Date: April 6, 2017
Non inverting op Amp; Summing Amplifier; Difference Amplifier
Activity 1: Inverting
op amp graphs
The first
activity done today involved revisiting inverting op amps to determine practice
our knowledge of the op amp.
The above picture shows the
equivalent circuit of a basic inverting op amplifier. Since we assume the op amp is ideal we can assume
infinite open loop gain, A, infinite resistance at Ri, and zero resistance at,
Ro. Therefore, we only look at R1 and R2. Since the R2 is connected to the Vo
section of the op amp it will act as the feedback resistor. The R1 will be the
initial resistor. We follow inverting op amp equation to obtain a gain of -3.
The graphs display input voltage on top and output voltage on the bottom.
Activity 2:
Noninverting op amp example
The second activity is an
example of how to solve a noninverting op amp circuit.
The above
picture shows the circuit we are working with along with the incorrect approach
we took to solving it on the left of the picture. The correct method of solving
it included doing nodal analysis at Va giving us the first equation. The second
thing was realizing that Vs is equal to Vb which is equal to zero for this
example. Then doing nodal analysis at Vb giving the second equation. We
simplified both equations and got the Vo to be -1.64. An important observation
of this example is that because Vs was equal to zero the circuit acted like an
inverting amplifier. If Vs had any voltage the results would not have been a
negative number rather a positive Vo.
Lab 1: Summing
Amplifier
Pre-lab:
In order to
get this summing circuit to preform the addition of the two incoming voltages,
Va and Vb, the three resistance must all be equal to each other, R1=R2=R3.
The picture above is the summing circuit we set up using all
three resistors that are equal to each other.
In the above picture is the results of the changing the
voltage at Va and keeping Vb constant. Since all three resistors equal each
other that means that this circuit follows the equation, Vo=-(Va+Vb).
Va
|
Vb
|
Vo theory
|
Vo exper
|
percent error
|
-4
|
1
|
3
|
2.96
|
1.33
|
-2
|
1
|
1
|
0.98
|
2.00
|
-1
|
1
|
0
|
0
|
0.00
|
0
|
1
|
-1
|
-0.97
|
3.00
|
1
|
1
|
-2
|
-1.96
|
2.00
|
2
|
1
|
-3
|
-2.05
|
31.67
|
3
|
1
|
-4
|
-3.43
|
14.25
|
5
|
1
|
-6
|
-3.43
|
42.83
|
The table above shows that for the most part the circuit
acts the way we want predicted except at one point where the data is skewed,
Va=3. However, the rest makes sense because we have observed that op amps
saturate at high voltages and the saturation is higher when the Vo is negative.
Lab 2: Difference
Amplifier
Pre-lab: First we determined the relationship between Va and
Vb which is that they equal each other because they are both connected to the
op amp from the positive and negative terminals and we assume ideal op amp;
therefore, the equal each other and they both equal zero. But both of them
equally zero does not go into deriving the difference amp equation.
In the Picture above we derived the relation ship between Vo
and V1 and V2. The circuit is called a difference amplifier because if the all
the resistances equal the same value then relationship becomes: Vo=(V2-V1).
Resistances are on the bottom left of the board. We let R1=R3 and R2=R4.
Furthermore, the results of when Vb=1 are on the bottom right and is the left
of the two sets of data. The one on the very bottom right is when we changed
the Vb to -1V.
V1
|
V2
|
Vo theory
|
Vo experiment
|
percent error
|
-4
|
1
|
10
|
4.27
|
57.3
|
-2
|
1
|
6
|
3.28
|
45.3
|
-1
|
1
|
4
|
3.27
|
18.3
|
0
|
1
|
2
|
2.01
|
-0.5
|
1
|
1
|
0
|
0
|
0.0
|
3
|
1
|
-4
|
-3.97
|
0.7
|
5
|
1
|
-8
|
-4.54
|
43.3
|
The table above( is for the results of when Vb=1 or V2=1)
shows that high saturation occurs at higher voltages but this is to be
expected. However, within smaller ranges of it does what we expect; it follows
the equation, Vo=R2/R1(V2-V1) or Vo=2(V2-V1).
The graph above shows the relationship between the input and
outputs of this circuit.
The above picture is our difference circuit.
In conclusion:
We went
over inverting op amps again. We continued our study of op amps by covering:
non-inverting, summer, and difference op amps. In the experiments, we tested
out the summing op amps and were able to determine That if all three resistors
are the same the input voltages are added up then made negative. The Difference
op amp circuit showed us that if the resistors R2/R1=R4/R3 we get a gain of the
ratio of the two different resistors we also determined that if all the
resistors were the same the input voltages would subtract which is why this is
called a difference op amp. In both experiments we saw that at higher voltages
there is a large saturation that occurs. There also appears to be more
saturation when the output is negative.
