R2R1
.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Non-Inverting Op-amp Configuration
_
+
_+vI
R1
+vO
R2
vf = voR1
R1 + R2︸ ︷︷ ︸β
Therefore, close-loop gain Af is given as
Af = limA→∞
A1 + Aβ
=1β=
R1 + R2R1
= 1 +R2R1
.
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
A Few other Op-amp Circuits with Feedback
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
A Few other Op-amp Circuits with Feedback
−
++−
−
+
+−
R1 R2
RL
vs
RL
rR2R1
vs
−
+
−
+
R2
RL
is
is
RL
rR2
(a) (b)
(c) (d)
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Outline
1 Introduction
2 Properties of Negative Feedback
3 The Four Basic Feedback Topologies
4 Op-Amps – Revisit
5 Summary
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
The General Feedback Structure (Signal Flow Graph)
Source LoadA
β
xs xi
xf
xo
+−
xo = Axi
xf = βxo
xi = xs − xf
xo
xs=
Axixi + xf
=Axi
xi + βx0=
Axixi + βAxi
=A
1 + Aβ= Af
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Filters
Low-pass:
H (jω) = A× 11 + jωτ
= A× 11 + jω/ω0
High-pass:
H (jω) = A× jωτ
1 + jωτ= A× jω/ω0
1 + jω/ω0
Cut-off Frequency:
f0 =1
2πτ
τ =
{RC for RC networksL/R for RL networks
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Properties of Negative Feedback
Gain Desensitivity:
dAf
Af=
1(1 + Aβ)
dAA
Bandwidth Extension:
Lowpass Filter : A1f =A1
1+A1 β ; ω1f = ω1 (1 + A1β)
Highpass Filter : A2f =A2
1+A1 β ; ω2f =ω2
1+A1 β
Noise Reduction:
SN
=Vs
VnA2
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Sampling & Mixing
• Series sampling or series mixing always increases the (output/input)Impedances.
• Shunt sampling or shunt mixing always decreases the (output/input)Impedances.
• Best Feedback Topologies for Various Amplifiers:
• Voltage Amplifiers : Series-Shunt
• Current Amplifiers : Shunt-Series
• Transconductance Amplifiers : Series-Series
• Transresistance Amplifiers : Shunt-Shunt
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus
Introduction Properties of Negative Feedback The Four Basic Feedback Topologies Op-Amps – Revisit Summary
Bye Bye Basics ...
Now, you got almost all the tools that you need to understand therest of the course !
4. Introduction to Feedback Amplifiers ECE/EEE/INSTR F244, Dept. of EEE, BITS Pilani Hyderabad Campus