Part 1: Op amp (cont.)
Today we continue to study some different op amp circuit.
Sinusoidal graph transformation. From the original f(t) voltage source, assuming that it goes through the op amp to shift its values above. There are two ways of shifting the graph: plus then add, or add then plus.Both ways have the same result. Two characteristics of the op amp that help to build this kind of circuit are the gain between the output and the input voltages, the limitation of the power supply voltage on the output voltage. The first process to create the desired graph is let the Vin go through the op amp with gain 25, then place the 25 DC voltage in series with the output voltage. The second process is we use summing amplifier to create the voltage Vout = A(V(in1) +V(in2)).
This is inverting op amp. Assuming the op amp is ideal with vp=vn and ip=in=0. From the circuit we have vp=0, then vn=0. We use the nodal analysis at vn, [v(in)-0]/Rs +[v(out)-0]/Rf = 0=> v(out)=(-Rf/Rs) *v(in). This formula also express the inverting characteristic of op amp with negative gain. From the formula and the limitation of the power supply on the output voltage, we deduce the output voltage as the picture describes: being inverted, and above the horizontal axis.
This is a different amplifier.
Non-inverting op amp. We derive the relationship between the V(out) and V(in) as
V(out)=[-(Rs+Rf)/Rf] * V(in) = -(1+Rs/Rf)*V(in). Rf<<Rs => Vout =Vin. Vout is always equal or greater than V(in) for the non-inverting op amp.
The unity gain buffer amplifier is to create the independence in the circuit, The output voltage equals to the input voltage but has a larger current because of the power supply.
Purpose: The lab aims to give students the ideal how a summing amplifier works, and verify the theory of the summing amplifier
A summing amplifier. Like the name of the op amp setup, the output voltage is the summing of the input voltage with appropriate constant. We notice the two create the summing amplifier the input voltages have to go into the same input terminal, in this case is the inverting input. Using the nodal analysis at inverting input, we retrieve the relationship between the output voltage and three input voltages, or more.
We do the pre-lab for a summing amplifier. The requirement is to create the output voltages were not saturated at all. From the general summing amplifier formula, we should choose R1=R2 to let the math more easily. Because we do not want to see the saturation, we choose R3 less than R1=R2. With the nodal analysis at inverting input and ideal op amp assumption, we deduce the formula,
V(out)=[-R3/R1]*(Va+Vb)
Vb is always 1V; we adjust Va to get the output voltage. The record is in the table. We get acceptable data, which meets our expectation and deduction.
Our experimental set-up
After the lab, the professor talk little bit about organized breadboard set-up. We should avoid cross wire or component, and advice to use different color wires such as red for positive, black for ground, yellow, blue, green for signal, and use different length wires. An organized set-up will help us follow the circuit and check any existing errors easily.
In the end, we discuss about the different op amp. We have a talk about the above circuit type (inverting, noninverting, summing, different). By nodal analysis t vn and vp or the voltage divider at vn and vp, we deduce that v(out)=0.3 v2. This deduction is the same as we consider that this circuit is the different op amp with va=0, vb=+/-5V. By applying the different op amp formula for the condition R1/R2 =R3/R4, we get the same result as the nodal analysis as
V(out)=R2/R1(Vp-Vn)=> Gain A = 33/100 = 0.33
Conclusion:
Today, we understand more about the op amp and discuss some popular om amps: the noninverting, summing, unity buffer amplifier, difference amplifier. For each kind of op amp, we use the nodal analysis to express the relationship between the output voltage and the input voltage. Also, we did
the lab of summing amplifier, We practice to sense intuitively the resistors' values for no saturation in the op amp summing amplifier. We get the measured values matching the our expectation.
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