21 - Inverting Voltage Amp & Op - Amp Relaxation Oscillator

INTRO: Today we return back to the familiar category of Op-amps, however this will be with an AC voltage source. Op-amps of course are circuit elements that amplify the input signals feeding into the amplifier. These are ideal devices because they allow a large amount of current/voltage to be changed with simply making changes to the much smaller input voltage/current feeding into the amplifier. The all-familiar guitar amplifier is a common example that many people have experience with.


Below is a voltage amplifier. Just like stating above, this device is capable of controlling the voltage/current through manipulating the smaller voltage/current that is feeding into it.



LAB: INVERTING VOLTAGE AMPLIFIER
In this lab we will build a an inverting voltage amplifier. We will do so with an AC source, resistors, an op-amp, and a capacitor. Like the prior labs, we will calculate circuit values prior and compare them to the experimental values at the end of the lab.


Below is the  circuit diagram that we will build. It is very similar to our prior op-amp setups, but this one has a capacitor in the top branch.


Below we completed the pre-lab for the lab. We calculated values using given values of frequency, resistance, and capacitance. We completed calculations for amplitude gain, as well as the phase change for all three of the frequencies we ran the circuit at.

Here we set up the diagram according according to the above schematic. We have our op-amp, resistors, as well as the capacitor hooked into our breadboard. We also have an analog discovery connected at the designated points so we can send a varying voltage through the circuit.


Here we had an input voltage of 100HZ


Here we had an input voltage of 1KHZ


Here we had an input voltage of 5KHZ


Conclusion: We then measured the difference between our calculated and measured amplitude gain as well as the phase shift. The percent difference between the amplitude gain was 3.5%, while the phase shift percent difference was 7.8%.


LAB: OP-AMP RELAXATION OSCILLATOR
In this lab we need to design an oscillating circuit that oscillates.. We will do so by using an op-amp, capacitor, and a resistor.


The following schematic is what we will model our circuit after. It is a bit more complex then the prior lab, however we are still using familiar circuit elements.

Below is the pre-lab where we calculated circuit element values. Since we know we want a frequency of 99Hz, we calculate a required resistance of 8371 ohms.

Below is a picture of our circuit, which is modeled after the aforementioned diagram. Also, the output of the circuit is below.



Conclusion: Plugging in numbers from the measured values, our percent error of the measured vs. theoretical frequency was 1.9%. I would say this is within the realm of acceptable error. Also, we learned how to construct a op-amp relaxation oscillator. I've been waiting my whole life for this moment. This is better then the time I met Falcor and saved the Princess, the Rock Monster, and Atreyu from the nothing. But alas, that is a story for another time.

20: Phasors - Passive RL Circuit Response

INTRO: Today we were reintroduced to the familiar concept of phasors. Phasors were introduced to us in the prior 4B class as a way to simplify working with circuits with oscillating voltages. In other words, phasors are synonymous with working with AC circuits. They are a complex number that is composed of a real and imaginary part.


Below is visual representation of the phasor as cartesian axes. The x-axis represents the real axis, while the y axis is the imaginary axis.
d

Below we began working with converting values from the time-domain to the polar/phasor domain. Using relationships we rewrite the voltage and then find the current doing mathematical operations in the phasor domain.

d

Below is another representation of circuit values in the phasor domain. We do the opposite in this exercise as we go from the phasor domain to the time domain. While doing multiplication and division is simpler in the phasor domain, doing addition and subtraction is easier in the time domain.


LAB: PHASOR
In today's lab we built a RL circuit and sent a sinusoidal input and observed the circuit response. However, instead of working in the time domain to describe and evaluate the circuit we will do so in the phasor domain.


Below is a visual representation of what we will be doing in this lab.


Below is a pre-lab where we calculated circuit values in the phasor domain. For three different frequencies we calculated the gain, as well as the accompanying phase change. As to be expected, we will be comparing these to the experimental values at the end of the lab.


As stated above, the circuit was composed of a resistor as well as an inductor. We hooked it up so we could also send a voltage through the circuit when need be.


Below are the graphs of the RL circuit during the three different scenarios.




To conclude our lab I made a graph summarizing the calculated and experimental data. As the table shows, the calculated and experimental are reasonably close, resulting in a percent error less then 6% in every category.

19 - Impedance

INTRO: Today we focused on a familiar concept of Impedance. Impedance (Z) is the ratio of the phasor voltage to the phasor current. In more familiar terms, the impedance of a circuit is the circuits resistance to alternating current. Impedance of a circuit can alternatively be calculated by summing the resistance, capacitance, and inductance in a circuit.


Below is a simple circuit with a voltage source, and impedances. Ignore the circuit values in non-time domain values,since it is unimportant for now.



 LAB: IMPEDANCE
 In this lab we will build a circuit and calculate the impedance of three elements; a resistor, capacitor, and inductor. We will then check our experimental values against our calculated ones.

 Below we drew and calculated the impedance values for our three circuits. The circuits are a normal resistive circuit, a RL circuit, and then a RC circuit. As seen as the pictures below, we list the calculated values for the impedance.


Resistive Circuit and accompanying graph at 1k frequency



 RC circuit and accompanying graph at 1k frequency



 RL and accompanying graph at 1k frequency



In the chart below we charted the values from all three of our circuits. Although just one graph per circuit is listed in the situations above, we ran each circuit three times at 1,5,10 khz. The experimental values were relatively close to our calculated values.

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.