page 44
5.1.2.5 - Weighted Sums
• The following circuit can be used to add inputs. If dissimilar components are used the inputs can be weighted
page 45
I1
R1
V1 |
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Rf |
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If |
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I2 |
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R2 |
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V2 |
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Vo |
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+
In
Rn
Vn
We can recognize that the op-amp inputs are both kept at zero volts, and that there is not current into the non-inverting input, we can find,
V- |
= V+ = 0 |
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I1 |
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V1 |
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I2 = |
V2 |
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In = |
Vn |
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----- |
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----- |
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----- |
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R1 |
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R2 |
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Rn |
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If |
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Vo |
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----- |
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Rf |
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∑ |
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I |
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I1 + I2 + In – If |
= 0 |
= |
V1 |
V2 |
+ |
Vn |
Vo |
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----- + ----- + … |
----- – ----- |
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R1 |
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Rn |
Rf |
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R |
V1 |
V2 |
+ … |
+ |
Vn |
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----- |
+ ----- |
----- |
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f R |
1 |
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2 |
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5.1.2.6 - Difference Amplifier (Subtraction)
• We can construct an amplifier that subtracts one input from the other,
page 46
R2 |
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Rf |
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V2 |
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+ |
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V1
R1
R3
Using the normal approach, we can see that both inputs are essentially voltage dividers,
V |
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= V |
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R3 |
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----------------- |
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1 |
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1 |
+ R |
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V |
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= ( V |
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– V ) |
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Rf |
+ V |
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---------------- |
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2 |
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2 |
+ R |
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Next, we can set the two inputs equal, and combine the equations,
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= V |
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= V |
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----------------- |
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= ( V |
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– V ) ---------------- |
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Rf |
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+ V |
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1 R |
1 |
+ R |
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o R |
2 |
+ R |
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R2 + Rf – Rf |
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Rf |
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Vo |
---------------------------- |
R |
2 |
+ R |
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= V1 |
R------------------ |
1 |
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+ R |
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– V2 |
R---------------- |
2 |
+ R |
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f |
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3 |
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f |
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V |
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= |
V |
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R3( R2 |
+ Rf) |
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– V |
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Rf |
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----------------------------- |
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( R |
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----- |
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o |
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1 |
R |
2 |
1 |
+ R ) |
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Note the result if all resistor values are equal, |
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Vo |
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= V1 – V2 |
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page 47
5.1.2.7 - Op-Amp Voltage Follower
• At times we want to isolate a voltage source from an application, or add a high impedance. This can be done using a voltage follower,
- |
Vo |
VI |
+ |
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We can develop some of the basic relationship for this circuit,
V+ = VI
V+ = V-
Vo = V-
Vo = VI
5.1.2.8 - Bridge Balancer
• Op-amps can be used for measuring the potential across bridges.