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Chapter 4The Operational Amplifier
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Ckts W/ Operational Amplifiers• Why Study OpAmps
At This Point?1. OpAmps Are Very
Useful Electronic Components
2. We Have Already Developed The Tools To Analyze Practical OpAmps Circuits
3. The Linear Models for OpAmps Include Dependent Sources
• A PRACTICAL Application of Dependent Srcs
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OpAmp Symbol & Model• The Circuit Symbol
Is a Version of the Amplifier TRIANGLE
The Linear Model
OUTPUT RESISTANCE
INPUT RESISTANCE
GAIN
75
125
1010:
501:
1010:
A
R
R
O
i
• Typical Values
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• -Vcc, when A(Vp-Vn)<-Vcc
• A(Vp-Vn),
when -Vcc< A(Vp-Vn)< +Vcc
• +Vcc, when A(Vp-Vn) >+Vcc
Vo =
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2 Ways of Using Op-Amps
• “Open Loop”: very high gain amplifier– Useful for comparing 2 voltages– Fixed gain, always at MAX OUTPUT!!
• “Closed Loop” with negative feedback– Useful for amplifying, adding, subtracting,
differentiation and integration (using capacitors)– Variable gain, controlled by resistor selection
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“Open-Loop” examples• Ideal Comparator and Transfer Characteristic
“Zero-Cross” Detector → Heart of Solid State Relay Cnrtl
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““Closed Loop” Example: Unity Gain Buffer Closed Loop” Example: Unity Gain Buffer
Controlling Variable = IRV iin
Solve For Buffer Gain
O
iOO
is
out A
RARRV
Vrecall
1
1 Thus The Amplification
1S
outO V
VA
0 inOOis VAIRIRV :KVL
0 inOO VAIRoutV- :KVL
Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995
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Consequences for Vp-Vn• Normally, A is 10,000 or more, so to avoid
saturation, abs(Vp-Vn) must be < Vcc/10000, or, if Vcc = 20V, about 2 mV which is negligible for most circuits
• With an Ideal Op-amp, A = infinity, so Vp = Vn to avoid saturation
• Negative Feedback resistors “force” Vp = Vn i.e. if Vp-Vn gets large, A(Vp-Vn) pulls back toward zero (more on this later)
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But…always remember Vcc/-Vcc limits…if Vo saturates Vp does not = Vn !!!
Terminal Characteristics for an ideal op amp in it’s Linear Range:
• Ip = In = 0 (very high input resistance=1MOhm)
• Io can be very large (coming from Vcc/-Vcc)
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Inverting Amplifier
Vo = -RfVs Rs
When in linear
region
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Inverting Amplifier with Feedback Path broken
• Vo= -AVs
Saturation
(unless Vs<2mv)
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Summing Amplifier
Vo = - Rf (Va + Vb + Vc) (in linear region)
Rs
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Non-Inverting Amplifier
Vo=(Rs+Rf) Vg
Rs
In linear region
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Difference Amplifier
Vo= Rb (Vb – Va) in linear region AND
Ra IFF Ra/Rb = Rc/Rd
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Common Mode Rejection Ratio
IF Ra/Rb =(1-e) Rc/Rc (e=very small)CMMR = abs(1 + Rb/Ra)
e
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Comparator, used in digital circuits
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Application, the Flash Converter
• Comparators quantize
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Encoder converts to binary