Day 11 Summing and Difference Amplifiers

Today we continued our journey with operational amplifiers. We've learned so far that depending on how you connect resistors and voltage sources in circuit with an op amp, you will achieve different mathematical operations out of them.

Summing Amplifier

The objective of the first portion of our lab is to model a summing amplifier and to analyze it in an actual circuit. Ideal summing amplifiers (which we will consider today) have a relationship between V-in and V-out as follows for the circuit below:

Reducing this equation using nodal analysis we get:

For our pre lab we were instructed to design a circuit that would fulfill the parameters: we would have a constant 1-V supply for Vb and a variable supply for Va. Our goal was to be able to plot the V-out while remaining in the linear region without hitting either +- saturation. Below was our circuit. 

As always, the funnest part of the lab was building the circuit. Below is our successful build. 

From supplying variable input voltages and recording the consequent output voltages, we collected the following data for the summing amplifier:

Below is a plot of that data. Our measured value is graphed in blue and our theoretical in red. 

Clearly, we satisfied the parameters of the lab. Between -4 and 5 volts, our summing amplifier never reached saturation, + or -.

Difference Amplifiers

This lab aimed at using an op amp to perform subtraction between two voltages. For ideal op amps we know the relationship between input and output voltage is as follows:

Since (roughly) R1 = R2 and R3 = R4:

VO = V2 - V1

Below is the difference amplifier circuit that we constructed. 

Below is our measured data for the voltage out, as well as the theoretical values that we expected. This data has a larger discrepancy from our theoretical than our summing amplifier had. This is seen below in the graph and also in our plot.

Below is the plot:

In conclusion, we successfully were able to model a difference amplifier using the OP 27 op amp. Our measurements stayed within the linear range before reaching saturation, which was the aim of the lab. There are many ways to utilize a single op amp depending on the surrounding circuit elements.

Day 10 Inverting Voltage Amplifier

Today is our first introduction to operational amplifiers, or op amps for short. Our first lab is centered on an inverting op amp, or an op amp that performs multiplication by a negative constant. Below is our circuit diagram that includes the OP 27 and its representation in the circuit. We have designed the circuit so that the Vout = -2 * Vin. The blue numbers around the Op Amp represent the pin terminals on the actual op amp. We have a supply rail from -5 to +5 that is powering the op amp.

Below are the actual measured value of the feedback resistor and the input resistor, respectively. Our ratio, therefore, is not exactly Vo = -2Vi, but very close.

Below is our successfully designed circuit. We have all of the resistors, input voltages, and supply rail voltages connected at the right pins. We had to connect the op amp across the bridge of the breadboard because otherwise the pins would be connected to each other which would make the op amp inoperable for what we needed.

The last step was to measure and plot our measurements for Vin vs. Vout, using Matlab. The graph of the data below demonstrates the properties of the Op Amp very well because we see that the amp saturates when approaching the supply rail voltages, and is inverted from the input voltage.

Op Amps have been some of the most interesting circuit elements to work with so far. They operate the same internally, but depending on how you design the circuit around it is what changes the operation of the op amp. Looking forward to learning more about the Op Amp.

Day 9 Maximum Power Transfer and Non-Ideal Power Sources

Max Power Transfer

Today we explored the idea of Maximum Power Transfer and Non-ideal Power Sources. Maximum power transfer occurs when the resistances inside the voltage source is 0, or close to it. That is what we would call an Ideal power source. If it were non-deal, then there would be a value for an internal resistance.

Our goal is to maximize the power delivered to our load resistor.

Our measured value of P is 2.82 mW.

We can see that using the simplified equation for ideal power sources, P = V^2/4Rth, our theoretical and measured values are almost identical.

Non-Ideal Power Sources

Because we don't live in a perfectly, ideal world, we have to practice our circuit analysis with more real life conditions: this means that our power sources are not going to be ideal. This lab aimed at experimentally exploring the behavior of non-ideal power sources.

Day 8 Thevenin's Theorem

Today's lab experimentally investigated Thevenin's Theorem. As a pre-lab, we wanted to determine the Thevenin Equivalent circuit of our given circuit diagram. We then will measure the load voltage in the original circuit, and then measure the voltage of the Thevenin equivalent circuit.

The semi-complex circuit of resistors and voltage supplies is below. Thevenin's theorem will allow us to simplify the circuit with a variable load, R thevenin, and V thevenin.

Our next task was to measure the current that would flow through our thevanin equivalent circuit, or the resistor R_L which we would measure with two different resistors. Theoretically our value was 54 micro-Amps. Experimentally our value was 55 micro-Amps.

Our second value of R_L was 8.1 k Ohms. Again, or theoretical values and experimental values were very close in magnitude.

For the last section of the lab we were required to create a circuit with two potentiometers, one that was fixed. Below is that circuit.

We measured the Voltage as the resistance was varied using the variable potentiometer. Below are those measurements.

Power as a function of load resistance is graphed below.