Lecture 5- Operational Amplifier - CAT-SOOP1. Operational amplifier: Intro Ideal op-amp is a...
Transcript of Lecture 5- Operational Amplifier - CAT-SOOP1. Operational amplifier: Intro Ideal op-amp is a...
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6.002 Spring 2020 Lecture 5 1
6.002 CIRCUITS ANDELECTRONICS
Lecture 5 - Operational Amplifier
February 20, 2020
Contents:1. Operational amplifier: intro2. An op-amp-based amplifier3. Methodology to analyze op-amp circuits: non-inverting amplifier4. Another example: inverting amplifier
Reading Assignment:Agarwal and Lang, Ch. 15 (§§15.1-15.3)
Handouts:Lecture 5 notes
Announcements:Soldering training session in lab tomorrow
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Doppler Ultrasound System
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Lab 3 – Doppler Ultrasound System
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1. Operational amplifier: IntroIdeal op-amp is a voltage-controlled voltage source:
Equivalent circuit of ideal op-amp:
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Op-amp can be used to enable numerous circuits, with applications in fields such as:– Signal processing– Instrumentation– Control– Power – Etc.
Inverting amplifier
Current-to-Voltage converter
Integrator
Band-pass filter
Sample-and-hold circuit
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Properties of ideal op-amp:
– Differential input– Single-ended output– Very large and constant voltage gain– Infinite input resistance à zero input current– Zero output resistance à can deliver or sink infinite output current at any output voltage– No saturation– Infinite bandwidth
Outputvs
Input
Output
The op-amp we will use in the lab: LF356
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Real op-amp:– Gain is non linear– Output signal limited by power supply
voltages (saturation)– Offset in output voltage– Input and output resistances less than ideal– Bandwidth limited– Gain and offset are temperature dependent
A better model:
+-
v+Voffset
Rin
Routi+
i-
+
-
vin+-vin-
vin+
vin-v-
+-
+
f(v*)
iOR
C v*
+ -
-+-
v+Voffset
Rin
Routi+
i-
+
-
vin+-vin-
vin+
vin-v-
+-
+
f(v*)
iOR
C v*
+ -
-+-
v+Voffset
Rin
Routi+
i-
+
-
vin+-vin-
vin+
vin-v-
+-
+
f(v*)
iOR
C v*
+ -
-
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2. An op-amp-based amplifier
• Consider a simple amplifier configuration:
Very large gain, but…– Output offset results in output even if no input signal– Output can easily saturate– Temperature sensitivity corrupts output voltage
“Open loop” configuration has large gain but it is unstable.
Need to find a way to “pin” the output to ground when there is no signal at the input.
Demo
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• Consider the following circuit:
How does it work?– When vIN=0, ideally vO=0– Suppose with vIN=0 there is output offset vO>0
à R1/R2 voltage divider results in v->0à v+-v-<0 drives vO to zero
– Now assume no output offset. If vIN>0, then vO>0 such that vO causes v+= v-
à vO//vIN gain of this amplifier is less than A!
“Closed loop” configuration à feedback path mitigates problems
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Amplifier gain (assume ideal op-amp):
Small-signal equivalent circuit model:
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Then:
Solving for vo:
As expected!
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Op-amp itself has “open-loop gain”: AOp-amp amplifier has “closed loop gain”: G
Why would anybody do this?à Traded-off gain for robustness!
Amplifier gain is set by ratio of two resistance values:à gain largely independent of temperature à also corrected output offset problem
Demo
G=
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3. Methodology to analyze op-amp circuits
• Look again at non-inverting amplifier:
How much is v+-v-?
Since A is very large, then v+-v-<<vIN, vO
In the scale of vIN, vO,
As Aà ∞
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Method to analyze op-amp circuits:– assume that Aà∞– assume that v+=v-
– work in large-signal domain
•Example: non-inverting amplifier
Voltage divider at output:
At input:
Combine these two equations and solve:
à i+=i-=0
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• Interesting limit of non-inverting amplifier when R1=0 and R2=∞:
This is called “buffer” or voltage followerUsed to buffer stages in a system
Assembly of a complete system much easier with adequate buffering of individual stages
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4. Another example: inverting amplifier
Consider:
Then:
And:
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Summary
• Op-amp = device with:– Differential input– Single-ended output– Very large but unstable voltage gain– Very high input resistance– Very low output resistance
• “Open-loop” use of op-amp results in unstable operation• In op-amp use, close loop and trade gain against stability• Analysis of op-amp circuits:
– Assume negligible voltage difference between two inputs– Assume negligible input currents