Tuesday, April 28, 2015
Day 17 - Tuesday, April 21, 2015 - Inverting Differentiator
Today we studied how op amps make differentiation and integration:
We did a couple of sample problems for a differentiating op amp. We figured what the signal output would look like depending on the three cases below.
Then we noticed something peculiar. When there is a sudden change in the input signal, there would be flat signal on the output side. This is shown on the bottom graph of the picture.
An Inverting Differentiator schematic looks like this:
For our pre-lab, we developed the function for V out. This is shown below:
Also we noticed, that w is not our regular frequency that we put in the Analog Discovery. So, we showed that w is the frequency we put in multiplied by 2 pi. This is on the bottom of the picture.
Then we calculated what our out put signal would look like if we plug in the values for our resistor and capacitor. We did this for three cases when f = 2KHz, 1KHz, and 500 Hz.
This graph shows the signal input and output when the f= 2 KHz.
We did a couple of sample problems for a differentiating op amp. We figured what the signal output would look like depending on the three cases below.
Then we noticed something peculiar. When there is a sudden change in the input signal, there would be flat signal on the output side. This is shown on the bottom graph of the picture.
An Inverting Differentiator schematic looks like this:
For our pre-lab, we developed the function for V out. This is shown below:
Also we noticed, that w is not our regular frequency that we put in the Analog Discovery. So, we showed that w is the frequency we put in multiplied by 2 pi. This is on the bottom of the picture.
Then we calculated what our out put signal would look like if we plug in the values for our resistor and capacitor. We did this for three cases when f = 2KHz, 1KHz, and 500 Hz.
Then we built our circuit and this is is what our circuit looked like:
This graph shows the signal input and output when the f= 2 KHz.
This graph shows the signal input and output when the f= 1 KHz.
This graph shows the signal input and output when the f= 500 Hz.
Thursday, April 16, 2015
Day 16 - Thursday, April 16, 2015 - Passive RC Circuits Natural Response and Passive RL Circuits
Today we developed some of the equations that we're going to use in lab. In RC circuits, we did a Kirchoff Current Law and ended up with the equation at the top of the picture below. Then we did some math and integration to solve for V as time changes.
Then we defined our time constant for RC circuits as the greek letter tau.
Our first lab of today was called Passive RC Circuits.
After the lab we looked at RL Circuits. After we did a Kirchoff Voltage Law, we ended up with the equation at the top of the picture which is a differential equation with I as our independent variable. So, we solved for the current.
Then we noticed that the current and voltage are very closely related to each other.
Our second lab of today was called Passive RL Circuits. But, we were running out of time so, Mason did for us and gave a demonstration.
Mason showed us what the signal looked like.
Then we defined our time constant for RC circuits as the greek letter tau.
Our first lab of today was called Passive RC Circuits.
After the lab we looked at RL Circuits. After we did a Kirchoff Voltage Law, we ended up with the equation at the top of the picture which is a differential equation with I as our independent variable. So, we solved for the current.
Then we noticed that the current and voltage are very closely related to each other.
Our second lab of today was called Passive RL Circuits. But, we were running out of time so, Mason did for us and gave a demonstration.
Mason showed us what the signal looked like.
Day 15 - Tuesday, April 14, 2015 - Capacitor Voltage-current Relations
Today we reviewed capacitors. A capacitor stores energy in an electric field. It is usually thought of as two parallel plates with the same magnitude of charges but different signs.
Also capacitance can change with the dimensions of the plates. \
Our diagram for capacitors does not represent a fundamental reality of capacitors which is that they are polarized. So since now we are recognizing this, we are going to draw it differently.
Capacitors can also change capacitance and we draw them like this.
Also, we can classify capacitors as axial and radial.
They can also be classified as electrolytic and tantalum capacitors. Tantalum capacitors are dry devices unlike the electrolytic capacitors. They are most useful when the circuit needs to be stable when temperature changes. In these capacitors, d is incredibly small.
There are also super capacitors
Capacitors are also rated according to their voltage.
There are also ceramic capacitors which usually have very small values. They are cheap.
There are many types of capacitors. A notorious type are capacitors of silver-mica. Mica is a national occurring type of rock that cuts in plates of rocks.
There are also adjustable capacitors.
There are also pyester film capactiors which uses a thin pyester film as a
Then we worked with equations and derived the energy in a capacitor.
In circuits, capacitors act as a short which means that we can draw them as open circuits.
Then we did our lab called Capacitor Voltage-Current Relations
Below is a picture of our circuit.
For our first input signal we put in a sinusoidal signal of amplitude = 2 V and offset = 0. And we tried three different frequencies:
a. Frequency = 1kHz
b. Frequency = 2kHz
c. Frequency = 100 Hz. Also, we changed the amplitude to 4 V.
For our second input signal, we put in a triangular signal with amplitude of 2 V and offset = 0. And we tried to see three frequencies:
a. Frequency = 1kHz
b. Frequency = 2kHz
c. Frequency = 100 Hz and we changed the voltage to 4 V
Also capacitance can change with the dimensions of the plates. \
Our diagram for capacitors does not represent a fundamental reality of capacitors which is that they are polarized. So since now we are recognizing this, we are going to draw it differently.
Capacitors can also change capacitance and we draw them like this.
Also, we can classify capacitors as axial and radial.
They can also be classified as electrolytic and tantalum capacitors. Tantalum capacitors are dry devices unlike the electrolytic capacitors. They are most useful when the circuit needs to be stable when temperature changes. In these capacitors, d is incredibly small.
There are also super capacitors
Capacitors are also rated according to their voltage.
There are also ceramic capacitors which usually have very small values. They are cheap.
There are many types of capacitors. A notorious type are capacitors of silver-mica. Mica is a national occurring type of rock that cuts in plates of rocks.
There are also adjustable capacitors.
There are also pyester film capactiors which uses a thin pyester film as a
Then we worked with equations and derived the energy in a capacitor.
In circuits, capacitors act as a short which means that we can draw them as open circuits.
Then we did our lab called Capacitor Voltage-Current Relations
Below is a picture of our circuit.
For our first input signal we put in a sinusoidal signal of amplitude = 2 V and offset = 0. And we tried three different frequencies:
a. Frequency = 1kHz
b. Frequency = 2kHz
c. Frequency = 100 Hz. Also, we changed the amplitude to 4 V.
For our second input signal, we put in a triangular signal with amplitude of 2 V and offset = 0. And we tried to see three frequencies:
a. Frequency = 1kHz
b. Frequency = 2kHz
c. Frequency = 100 Hz and we changed the voltage to 4 V
Day 14 - Thursday, April 9, 2015 - Temperature Measurement System Design
Today's lab consisted of building a temperature sensor. That works in a manner as shown in the graph below:
So, to built this system, we start by building a wheatstone bridge separately. We make the difference of voltage at the middle zero as shown in the following schematic:
For this we built a whitestone bridge and added a potentiometer. Then we changed the resistance on the potentiometer to make the difference in voltage at the middle of the whitestone brige zero, but we got close to 0.056 V.
Below is a closer picture of the wheatstone bridge with the potentiometer
After we built the whitestone bridge, we built the next part of the circuit.
At first we thought it wasn't working right, so we re-constructed it. And, it looked like this:
Then it worked and we got that it was inverting the voltage by a factor of -1. This corresponds with the values of our resistors.
Then we took a video of it changing.
So, to built this system, we start by building a wheatstone bridge separately. We make the difference of voltage at the middle zero as shown in the following schematic:
For this we built a whitestone bridge and added a potentiometer. Then we changed the resistance on the potentiometer to make the difference in voltage at the middle of the whitestone brige zero, but we got close to 0.056 V.
Below is a closer picture of the wheatstone bridge with the potentiometer
After we built the whitestone bridge, we built the next part of the circuit.
At first we thought it wasn't working right, so we re-constructed it. And, it looked like this:
Then it worked and we got that it was inverting the voltage by a factor of -1. This corresponds with the values of our resistors.
Then we took a video of it changing.
Day 13 - Tuesday, April 7, 2015 - Inverting Voltage Amplifier
Today's lab was called Inverting Voltage Amplifier. In here we calculated the gain and built a circuit to test our predictions regarding the gain.
Our data is displayed below:
The data shows that the circuit reached saturation at high and low voltages.
Below is a picture of the circuit.
Our data is displayed below:
| Vin | Vout |
| -3 | 4.174 |
| -2.5 | 4.179 |
| -2 | 4.185 |
| -1.5 | 3.343 |
| -1 | 2.2461 |
| -0.5 | 1.1345 |
| 0 | 0.0248 |
| 0.5 | -1.0819 |
| 1 | -2.1932 |
| 1.5 | -3.312 |
| 2 | -3.391 |
| 2.5 | -3.382 |
| 3 | -3.374 |
| 3.5 | -3.368 |
| 4 | -3.364 |
The data shows that the circuit reached saturation at high and low voltages.
Below is a picture of the circuit.
Thursday, April 2, 2015
Day 12 - Thursday, April 2, 2015 - Celebration of Knowledge
Today was the day of our first Celebration of Knowledge
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