D 12 - Capacitors and Inductors

We started the day with a discussion of why sometimes there is a spark when we plug stuff in, turns out to be because of capacitors and having mechanical engineers design electric circuits.

White Board work of why and how Capcitors charge. It is a function of A and d. Area and distance.

We then were asked to design our own version of a variable capacitor.

White Board work of our variable capacitors. Mine is on top with a triangle screw to close d, and Jon's is on the right with a squeezer on top to change d.

We then move onto solving for the energy in a capacitor, with P = VI and taking the integral. E = 1/2CV^2

White Board work for finding E. E = 1/2CV^2

We then drew the change of current over time. It is important to understand that the slope is what define the integral. Constants turn into linear and linear turns into parabolic.

White Board work of I versus t and we use the slope for the V versus t graph.

White Board work of V versus t took integrals of I.

We move onto an example of a DC capacitor circuit.

White Board work of the DC circuit, we turn capacitors to "open" and find Req.

More White Board work,  we found Va = 4 , Vb = 8V, then found E1 = 0.016 J and E2 = 0.128 J.

We then moved onto the lab of the day:
Capacitors Voltage-current Relations
Prelab:
We then sketch the "phase" shift the capacitors causes.

White Board work of the sketches of graphs for the capacitors. Sine wave. The shift is pi/2.

More White board work of the sketches with square waves and saw tooth wave. This also has the pi/2 shift. from I to V.

Picture of the capacitor circuit below.

Picture of our capacitor circuit.

More white board work with the equations used for Ir and Ic.

Picture of the signals before capacitor and after on the resistor.

Picture of the sine-wave going through the capacitor.

Picture of the freq 1khz period of 1ms and amp of 114 mV the M1 math value is 77uV,  C2 amp is 2 V freq of 1khz and period of 1ms.

Picture of the second sinewave input at 2 khz.

Picture of  C1 freq 2khz period 200us amplitude 218mV, and C2 amp 1.98V freq 2khz period 500us with M1 math value being 76uV.

Picture of the square wave being fed into capacitor.

Picutre of square wave, C1 amp 18 V freq 100 hz period 10ms, C2 amp 2.7 V freq 100 Hz period 9.99 ms M1 math value of 75 uV.

More sketch for the prelab for the sine wave, triangle wave and square wave expected outputs.

White board for prelab expectations of the output across the resistor. Our expected results matched the output graphs from the oscilloscopes taken for each one.

We then move onto how capacitors work in series and parallel. We did an example with capacitors below.

White Board work of capacitors in series and parallel, series you C1C2/(C1+C2), parallel add C1+C2.

More White Board work, with talked about how finding C and finding L.

Lastly we talked about how Inductor are like everything like a capacitor but different. Like for adding in series and parallel they the opposite. After 10 minuets of inductor knowledge can be summed on the white board picture below.

White Board knowledge of summarizing Capacitors and Inductors, same thing but different.

In summary we learned how capacitors charge up and how find the energy stored in a capacitor by using E = 1/2CV^2. Learned that capacitors in a DC setting act like an open. Did a lab on capacitors and found the phase shift of pi/2. Talked about inductors how they relate to capacitors. We found our expected graphs matched the output on the oscilloscopes. We then finished the class with an example of capacitors in series and parallel. In series C1C2/(C1+C2) and parallel C1+C2. Lastly we said inductors behave opposite of capacitors and made a white board with all the difference on it.

D11 - Op Amps 2

We started the day with talking about unity gain buffers were Vin = Vout. And then moved onto an Inverting Amplifier with a square wave being input to it. We drew our predicted sketch of Vout.

White Board work of showing the amplification of the Op amp signal, note how the second graph raises above zero.

White Board work on the Inverting Op amp with a sqaure wave. Vout = -Rf/Rin*Vin. If -Vcc is tied to ground no voltage output below zero will be shown.

We then move onto an example of an ideal Inverting Op Amp. Vs = 0

White Board work, we used Node Voltage on the negative node of the Op amp.

More White Board work, we found Vo in terms of Va and plugged it into the other Node b and got Vout = -3.27 V.

We then move onto the Non-Inverting Op amp. We discussed its properties and came out with the formula Vout = (1+Rf/R1)*Vin.

White Board work of getting the formula for a Non-Inverting Op Amp.

We further talked about a summing amplifier and showed that -Vout = Rf/R1*V1 + all the to other input resistance under Rf * there respected V's.

White Board work of coming to the conclusion of -Vout = V1 + V2 + V3 if all the resistors are the same in a summing amplifier.

We then move onto the lab:
Summing Amplifier.
PreLab:
Va and Vb should see input of at least R1 and R2 being 1 k ohms.

Picture of our summing amplifier circuit.

Pre lab White Board work. R1 = 5.8 k, R2 = 5.8k k, and R3 = 4.8 k and Vb = 1 V.

White board Data, ranging Va from -4 V to 5 V. Vout responded with 2.44 V to -3.45 V, respectively.

We then move onto a Difference Amplifier. The difference amplifier amplifies the difference between two inputs and rejects any signal common to the two inputs. We were asked to sketch some graphs.

White board work of the sketch required of class, not sure of what? Difference amplifiers?

Anyways, we then asked to an problem with designing a difference amplifier with gain of 2 and common mode of input resistance of 10 k ohms at each input.

White Board work, circuit schematic of difference amplifier and used Vo = R2/R1(V2-V1). We found R needed to be 20 k ohms.

We then move onto more examples of difference amplifiers.

White board work of a square wave being fed into the difference amplifier.

More White Board work, right side of the same problem, we used Node voltage Va and Vb found Va = Vb and then got Vout = 1/3 Vin.

In summary we talked about many types of Op Amps starting with unity buffers which just output Vin,  Inverting Op amps which invert and amplify the input, and Non-Inverting Op Amps, which amplify the input and lastly Difference Op Amp which amplify the difference of the inputs. We did a lab for the Summing amplifiers which take each input resistance under Rf and times it with their respected V and sums them together. And finished the class with examples of difference amplifiers which was suppose to be another lab but did not do, however our white board work showed the important relationship of r1/r2 = r3/r4 is in the difference amplifier.

D10 - Op Amps 1

We started class with OP Amps. Op amps behave like a voltage controlled voltage source. Op amps come in packages. The DIP type is the one we work with with the number going 1 to 8 counter clockwise. We were asked to draw the difference in a open and close loop Op amp.

White Board work showing our interpretation of open loop and close loop Op amps.

We then move onto an example of an inverting Op amp. We were asked to find the gain when Vs = 2 V.

White Board work, First we drew the equivalent circuit and then used gain  = Vout/Vs.

Matlab work of the White Board example. Used node voltage and matrix math. Gain came out to be -2

More White board work, that was used in Matlab.

We then tried another example. To find gain, Io and Vs = 1 V.

White Board work, drew equilavent circuit, and used node voltage.

Matlab work of the White Board work.

We then moved onto the lab of the day:
Inverting Voltage Amplifier

Pre lab schematic of the lab. And was also used for the last part of the day.

Picture of the Op amp. R being 1k each.

Voltage data from -3v to 4v note that points when its sat after 2 V.

Matlab Work of the lab. We find the linear region, note the point after 2 volts the Op amps starts to saturates. Also note that it starts negative since it is an inverting Op amp.

More MatLab work done, intputting date for the graphs used,

More Matlab work this one shows the values of the resisters and v outs.

Extra white board work to show a better picture but turned out crappy.

In summary of our class today was focuses on the OP amp and how useful this piece of technologist change the world. We end the class with another Ideal Op example and to find Vo/Vs is just to use the formula Vout = -R2/R1*vs so with a little algebra Vo/Vs  = R2/R1 for an inverting amplifier.

D9 - MAX Power Applications Source Modeling

We started the day with talking about power and how gasoline production has increase over the years. We started with maximum power transfer to a load. And was ask to use the formula P = i^2Rload. We draw the graphs Power versus resistance.

The use of max power transfer when Rth = Rload.

White Board work of getting the formula result for Rth = Rload

We then also came to the conclusion of Pmax = Vth^2/4Rth, only when Rload = Rth.
Afterwards We were asked to do an example.

White boar work to find Rth

White Board work, Rth was found out to be 12 and then found out max powers with different Rload's. Max is achieved when RL 12 is the same as Rth which is 12.

We then moved on to a motor example showing how the motors can get max power.

White Board work of the motors each one being in parallel.

More Whit Board work with us finding Rth = 0.052 ohms.

Last bit of White Board work, we used the V^2/4Rth since RL is = Rth.  Answer is 5.8A hours.

We then movd on to another max power transfer example.

White Board work, we remove the Rload and found Req = 9 ohms.

More White Board work with Vth = 22 Volts and getting isc = be 22/9 or 2.4 A.

After our last class example we moved onto the lab.
Maximum Power Transfer:

Picture of our ciruit with a Pot and Rload.

White Board work, R = 4.64K ohms. Diagram of circuit at top and Vout data at the bottom.

Picture of graphing Power and Resistance. Note the max when Rload = Rth.

Right side of the Graph of Power versus Resistance.

More data used, from R being 1k to 10 k, max power is when Rload is = Rth of 4.64 k ohms. 

 

We then finished the class with talking about source modeling and how a DMM Galvanometer read current and resistance. Lastly we did an example to find out Vout.

White Board work to find Vout = 12.29 Volts across terminals a,b.

In summary we learned about how and why maximum power transfer if done when Rth = Rload. We talked about the steps needed to find Req and then did a lab on maximum power transfer. We showed that with the measurements that when Rth = Rload the graph was at it's peak. Lastly we finished the class with talking about source modeling and how DMM's and Galvanometer take readings. We finished the class with last example of finding Vout in a circuit.