Day 19

the first problem of the day was a real stumper, Although it looks like the work we did was on the right track I'm not sure why the equations have been crossed out. We found out the total impedance  then multiplied it by the given current to get the voltage. 

WE are introduced to a lab that finds the impedance of the circuit at the top with either a resistor, inductor, or capacitor in series. We also found the admitance and the phase shft.

We updated the values for the inductor as we did the calculation wrong.

Then we did an example with all three n one circuit and then we found the current running through it.

Day 18

My first introduction to AC circuits. Here we are learning to translate between a time constant and phasor state for voltage.

Some simple equations that ae implemented all the time. We change to phasor to make the multiplication easy and than convert back to the time domain.

Here we are continuing to add everything together, here we split up the time domain to a complex rectangular for and then adding the 3 components together then converting back. 

Introducing lagging and leading concepts as well as calculating voltage using impedence of a cicuit element. we also introduce snittler the company logo and name.

'

Just doing another example, you think that we'd get the hang of it after covering the same stuff the entire day.

Day 17

Today we continue second order circuits. The question above is an example to help us get back into the groove of things. We are trying to find athe current and the voltage and the answer got cut off from the picture in the end. although the answers ended up being 20V and 0A.

Now we moved on to parallel step response circuits. here's an example but the really important parts have to do with whether the system is overdamped underdamped or critically damped. depending on the dampness we use different equations. These ones:

Here we are doing a lab with parallel step response that we first modeled in every circuit. This way we dont have to do any calculations to get some predictions for the circuit that we made. You can see the little damping that occrs at the top and bottom peaks.

Here's the output that we got on waveform, there's a bit of noise but the same damping that was observed in every circuit.

Here's the circuit that we created on the bread board. We are measuring current over one of the resistors.

Here we still did the calculation to predict what the current outcome should be. We got 41.6mA.

So after we got the current we have this loooong algebraic or maybe calculus equation to get voltage.

Day 16

Today was an interesting day. I moved from table to table giving aid to those who had no one but themselves until my group arrived and I abandoned the others. Hence the song that is my answer to this question. I cant remember what this question pertains to, it seems simple enough just finding the voltage across a resistor by finding the current going through it and then multiplying by the resistance.

Here  we treat the same circuit as above but are replacing the resistor with an inductor and a capacitor.
We use KVL to solve for something I'm misremembering here and I cant really read the writing on the board, the subscripts any way. It would seem that we are trying to find the voltage across the capacitor

Here's basically the equations need for the second order circuits. I was trying to work around a mnemonic device with all the variables though I'm not sure it helps.

We created our own damping circuit, the point was to make something that would level out a signal.

Here's the plot of our results, and Javier's face. We can see that the current gets dampened as soon as the experiment starts. The oscillation continues until the voltage reaches zero.

this is the differential equation we got from the lab. you can see the the progress of the derivation.

These are the equations and values that were required for the blog( this very one) from the lab that we did. As you can see the values are rated a thumbs up.

Day 15

Lab 19: Inverting Differentiator

In this lab, we explored another mathematical operation that can be performed by op amps; differentiation. Essentially, you can set up the op amp as an inverting amplifier, but replace input resistor with a capacitor. Essentially, if you feed a time-varying signal into the differentiator, it will output the derivative of the signal function with respect to time.

We used a 1.0 uF capacitor, and were instructed to choose a resistor that would give us a gain of -1. Since gain = -RC, we initially chose R to be 1.0 MOhm, but for some reason the op amp would saturate, so we kept swapping it for lower and lower resistors until we achieved a circuit that did not saturate. We also had to turn down the input voltage, but eventually we found that a 1 kOhm resistor and a 100 mV supply did the trick. The circuit, as well as the WaveForms oscilloscope, are pictured below:

Actual Resistor and Capacitor values

Photo of the actual circuit

Sinusoidal wave being fed into the circuit. f = 1 kHz, V = 100 mV

Yellow = Input Voltage, Blue = Output Voltage

f = 1 kHz

 f = 2 kHz

f = 500 Hz

In Class Examples

1. Sketch the input and output waveforms for 1kHz sine wave, triangle wave, and square wave inputs.

2. Given vC(t) = [5 u(t) +6 r(t)] V, find iC(t) for the circuit shown.

3. Find the step response v(t) and i(t) to vs = 5u(t)V in the circuit below:

4. Example: Find v0(t) for t>0 in the circuit below.

I am literally just taking this blog from someone else, I wasn't here for this class so I feel that my experiences of the day would not be beneficial to the contribution of this blog so someone elses' will have o do.

Day 14

Here's the summary table for the RLC circuits, as one can see the capacitors and inductors are almost mirrored and the resistors are the normal equations that we have been using since the beginning of the semester.

After this little review ( something to catch up on the inductors as it was hardly covered the class before)  we moved on to first order equations, these become involved when switches are used. It starts from adding the currents across an capacitor and a resistor then integrating to find the voltage across the capacitor. after word we get the equation v(t)= V_0 *e^(-t/RC) and then we let tau be equivalent to RC and replace it in the equation. The current across an inductor is found the same way with the current being : i(t)=I_0 *e^(-tR/L) and tau represented by L/R. from both we can use V=IR to find out any missing values by either multiplying by the resistance or dividing.

This picture demonstrates the values of the calculated portion of the lab including the initial and degrading current as well as the time constant tau. The top right shows a represntatin of the circuit that has been built below.

Here we did a lab with an inductor showing the charge and then discharge. instead of a switch the power was simply turned off. Using waveform we measured the voltage across the inductor. 

This video shows the graphical out put represent by having power supplied to the circuit and then removed. we can see the clear voltage drop after the power is removed in the inductor and when it is supplied there is a bit of degrading slope as the induct gets charged and discharged.

Day 13

Our design to create a variable Capacitor. as the plates come closer together the capacitance raises.

This is a basic overview of capacitors that most should remember from physics 4b as well as some circuit syntax.

 Here are some equations of note to use when considering capacitors, power , and energy held in them, however there is very little use in this information concerning this class.

These are the graphs of voltage and current over time for a capacitor, or at least a rough estimation of it.

as Capacitors reach capacitance they act like open circuits so we write them as such and then we can solve for the voltage across them and after tat we can find the energy stored in them.

Here we are running these graphs of voltage across a simple rc circuit and hoping to produce the currents on the left.

 Here's a video of Mason blowing up a capacitor by running current in the wrong direction. or some of it, the video was rather long so it might not be there.

THis is an overview of the day by introducing the differences between capacitors and inductors, This is perhaps the most important picture of the day as all the equations that will be used on the home work and celebration.