Day 23 AC Op Amps and Oscillators

We started the day with another picture this time of an OP amp buffing it up. This was a way to introduce us to steps to analyze AC circuits the steps are:

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.

The key to analyzing op amp circuits is to keep two important properties of an ideal op amp in mind:

1. No current enters either of its input terminals.

2. The voltage across its input terminals is zero.

 
We started with an example to work out. White board work below.

White board work, first step is to transform into the phasor domain.

White board work continued, we then move onto node analysis of the op amp. Then back to time domain.

Later we talked how hard it is to find omega with a omega is never given.

Picture of the algebra need to find omega.

Our attempt of the algebra below.

White board work continued after a lot of algebra omega an RC cancel out and it turns out gain  =3, which allows for Vout/V2 = 1 + Rf/Rg = 3, Rf = 2Rg, limited to under 1Mhz..

We then move onto the lab of the day: Inverting Voltage Amplifier we Skipped! but did something else.... like..:
                                        OP AMP RELAXATION OSCILLATOR

Picture of the Relaxation Oscillator, we followed this diagram but with our numbers for freq of 847.

We set up the circuit in every-circuit to test it. We got close to 876 hz.

Picture of the circuit at 876 hz.

We were offended being off be 20 hz, and so we decided to try again and get it to 848. Close enough.

Picture of a much closer frequency of 848 hz, only off by one hz.

After getting it to work in every-circuit we move onto real life. But first we drew it on the white board. We used T = 2RC*ln abs(1+b)/(1-b). We need to find a R value to get our frequency to 847 hz. We found R to equal 537 ohms.

White board work for the prelab and other stuff.

White board work continued, another picture useful I think it is.

Another picture to show our frustrations of it not working yet...

Picture of our circuit neatly wired and presentable, thanks to Edgar as always!

Picture of the signal out put. And the frequency is...

Picture of the frequency, is 823 hz. Is it close enough?

Yes, because the value of R we got close to was 545 ohms, so in theory that is the frequency we got is perfect!

White board work, but we accept reality.

Finale picture.

After the fun lab we talked about instantaneous and average power. P = VI. S = VI conjugate. We then move onto the subject of maximum average power transfer. Rload = Rth. Xload = -Xth. Which leads to Pmax = Vth^2/(8Rth). We then tried an example below.

White board work for Power. Transform to phasor, do parallel, and then add up the Z's and then take the Zload = Z conjugate.

 

In summary we started the day with talking about op amps, and to dissect them with phasor components and use the knowledge we have to get the information we want. We do node analysis and remember no current enters the inputs, and voltage across its input terminal is zero. We then did an oscillation circuit to be biased to a frequency, of 847 hz. Lastly close the day with talking about power and max average power is when Rload = Rth and then Xload = -Xth.

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.

Day 21 Sinusoidal Analysisc

We started the day with talking about impedance and admittance. V = ZI, V/I = jwL, V/I = 1/jwC.
We then wrote it down on the white board.

White board work of finding Z. Z = R + jX

We then move onto an example to do.

White board work we used 10 cos4t. First we found the phasor domain of the circuit. and then used i = vs/Z

White board continued. i = Vs/Zc and Vc = IZc.

White board work we had to multiply top and bottom with the conjugate of bottom to get the numbers right.

We then move onto another example.

White board work, used Zc = 1/jwC, -j = -90 degrees.

We then move onto the lab of the day: Impedance
Prelab: White board work of the prelab for phasor for each Vr and V(t). Plus other information.

White board work of the prelab.

White board work of pre lab with circuits drawn and values.

White board work of more prelab and other stuff.

Following pictures of the lab, data and white board at the end.

Picture of the signals with data at bottom. period is 1ms. Vin 1.5V, Vout .5 V.

Picture of data for 1khz signal, Vin = 1.37, Vout = 600 mV. Period  = 1ms.

Clearer picture of the one above.

Clear picture with R = 100 ohms, same data as above.

Clear picture then before same data for 1khz signal. Period 100 us.

Picture of Vin and Vout for 1khz, R = 100.

Picture for 10 khz.

Picture of data at 10 khz, Vin = 1.3V Vout = 570 mV. Period = 100us

Picture with capacitor at 1khz.

Picture with capacitor added C1 = .47uf

Picture same as above for data.

Picture of data at 1khz for Capacitor. Vin = 1.5V Vout = 535 mV. Period 1ms.

Picture at 5kz for C1.

Picture of the signals for 5 khz capacitor. Period 1.6 ms.

Picture of data same signal as above.

Picture of data at 5khz capacitor. Vin  = 1.45 V, Vout = 156 mV. Period is 200 us.

Picture of capacitor at 10khz.

Picture of signal at 10khz for capacitor.

Picture of data of same signal as above.

Picture of data of signal at 10khz for capacitor. Vin = 1.5 V, Vout = 116 mV. Period 100 us.

Picture of 1khz inductor. L = 1m H.

Picture of signal of 1khz inductor.

Picture of data same picture as above.

Picture of data of 1khz inductor. Vin = 1.5 V, Vout = 250 mV. Period = 1 ms.

Picture of 5khz inductor.

Picture of 5khz signal of the inductor.

Picture of data same as above.

Picture of data for 5khz signal of inductor. Vin = 1.4 V, Vout  = 927 mV. Period 200 us.

Picture of 10khz of inductor.

Picture of the 10khz signal for inductor.

Picture of data same as above.

Picture of data for 10khz inductor. Vin  = 1.4 V, Vout = 1 V. Period 100us

Picture of the inductor circuit.

Picture of the inductor circuit. Edgar does great wiring.

White board work of post lab stuff and calculations.

White board work of post lab work and calculations.

More post lab white board work.

White board work continued for lab.

Octave work that Jon did for us. Fancy and efficient work!

Picture of the Octav work for the three circuits with having in order R = 100, and then current and then Voltage. This would be our tabulate for post lab.

In conclusion of the lab we saw the Vout differ for each different frequencies. The period also change with frequency. Depending on the type of circuit for the Capacitor circuit the change of frequency cause the voltage to drop for each increase of frequency and the period to change to 100, 200, and back 100 us for 1k, 5k, and 10khz respectively. For the Inductor circuit the change of frequency case the voltage to increase and the period to change to drop from 1ms, 200us to 100us for each change respectively. The calculations were done by Jon and all are correct.

Lastly we did example of combining Z impedance.
We worked an example.

White board work of example. First transform everything to phasor domain. Do parallel Zc||Zl and then add R. Then voltage division. Lastly back to time domain.

White board work of changing to phasor domain and back to time domain.

Lastly we talked about phase shifters.

White board work of the example.

In summary we started the day with impedance. We had examples of how to change capacitors and inductors to the phasor domain. We then did a long lab for three frequency and see how the R,L,C circuits behave with different frequency. We learned that for C circuits frequency increase caused Vout to drop and the inverse is true for L circuits. For R it didn't matter. Lastly we talked about phase shifter and how they can be useful.