Download CSCI 2980: Introduction to Circuits, CAD, and Instrumentation

EENG 2610: Circuits Analysis
Class 7: Operational Amplifiers (Op-Amp), 2/2
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas
Op-Amp Circuit Analysis
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General rule for op-amp circuit analysis
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Use the ideal op-amp model conditions
Write nodal equations at the op-amp input terminals
Ideal Model : RO  0, Ri  , A  
i  i  0
v  v
Example 4.5: Determine vo
Example 4.6: Determine vo
This is a precision differential voltage gain device
1
v2
va
2
Comparator
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Comparator is a variant of op-amp
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Ideal comparator and its transfer curve
 VCC ,
VO  
 VEE ,
if (V - V- )  0
if (V - V- )  0
Comparator is designed to operate with the outputs saturated
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Op-amp is not.
Comparator is fast and less expensive than op-amp.
Zero-Crossing Detector
- A Common Comparator Application
5 V
VS
pull-up resistor
 VCC ,
VO  
 VEE ,
if (V - V- )  0
if (V - V- )  0
Equivalence
Important:
A series connection of current
sources or a parallel connection
of voltage sources is forbidden
unless the sources are pointing to
the same direction and have
exactly the same value !
Linearity
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Linear circuits are described by a set of linear algebraic equations
Linearity requires both additivity and homogeneity (scaling)
Example 5.1: Determine Vout using linearity
Superposition
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Principle of Superposition
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In any linear circuit containing multiple independent sources, the
current or voltage at any point in the network may be calculated
as the algebraic sum of the individual contribution of each source
acting alone.
When determining the contribution due to an independent source,
any remaining voltage sources are made zero by replacing them
with short circuits, and any remaining current sources are made
to zero by replacing them with open circuits
Dependent sources are never made zero when using
superposition.
This principle can be used to reduce a complicated problem to
several easier problems – each containing only a single
independent source.
Example 5.3: Use superpositon to find Vo
v2
v1
We set to zero the voltage source
v0
Now we set to zero the current source
Example 5.4: Use superpositon to find Vo
i2
i3
i1
Applying Superposition
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Step 1: In a network containing multiple independent sources,
each source can be applied independently with the remaining
sources turned off.
Step 2: To turn off a voltage source, replace it with a short circuit,
and to turn off a current source, replace it with an open circuit.
Step 3: When the individual sources are applied to the circuit, all the
circuit laws and techniques we have learned or will soon be learned,
can be applied to obtain a solution.
Step 4: The results obtained by applying each source independently
are then added together algebraically to obtain a solution.
Important:
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Superposition cannot be used to determine power because power is a
nonlinear function.
Dependent sources are never turned off when applying superposition
technique.