04/05/2016

04/05/2016: Phase Shift and Continue with Op Ams

I. Introduction:

Today, we started out with a simple graph of sinusoidal wave. The question is how would the function change if shift the graph to stay totally positive. We spent part of our time to do some op am circuit, including the inverting, non-inverting, summing, and difference.

First, I wrote down the general equation. I missed the sin there so it should be Asin(kx+wt). The second graph is exactly the first one except its amplitude is 25 and it shifts up 2.5 unit.

Next, we were given a simple op am circuit, Professor Mason to find the ratio between Vout/Vin, in this case, we have inverting op am circuit, therefore, the ratio would be R2/R1=-3

Here we were given another inverting op am circuit. Since Vs is connected to the ground, the voltage of the negative input would be equal to the Vs=0. Using nodal analysis, the would be able to find the Va and Vo. Vo is always greater than or equal to Vin for the inverting op ams

Here is the formula for non-inverting op am cicruit, we have V1=V2=Vi, using that application, we simplified it to Vo/Vi=1+Rf/Ri

Here is the formula for the summing amplifier circuit, Notice that as we add more branch of voltage, we simply need to add up more terms into the formula

II. Experiment with the inverting and summing amplifier op am circuit:

The op am circuit here is actually the combination of the summing amplifier and inverting op am circuit. Notice that the input is given the summing amplifier and the output is given by the inverting op am circuit.

Here is our set up for this lab, next time we should utilize more short wire to make it easier to debug. A good matching color with the analog discovery is also a good practice to follow

Here is our result, notice that since  we have inverting op am circuit, the output would be the opposite sign of the input we choose R1=R2 to simplify our work

For this problem, the output is more complicated than we thought. It was actually one of the mastering engineering homework assigned on that day. R4/R3 due to the fact that

Here we were given a difference amplifying circuit. By applying the nodal analysis, we actually be able to find the gain of 30.33

V. Summary:
For today lab, we spent most of the time understanding more about three more types of op ams: non-inverting, summing amplifier, and difference. With the nodal analysis approach, we were able to derive formula for all those types of ams. We also spent some of our time do the summing amplifier lab at the end to verify that our derivation is correct