29-Mar-2016: Day 11

Exercise 1:

Operational amplifiers (op amps)

Op amps are small intricate circuits that essentially do math operations (i.e. sum, multiply, differentiate...etc). 

Generally they are "dumb down" into the small triangular circuit you see below. There is a voltage drop between two terminals (inverting and non-inverting terminals) on the left side which is the voltage input side, and a seemingly disconnected voltage output on the right side. While drawn disconnected, the voltage output is actually dependent on a gain value multiplied by the voltage input. In reality the internal structure is too horrifying to even imagine at this level of electrical analysis. 

We were asked to try and describe the meaning of open and closed loops.

Above, you see our failed attempt at open and closed loop, which actually describe whether the output has a way sending feedback to the input (i.e. open = no feedback, closed = yes feedback). Feedback is great because it allows the user to operate in a linear range.

Exercise 2:

Analyzing circuits with op amps.

Given a simple circuit with an op amp, we were asked to redraw it to its equivalent circuit, as shown below.

Using the redrawn circuit, we are now asked to determine the gain. As it turns out, gain of an op amp is the ratio of the output over the input voltage, as seen below.

Continuing with the same circuit we go a step further in determining the gain value, given what we have.

Exercise 3:

More practice...

Attempting to solve for the gain again, we quickly discovered that mesh grid method is much more of a mess to analyze than node analysis.., With that said, NODE ANALYSIS is the way to go when analyzing these circuits with operational amplifiers.

Exercise 4:

Inverting Voltage Amplifier Lab

It turns out that gain can more simply be expressed as the ratio between the resistor that closes the loop and the resistor that connects the voltage input to the op amp. By selecting a set of resistors that would give us a ratio of 1:2. Seeing as how this is an inverting op amp what we will see is in terms of  voltages is a negative gain.

V_out = -(R2/R1)*V_in

R1 = 1.8k Ohm
R2 = 3.6k Ohm

Above is a horrifying mess of equations that were done just for the sake of doing. Instead we may use MATLAB to as usual compare theoretical and experimental plots of data. Below is the theoretical calculations.

Below is the collected data.

Graphed together, below, it is easy to see that the theoretical and experimental line up almost perfectly... at least for a moment. What happened on the outer ends of the experimental plot? Well, as it turns out, the op amps have saturation points where essentially a no further change in voltage occurs.

Saturation Voltage range
1.5V < V_out < -2V

Gain = 2