Day 21 (Day23 on notes)

Today we went over how OP Amps work in AC circuit, and did the Inverting Voltage Amplifier Lab and the Relaxation Oscillator lab to see how to see how they would work in real life.

Here we did an example of an op amp in the frequency domain.

Inverting Voltage Amplifier Lab:

The purpose of this lab is to see the amplitude gain and phase difference between the output and input signals of a inverting voltage amplifier circuit.

Our theoretical values for gain and phase shift are on the right side on the right side of the picture in the pre lab section. 
For our results shown in pink, we got a fairly close to zero percent difference for the 100 and 1000 Hz. For the 5kHZ we had a substantially higher error in gain which may be due to the op amp working outside of its frequency range.


Input wave is at 100Hz at 2V shown in orange and the output wave is in blue.

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Input wave is at 1kHz at 2V shown in orange and the output wave is in blue.


Finally, here is the input wave is at 5kHz at 2V shown in orange and the output wave is in blue.

Here is a picture of our circuit.

Op Amp Relaxation Oscillator Lab:
The purpose of this lab is to construct a relaxation oscillator, which is a type of device that will act as a switch when a certain voltage is applied to one of its terminals. This voltage is usually the voltage across a capacitor that is being charged or discharged.


Here are the predictions according to Everycircuit.


Above is what we measured with the oscilloscope with an input of 733 Hz at 2V.

There is rounding error when we measured the pots resistance with the multimeter so we were not able to get the exact value. Also we treat the op amp as ideal so that too may contribute to our fairly high error calculated above.

Day 19 (day 21 on notes)

Today I could not make it to class because I attended my friend's funeral. He was a truely kindhearted person that always saw the good in people and had such a unique way of making people smile. My prayers go out to his parents and siblings and may you rest in paradise brother. 

The program for the service

The funeral at Forrest Lawn Memorial Park

Day 20 (Day22 on notes)

Today we learned how to use phasors on the same circuit analysis techniques that we used with DC. We also did a Phasors: Passive RL Circuit Response Lab.

Above we used NODAL ANALYSIS and converted circuit components to phasors and solved for node voltages.

Here we used MESH ANALYSIS to solve for mesh currents on an ac circuit.

Phasors: Passive RL Circuit Response Lab:
the objective for this lab is to measure the gain and phase response of a passive RL circuit and compare with theoretical values. We will only be concerned with the steady-state response.

Above is our circuit layout where we will measure input and outpout voltages.

Above we have an input sin wave of 2V and 10kHz in blue and output wave in orange.

Above we have an input sin wave of 2V and 20kHz in blue and output wave in orange.

Above we have our theoretical values and our measured values. On measured data, gain is calculated by Vo/Vi and phase angle by deltaT/T*360.

Above we use SOURCE TRANSFORMATION on the left side and on the right we use THEVENIN EQUIVALENCE on the right using phasors.

Day 18 (Day20 on notes)

Today we went over sinusoidal graphs that are represented as phasors, phasor math, and related phasors to solve ac circuits.

Above are components and relationships of sinusoidal graphs and some trigonometric identities.

Above we add too sin functions using the trig identities and then graph individual phasors.

On the right side of the picture we have the rectangular, polar, and exponential form that a sin can be written as and operations (phase angle operations are wrong, check below). The left side is an example using those operations.

The correct operation equations.

Above we practice the multiplication operations of phasors.

More examples of operations and converting to different coordinate systems.

Here we have an example where we use phasors to find current in the frequency domain.


Here are the relationships and how phasors for components(L,C) compare to R.

Day 17 (Day19 on notes)

Today we learned about second order systems in parallel and did a RLC Circuit Response Lab.

Above is an example of a RLC circuit in circuit as review for what we did in day 16.

Above is an example of a RLC circuit in parallel. It should be noted that the equation for alpha changed and the rest is the same -> alpha=1/(2RC).

RLC Circuit Response Lab:
the purpose of this lab is to model and test a RLC circuit in parallel. On our pre-lab, we calculated values for omega and alpha and found that our circuit will be underdamped. We will be comparing these theoretical values with measured values. A 2V 500Hz square wave will be the voltage input.

Above is a picture of our circuit.


Above we have the output voltage were we can see that our circuit is very close to a criticllydamped curve which, based on our alpha and omega values, seems unreasonable.

We attempted to do a manually curve fit (not great) to find alpha, then used the period of the graph to find omega. As we can see we have a huge percent error which indicates something in our circuit is not working properly. We made sure to include actual measured resistances in the circuit for our theoretical circuit but did not change much. After much tinkering, we believe some faulty component was causing our circuit to behave differently than we predicted.

Day 16 (Day18 on notes)

Today we learned about second order systems - RLC series circuits and performed a Series RLC Circuit Step Response Lab.

Above we have a RLC circuit in series and derived a characteristic equation based on the second order differential. 

We then let alpha=R/(2L) and omega=sqrt( 1/(LC) ) from our characteristic equation. Based on these individual values, we can determine the response of the RLC series circuit as shown in the bottom of the picture.

Here is a small summary of the equations for the overdamped, critically damped, and underdamped responses along with graphs.

Above we worked on a series RLC example.

Series RLC Circuit Step Response Lab:
The purpose of this lab is to

We had to build a RLC circuit with the values listed above and measure its voltage across the capacitor when a 500Hz 2V square wave for input voltage. We see that our circuit will be underdamped.
On the bottom we had to find a value for C that would make our circuit critically damped but we didn't have components in class to do so.

Above is our circuit.

In the fist picture we have our input voltage and the second picture is the output voltage.

With an exponential curve fit, we get V(t)=0.43*exp(-2340t). This was done manually so we are unsure if the curve fit was done correctly which would explain why our alpha is significantly smaller than our theoretical value.

Day 11

Today we went over inverting, non-inverting, summing, and difference amplifiers. Also, we did labs on summing and difference amplifiers.

Here we took a look at the effect of waves when saturation in the amplifiers occurs. We found a saturation voltage output of around 4.2V and -3.5V with the op amps used in class.

Above is an example problem of an inverting amplifier where we used nodal analysis to find Vo.

Above is a derivation to find Vo on a non-inverting amplifier in terms of Vi, Rf and Ri.

Summing Amplifier Lab:

The purpose of this was to compare measured output voltages with theoretical output voltages.

For our pre-lab, we were to find a ratio of resistance values Rf/Ri such that we wont reach saturation voltages. We picked 6.8kOhms for Ri and 3.9kOhms for Rf (Ri=R1=R2 and Rf=R3). The equation left of our table is the equation that was derived for Vo.

Above is our circuit set up. Unfortunately we did not take a picture with the waveform generators wires hooked up.

Based on our results, we can say that our derivation to determine the output voltage is goo since most of the voltages were at a small percent error. We believe any error in are measurements is due to treating the op amp as ideal and resistors to have exact resistances throughout the experiment.

The purpose of the Difference Op Amp Lab is to compare theoretical output voltages with measured values.

 
Is the result of the derivation for output voltage on a difference amplifier in terms of input voltages and the four resistors. But when all resistors are equal to each other, the the output voltage is just Vo=V2-V1. We will be testing this case in our lab. 

Above is a picture of our circuit and measurements made for the lab.