Day 22 Sinusoidal Circuit Analysisc

We started the day with a picture of a mouse eating a cheese, cat eating the mouse, and a dog eating the cat. This was done to help us understand analyzing an AC circuit takes steps. We talked about three  in particular:

1.  Transform the circuit to the phasor or frequency domain.

2.  Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, etc.).

3.  Transform the resulting phasor to the time domain.

We were asked to use our brain and try to remember the techniques learned and which ones we used to analyze the circuit. White board picture below.

 

White board work of what type of techniques we have used in the pass and can be used in AC circuits.

After discussing that we were asked to try an example that would show case a good question to use node analysis.

White board work of node technique at node 1.

White board work continued for node 2.

White board work continued we changed everything to the phasor domain,

We then move onto another example that would show case a good example to use mesh analysis.

White board work, we used mesh analysis but first we need to transfer to phasor domain.

We then move onto the lab of the day: Phasors, Passive RL Circuit Respond
Prelab: White board work has most of the pre lab
The cut of freq = R/L = 47/1e-3 = 47khz
partd) WE found our low and high frequency agree with our prelab numbers. The divide by 10 cut-o0f showed no result and regular had the best Vout, and the times 10 cutoff showed no results as well, so our circuit behaved as we thought it should.

White board work for prelab, only left side, this one is for the cut-off freq by 10. It has gain of .0214 and phi = 5.7. Our experimental for gain is 2.35 and for phi = .6912.

d

White board work of prelab for the regular frequency, gain = 11.35 and phi = 0.09. This match our prediction that we should have the highest gain here.

White board work of the 10 times of the cut-off frequency, gain = 0 and phi = 170. Again we found our prediction in the prelab match our experimental.

Picture of the signals to follow our prelab. Freq = 7.48khz so, cut-off/10 low freq.

Picture of the signal source blue,, voltage across the inductor is yellow, and the red is current of the circuit done by the match channel.

More picture data of the source above.

Picture of the data from the source. Vin = 1.26 V, Vout = 111 mV, M1 = 26mA, freq = 7.48 khz, period 134 us.

Another picture of the data, clearer!

Picture of the signals to follow our prelab. Freq = 748 hz so, corner freq.

Picture of signal at 748hz, blue is signal in, V over inductor, red is current.

Another picture Clearer! Same as above.

Picture of the data of the signal above. Vin = 187 mV, Vout = 80 mV, M1 = 4.8 mA, Freq - 748 hz.

Picture of the circuit used. Real life.

Picture of the inductor at work!

Picture of the signals to follow our prelab. Freq = 75 khz so, cut-off freq*10, so high freq.

Picutre of the signal very clear! Blue is Vin, yellow is voltage across the inductor which is zero beacuse inductor doesnt do well if handling such high frequency, and in turn M1 the current is zero as well, cause the inductor is trying to catch up so fast nothing happens.

More picture of data of the 75 khz. Vin = 2 V, Vout = 16 mV, M1 = 43 mA, freq = 75 khz, T = 13 us.

Another picture for data and signal looking.

Another picture looks pretty to me.

No post lab but I will say this was a fun circuit to build and an easy way of seeing how omega affects the out voltage and period. Our numbers look funny but I blame Jon for not doing the math and letting me and Edgar do it.

We then move onto talking about superposition theorem and how useful it can be in AC, since AC can have circuits with power sources with different omegas.
 We move onto doing an example.

White board work of an example of using super position.

We then move onto the source transformation. We talked about how V = ZI and I = V/Z, thus it allwos for source transformation. We then move onto an example to try.

White board work of source transformation. Vs in series, Is in parallel.

Lastly we move onto Thevenin and Norton equivalent circuits. Vth = Zn*In and Zth = Zn. Vth = open circuit voltage and In - short circuit current. We tried an example on the white board.

White board work of a Thevenin example, we convert to phasor domain and Z impedance and then use mesh analysis and node voltage.

In summary we start the day with a beautiful picture of a not so dogging eat dogging world but one where steps are needed for analysis AC circuit. Pretty much use everything you learned and turn into phasor domain. We then did a fun lab on a passive RL circuit, and found how omega, omega times 10 and omega/10 affect a circuit. We found that our prediction were right that when the omega is far from the sweet zone there is no Vout. Lastly we talked about and did some superposition, source transformation and thevenin example. Things to note is that superposition is the only way to handle different omega source, and thevenin is as powerful as it was before. And we left with the feeling that it is a dogging eat dogging world and it is a dog name E44.