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.