18 - Osciloscopes

INTRO: Today we discussed several topics, however we focused mainly on the oscilloscope. Although we had a lab planned, that Professor Mason had just made the night prior, we were short on time so we had to skip it. With that being said, this lab entry will be fairly short.


 Below is the face of an oscilloscope. An oscilloscope is a device used to measure the frequency of a signal. The screen is used to present the waveform signals in a graph format, to make the information more understandable.




 Below is a collection of the waves that can be displayed on the oscilloscope screen. Sin, triangles, and square waves are just some of the waves that can be displayed on the screen.


LAB: Professor Mason said to skip
Professor Mason told the class we were better off focusing on the material presented in class then attempt the lab which he briefly showed us.

17 - Parallel RLC Circuit Step Response

INTRO:  Today we are covering a similar topic to the one discussed in the prior lab day. Instead of series RLC, we will be covering parallel RLC circuits. Although they involve the same circuit elements, several equations change, including the neper frequency equation.

Below is a diagram comparing a series and parallel RLC circuit. Regardless of how the element(s) are spread through the different parallel branch, the parallel RLC equations will work for all examples. On the right side of the picture, you can see the diagram with a resistor and capacitor in parallel with a resistor and inductor.

LAB: PARALLEL RLC CIRCUIT RESPONSE

In this lab, we will model and test a parallel second order circuit containing two resistors, a capacitor and an inductor. We will use a step response for the voltage source.

  

In the below picture we drew our circuit as well as calculated some values. Something to note is that the value of alpha changes compared to a series RLC circuit. Alpha is now 1/(2RC).

 Below is the circuit that we built. As you can see, we have an inductor and a capacitor in parallel, both with a resistor each in series with each of them.

16- RLC Series Circuit Step response

INTRO: Today we covered RLC circuits, which are circuits that involve at least one capacitor, inductor, and resistor. Due to the inclusion of three circuit elements, as well as an EMF, there are certain equations that can be applied to different elements to get circuit values. Although the equations can be overwhelming at first, once you know where to apply them, RLC circuits become easy to break down.

Below is a basic diagram for a RLC Series circuit. RLC Circuits are also called 2nd order circuits. This is because differential equations are involved when finding expressions for circuit element values.

LAB: RLC SERIES CIRCUIT SERIES RESPONSE

In this lab we will be working with 2nd order circuits. In Part I we will analyze the circuit with a step response. In Part II we will redesign the circuit to make it critically damped.

In the pre-lab we calculate capacitance, alpha, and omega. Alphais called the neper frequency and omega is the damping factor. These values are important because they classify a RLC series circuit into one of three situations: underdamped, critically damped, and overdamped.

Here we built the diagram as modeled from the lab. We have a resistor, inductor, as well as a capacitor all in series with a voltage capable of being applied at each ends.

 

Here we have written down the experimental values that we obtained during our work with the circuits. As alpha is bigger then omega, our circuit is underdamped. As for part II of the lab, we also calculated a capacitance of 3.3 would make the circuit critically damped.

15 - Inverting Differentiator

INTRO: Today we revisited the circuit element family of Op Amps. As a refresher an op amp is a circuit element that amplifies the values going into it. It is also capable of doing mathematical operations, as the name implies. Today we dealt with a specific type of Op Amp, the inverting differentiator.

Below is a diagram of an op amp circuit. The differentiator produces an output that is proportionally based off of the rate of change of the input. In other words, it is dependent on the derivative of the input signal. This is ideal since you know have the ability to change large amounts of voltage/current based off of much smaller changes of current/voltage.

LAB: INVERTING DIFFERENTIATOR
In this lab we will examine the forced response of a circuit involving an inverting differentiator. We will use varying frequencies for the input and measure the values at the output.

Below is a the pre-lab where we calculated values for the circuit. Our calculations involved the input voltage and calculating the output voltage that we should receive. We will compare these to our measured values when we set up our circuit.


Below is a picture of our circuit with or circuit elements connected per the lab instructions.


In the following graphs we used sine waves at 0.5, 1, & 2 Khz. Our calculated values were not too far off from our experimental data.

The following chart summarizes the values obtained from calculations and the experiment. At lower values our percent difference was 1.9, but it increased to around 5% at higher voltages. We are working with budget equipment, as well as with moderate knowledge of circuits, so I would say the percent difference is within the realm of our experiment.

14 - Passive RC & RL Circuit Natural Response

INTRO: Today we began we RC circuits. RC circuits, or first order circuits, include a capacitor, as well as a resistor. They are also called first order circuits, since the derivation of circuit element values involves first order differential equations.


Below is a diagram of a RC circuit. In this case you have an EMF (battery), capacitor, resistor, and a switch all connected in series. The capacitor will charge when it is in a completed circuit. When it is fully charged, the current can no longer flow as there is no potential difference between the EMF and the capacitor. If the capacitor is put into a completed circuit with a resistor and no EMF, it will discharge and temporarily power the circuit.

LAB: PASSIVE RC CIRCUIT NATURAL RESPONSE

In this lab we will examine the natural response of a simple RC circuit. We will use a time varying voltage source and switch. The natural response is the response of the capacitor on the circuit when the EMF is disregarded. Just to mention, the EMF response is called the forced response.

Below is a diagram of our circuit for the RC Circuit. In the pre-lab we calculated Tau (t), which is called the time constant. This value is Resistance/capacitance and is used as a marker on the capacitor discharging in the circuit. We calculated our time constant to be .015seconds, which is the discharge of the capacitor with no EMF connected in the series.

Below is a picture of the circuit we actually built. At first it may look different from the diagram above, but that is because we simply placed 3 capacitors in series to create an equal capacitance of what we wanted. We did this because we did not have the correct single capacitor in stock. 

 

Below is the voltage graph of the passive response of our RC circuit over 1 time constant. The graph is what to be expected of a normal discharging capacitor. Our experimental Tau was .020, which was off by a large percentage from our theoretical value.

LAB: PASSIVE RL CIRCUIT NATURAL RESPONSE

In this lab we will examine the natural response of a simple RL circuit. We will use a time varying voltage source and switch much like the above circuit.

Below is our circuit, with the inductor being the black cylinder in the center of the circuit. For an RL circuit, tau is inductance over resistance. Also, 5tau is when both an RC and an RL circuit are considered fully discharged.

We were short for time, so Professor Mason had to share the per-calculated results of the Lab.

13 - Capacitor Voltage -Current Relationship

INTRO: Today we began dealing with capacitors, which we have previously covered in our Physics class. Although we did the basics of capacitors in circuits, we will go much more in depth with this circuit element in this class.

Pictured below is a capacitor. Capacitor are circuit elements that store energy/voltage in the Electric Field between two plates within itself. When charged, a capacitor can directly power a circuit for a short time since it has stored voltage. This is temporary though, since the voltage will eventually balance itself out. Capacitors are measured in capacitance (C), which is essentially how much energy a capacitor can hold.

 

LAB: CAPACITOR VOLTAGE - CURRENT RELATIONSHIP

In this lab we we see what relation exist between the voltage difference across a capacitor and the current passing through it. From what we know from capacitors, the higher the current should slowly decay while the potential stored inside the capacitor increases.

Here is a picture of our circuit diagram with a resistor in series with a capacitor. We will use several time-varying signals to power our circuit.

 

The time-varying signals we used our displayed below. We will use the common sine function, as well as the more uncommon triangle function.

 

Below is a picture of our diagram. We have the voltage going in and out, as well as the resistor in series with our capacitor.

 Below are the aforementioned time-varying signals that were applied as the voltage. The first two graphs show sine functions at 1 & 2 KHZ, as well as a triangular function of 400HZ.

 

Viewing the graph below you can see the relationship between the voltage  and current. They are out of phase by practically 90 degrees. This experiment backs up what we already know about capacitors, that the current drops to 0, when the voltage reaches its' max.

*12 - Temperature Measurement Design

INTRO: Today we mainly dealt with a lab that incorporated familiar and unfamiliar components. We again use the thermistor, a device previously described, to create a relationship between temperature and circuit element values.


Pictured below is a thermistor. Since previously mentioned, the following description will be brief. This circuit element changes the current, and accompanying voltage, flowing through it based off of the temperature of the thermistor. For example, to change the current, holding the thermistor, would change the current through it since you are heating it up.


LAB: TEMPERATURE MEASUREMENT SYSTEM
In this lab we will design a DC circuit that will ultimately allow us the ability to determine the temperature. We will use a thermistor, a difference amplifier, as well as a Wheatstone Bridge Circuit.

Pictured below is the basic setup of our circuit. We will go from the thermistor to the Wheatstone Bridge to the Difference Amplifier


 Below is a diagram of our wheatstone bridge circuit. This circuit design is useful since wheatstone bridge circuits are often used to convert variations in resistance to voltage variations.


Here are our measured values for our setup


 Below is a picture of our circuit. As you can see on the right side of our circuit, we have placed a potentiometer. A Pot makes this circuit much easier to since it can be set to the correct resistance to meet our needs.


The next part of the circuit is to go through the OP AMP. We used a difference amplifier to measure the difference between the input and output voltage. Pictured below is the difference amplifier we built