The PreFinal Op-Amp Jamboree

Objective: We conststructed 4 different op amp circuits from which we had encountered during the class. The first was the voltage follower with the added twist of a 10 Mega-ohm resistor in line with the voltage input. Second we constructed an inverting op amp. Third we put together a non inverting op amp. Lastly we made a summation circuit. for simplicity's sake I choose to use resistors as close to 6.6k as I could find.

The Voltage Follower

       Here we can see what is to be expected. In order for the voltage difference between the positive and negative terminal to be approximately zero the negative terminal is also the 2 volts. The V out tied, via a short, to the negative terminal means it is also a 2 volts and thus we achieve the voltage follower. 

       I also applied a DC source to the circuit so it would be easier to tell that the circuit was working. I did this one without the larger resistor in line of the voltage.

       When you add in the larger resistor you don't actually follow the voltage you are putting into the system because you have created a voltage divider in front of what you actually want to do. It is also important where you put the resistor. If you place it in line with the output voltage you end up swamping the system because that side has a tiny resistance. the resistor between the positive and negative terminal is actually much larger. 

The Inverting Op Amp

      Starting with the current passing through the resistor, we know the voltage at the positive terminal must be zero since the negative terminal is tied to the ground. The second condition of an ideal op amp means no current can enter either positive or negative terminals. This allows us to equate the current towards the op amp ((v in - 0)/r1) to be equal to the current leaving the op amp, (0-Vo)/Rf. solving for Vo is where end up with the formula of Vin(-Rf/R1).

Inverting Op-Amp
Theory
Rf	6.68E+03
R1	6.71E+03
Vi	2.00
V0	-1.99
Measured
Vi	2.50
V0	-2.50

The Non-Inverting Op Amp

       Here we do a little shuffle with the voltages. A source is applied to the positive, to keep a current from entering the terminal the negative value has to also the the same as the applied voltage. We can then equate the voltage flowing from the negative terminal to ground, (Vin/R1)  and a voltage from the Vo terminal to the junction, (Vo-Vi)/rf. We rearrange the terms, solving for Vo. What we get is the term Vo = Vi(1-Rf/R1) 

Non-Inverting Op-Amp
Theory
Rf	6.60E+02
R1	6.68E+03
Vi	2.00
V0	1.80
Measured
Vi	2.00
V0	1.80

The Summation Circuit

       Here we have a very similar situation to the inverting op amp. Tying the negative input to ground places a zero voltage node between the two input voltage and the output voltage. We can use the same strategy of equating the currents into and out of the node. The two input currents are V1/R1 and V2/R2. The output current is (0-Vo)/Rf. Solving for Vo yields, Vo = -Rf*(V1/R1 +V2/R2). 

Summation
Theory
R1	6.62E+03
R2	6.63E+03
Rf	6.66E+03
V1	2
V2	2
V(out)	-4.02
Measured
V1	2.06
V2	2.07
V(out)	-4.27

       At first, I had some problems getting this circuit to act properly but once I changed from the 4 in one op amp to the single op amp there was nothing to it. I choose values to get me as close to a straight summation as possible.