11 - Op-Amps

INTRO: The Operational Amplifier is an electronic device that we will be covering today. This device, commonly called an Op-Amp, is capable of amplifying the input voltage. It also has the ability to reverse the polarity of the input voltage and performing mathematical operations. It is this last property that puts the "operational" in the name. The ability of the op-amp to perform many functions comes from the complex inner-workings, as well as the multiple inputs available.


 
We began class by writing down the 5 circuit elements that we have covered thus far. It was a good review to be able to consolidate everything we have worked with down to 5 categories. 

 
This above picture demonstrates the input availability on the bottom diagram. As mentioned above, this is key in allowing the op-amp to perform many functions
  
LAB: Inverting Voltage Amplifier
In this lab we will explore a type of op-amp. The inverting type reverses the polarity of the input voltage, as well as amplifying it. 


Above is our pre-lab where we found a relationship between Vin and Vout. After some work we arrived at Vout equaling -2Vin, which makes practical sense given the ability of the inverting op-amp.

 
Above is a picture of our circuit set up as the diagram requested. A key property of inverting amps is that the output voltage goes back to the inverting input, after going through a resistor of course.

 
 Above is the graph of Vin vs. Vout. As we predicted earlier in the pre-lab, they do have a 2-1 relationship. It is also important to note that just like a transistor, the op-amp experiences saturation, which can be seen in the above diagram.

10 - Maximum Power Transfer and Non-Ideal Power Sources

INTRO: Today we explored the idea of Maximum Power Transfer and Non-ideal Power Sources. Maximum power transfer occurs when the resistances inside the EMF is 0, or close to it. That is what we would call an Ideal power source. If it were non-deal, then there would be a value for an internal EMF's resistance.

LAB: Maximum Power Transfer
In this lab we will be working with the concept we just learned to attempt to maximize the power delivered to a load resistor.

Above we measured Pmax. In order to do this, we had to make some assumptions, such as Rc being larger then Rs.


Here is a picture of our circuit diagram. We connected according to the diagram provided in the lab manual.

Here we have some calculations of the circuit in regards to power

LAB: Non-Ideal Power Sources

In this lab we will explore non-deal power sources. This is a topic that has not been covered yet, because power sources are treated as being ideal out of simplicity. The aim of this lab is to illustrate some of the effects of non-ideal power supplies.

Here we made some calculations with and without the resistance of the source. Like i mentioned above, the resistance of the source is what differentiates between a ideal and non-ideal source.



At #2 above we have a comparison between different external resistances and the internal resistance of the EMF. As you can see, the internal resistance goes down as the external resistance goes up. This goes in line with what we have begun learning.

9 - Thevenin's Theorem

INTRO: Today we explored the very important Thevenin's Theorem. Thevenin's  Theorem is very useful for circuits that involve many circuit elements and a variable resistor. If there were to be a change in the resistence of the variable one, all the other values would need to be recalculated for the rest of the diagram. This theorem allows you to rewrite the remainder of the diagram as a voltage source and a resistor in series.








Here we used Thevenin's Theory for the first time. The Rth is found by getting rid of all the independent circuit elements and solving for R. Finding Vth is not too difficult, all you have to do is use one of our prior analyzing methods to find it.


Here we used Everycircuit, which is a program that allows you to set up and gives values for your circuits. Although it is a great tool, as engineers we still need understand why the values are what they are. We need to learn and understand the concepts behind those values, which is what differentiates us between technicians. Damn technicians, DEY TOOK OUUUURRRR JOBSS

LAB: THEVENIN'S THEOREM
In this lab we are going to explore the concept further. 

 
Here we used the theorem to solve for values in the circuit. We then used Everycircuit to check the answers that we got.


Above is a picture of our circuit. We used a variable resistor, called a POT, which allows us to measure different values of the circuit elements when we vary the POT






Since we kept changing the resistance, we made values of what we calculated and measured across a circuit element. Above is a table of all of the values at different resistances.


Here we graphed our Power vs. Load Resistance. It increases until it tops off and begins falling by a bit.

8 - Time Varying signals & BJT Curve Tracers

INTRO: Today we dealt with Time Varying signals and BJT Curve tracers. Time Varying Signals are a concept we have covered several time over the physics series. With time, the signal changes, often in geometric shapes. A BJT Curve tracer is a newer concept that will be further explained later on in the blog.

Above we used the Waveform Generator to create time-varying signals. There are two different types of signals on the left and right

Here are two additional time varying signals.We have a triangular one in this picture

LAB: Time-Varying Signals

In this lab we dealt with time-varying signals, which were described above. We estimate what the Vout and Vin are going to be with our time-varying signals.

LAB: A BJT Curve Tracer

In this lab our purpose is to investigate the collector current vs. the collector voltage of a BJT Transistor.

 

Above is the diagram that we are using for this lab. You should be able to recognize the BJT configuration from the prior lab.

 

Here is the physical circuit that we used for this lab.

Here is the graph of our 5-step voltage supply. As all the graphs show, we have the threshold, a linear relationship, and then saturation.

7 - Mesh Analysis

INTRO: Today we covered another analysis method, Mesh Analysis. This method uses the concepts of mesh's, loops with no loops within. We deal with currents and use KVL, instead of KCL and using voltages which Nodal uses. It is ideal for circuit with many elements in series.Coupled with Nodal Analysis, it gives us two strong methods to evaluate circuits.

 Here we tried our first attempt at mesh analysis. Drawing our loops, and writing out our KVL equations for both we are able to get a system of equations. Just like nodal analysis, we plug this system into FreeMAT to solve for the variable current.

 Here we tested our knowledge of mesh analysis with a group quiz. We moved it up to 3 loops. The only tricky part was when you have two currents going against eachother on a shared resistor.

LAB: Mesh Analysis III

In this lab we are going to build a circuit with several elements.Just like we did above, we will analyze the circuit with mesh Analysis.

  In the pre-lab we used mesh analysis to determine the values of our circuit elements. It was still a bit difficult since it was a new concept, but we arrived at some numbers.

 

Here is a picture of our circuit

Below is the Pre-lab. We calculated the current and voltage and compared it to the measured value with the percent error. It was relatively close, with the highest discrepency being just 3.8%

6 - Nodal Analysis

INTRO: Today we covered a very useful analysis method, Nodal Analysis. with Nodal Analysis we look at all the nodes in the circuit and denote one as a ground. Then at the other ones we use KCL to sum the currents going in and out of the node. If we are expressing the currents as voltages and resistances, then they are on the left side of the equation. If we are explicitly given the currents, they go on the right side of the equation.

 

 LAB: Nodal Analysis

In this lab we designed a circuit containing multiple sources. However, it would be very difficult to analyze the circuits with our traditional techniques such as KCL and KVL This is why we use nodal analysis to calculate some values.

During the pre-lab we made the above calculations with nodal analysis

 

Above is the diagram of our circuit

Above we set up the circuit used our multi-meter to measure values. Using the percent error formula, we found a very low error for both of our calculated nodal analysis voltages.

Above is pictured the actual circuit that we set up. As the picture shows, it is composed of two arms, a watch, and a black wristband. Just making sure you're actually reading this.

 Above are some more calculations to make ourselves familiar with nodal analysis. After working with this method, I feel very comfortable and confident using it to analyze circuits.

5 - Temperature Measurement System

INTRO: Today we did some review of what we had already learned and applied it to some more practical circuit building. We also built a new circuit which incorporates new types of resistors.

Below we are given a circuit and asked to evaluate it. We used a concept like Nodal analysis to evaluate the circuit and express terms in other circuit terms.

LAB: Temperature Measurement System

In today;s lab we design a circuit with an output voltage which provides a temperature measurement. We used a thermistor which is a device that changes with temperature. By holding the thermistor, it would get hotter, which would increase it's resistence.

In the pre-lab, we calculated some measurement of resistance within the circuit

Below is a picture of our setup for the circuit. At the top the symbol with the resistor and an arrow through it signifies a variable resistor, which is what the thermistor is.

 

Here is our setup of our diagram.

Below are our results for the lab.

Here we calculated the percent error in our experiment.

4 - Transistors

INTRO: Today we were introduced to the transistor. A transistor is a circuit element that can control voltage or current. A transistor can be controlled by voltage or current.

Here we started off with a basic circuit problem. Still reviewing some basic circuit methods, we Solved what our resistance needed to be under certain situations. Since we had a current restriction of 10MA tops, and a Voltage range, we solved for the following values of current.

Here the hotdog told Professor Mason the tale of its' birth. It was a story wrapped in mystery, magic, and a narration that was so thrilling it can only be compared to the final seconds of the academy award winning, blockbuster ultra holiday hit, Jingle All the Way. After hearing this tale of a lifetime, Professor Mason shed a single tear, and promised the dying wiener he would never harm another frank ever again. He was never the same....

 

Until 5 seconds later when he instantly reversed his promise and torched another bratwurst from the inside out


Here professor Mason challenged the last hotdog to a game of rock, paper, scissors.If it won, he would promise to set it free. The hotdog was jubilent, like a child on Christmas receiving the best gift of all, the BLU-RAY Directors Cut, Arnold Cut, of the All-time smash super hit, Jingle all the way. Sadly Professor Mason chose rock  and the hotog realized it never stood a chance, a hotdog could never be a rock, paper, or scissor, only a hotdog..... It was a lesson in philosophy that the hotdog never forgot would remember forever ........ until 5 seconds later when Professor Mason ate it whole.



LAB: Dusk to Dawn Light
In todays lab we dealt with a transistor and a dusk-to-dawn light. Like I mentioned in the intro, a transistor needs a certain voltage or current to let voltage or current flow through it. The dusk to dawn resistor increases resistances the darker things get.

Here is a copy of the circuit diagram. The only other element not mentioned is the LED, which is under the transistor. A LED is a diode, which is a one-way valve for current.

Below is a video of the circuit in action, with the darkness covering the resistor, the transistor gets stimulated with the right aount of current and the led lights up.

3 - Freemat

INTRO: FreeMat/MatLab is a technical software application with a focus on numerical computation. It also is able to assist in graphing and data visualization. Due to our work with circuits, we will be working with various systems of equations. The matrix's that result will be easily solved with the application of FreeMat.

Above I ran performed exercises from the first half of the handout which focused on familiarizing oneself with the input commands and the functionality of FreeMat. Creating matrixs, row & column vectors, and matrix operations are some of the tasks I performed.

Here I worked with the plotting functions. I used the hold function to plot more then one data set on the same graph.

 Above I solved a system of simultaneous equations from the packet. The answer is -0.1857 Amps.