Day 21

Inverting Voltage Amplifier Lab

Today we went over steady-state responses and how they reacted to a sinusoidal voltage input. For this lab we will have the same frequency for both the input and output voltage but they will have different amplitudes (depending on the gain of the circuit) and different phase angles.

Pre-Lab

Here we are given the circuit diagram for an Inverting Voltage Amplifier

Here we are calculating what the gain and phase angle will be at different frequencies.

Here is an overview of all our calculations for the circuit

Here we are comparing our experimental values to our theoretical values.

And yes, a sexy pic of the built circuit.

Graphs

Here is the graph of the circuit at 100Hz.

Here is the graph of the circuit at 1kHz.

Here is the graph of the circuit at 5kHz.

Here is an overview of all our calculations, experiemental values, and percent error

Overall, this lab was a huge success as we can see the percent errors were all under 1%.

Op Amp Relaxation Oscillator Lab

We can get a relaxation oscillator when we design the circuit to have a device that will act as a switch when certain voltages are applied to one of the terminals. The "switching voltage" is across a capacitor that is being charged and discharged.

Here we just calculated the value of the resistor R.

 Sexy

Here we can see the voltages for the Op Amp Relaxation Oscillator

Overall, this experiment was a new way to see how oscillators within circuits worked.

Day 20

Phasors: Passive RL Circuit Response Lab

In today's lab we are experimenting with gain and phase response of a passive RL circuit. We can can come up with these theoretical values mathematically and then we can compare them with experimental values.

Pre-Lab

For the pre-lab we were able to calculate values for the amplitude gain and phase difference between the input voltage and input current. We also calculated the cut-off frequency of the circuit. (Both pictures)

What is a lab without a sexy pic of our circuit.

Here we used a function generator to apply a sinusoidal voltage to the circuit. These graphs display the behavior between the voltages (Viewer Discretion Advised).

Overall, the measured values for the experiment held true to the theoretical values of the pre-lab.

Day 19

Impedance Lab

Today we are looking at three different circuits and comparing the impedance of each of these circuits.

Here we are given our three circuits. One has 2 resistors, another has a resistor in series with an inductor, and the last has a resistor in series with a capacitor.

Here we are measuring the output current from the 47 ohm resistor and the output voltage of the 100 ohm resistor.

Here we are calculating the theoretical values of each of the circuits so we can test them to the experimental values.

Here are some sexy pics of the circuit with the resistor and the capacitor in series.

Here is our updated data sheet with values of each of the circuits at different frequencies.

And now here is a sexy pic of a circuit with an inductor in series with a resistor.

This is our updated data sheet from the above experiement where we are testing the inductor in series with the resistor at different frequencies.

Graphs

Here is the collection of graphs and plots for each of the circuits at different frequencies. We can see that each one behaves differently and how different circuits are out of phase. We can see how some circuits will lead and others will lag.

Overall impedance ties a lot of ideas together and we can see how different components will affect the overall behavior of the circuit.

Day 18

No Lab on this day

But we went over phasors.....yay!

Day 17

RLC Circuit Response Lab

In this lab we were testing a RLC circuit, but this time it's not in series. So with this lab we will have a different experience then in the previous lab. Here we used a capacitor, inductor, and 2 resistors. Once again we are testing the step response and comparing the measured values to theoretical values that we derived from equations in class. These values include the damping ratio and natural frequency of the circuit.

Pre-Lab

For the pre-lab we are given the design of the RLC circuit and we are to calculate what the natural frequency and the damping ratio should be. All these values are easily obtained by the equations that we derived in class where we can compare alpha to omega.

This is the graph of our circuit in Analog Discovery where we see under damped cases every time there is an abrupt change.

Overall, we can see the relationship the circuits have in each other depending on the arrangement of the circuit and how this will affect the damping and natural frequency of the circuit.

Day 16

Series RLC Circuit Step Response

Here we are testing RLC circuits in a series which results in second order differential equations. We can analyze and test the step response of these circuits. Here we can test can theoretical values derived from equation that we did in last with actual experimental equations. The types of behaviors we are looking for are damping ratios and natural frequencies. We can also design any circuit to behave in any of the three functional modes of overdamped, critically damped, or underdamped. We can do this without changing the frequency or DC gain of the circuit.

Pre-Lab

Here we have calculated a certain RLC circuit which came out to be underdamped. This is where we use Euler's Method to replace the complex general solution with cosine and sine.

Here we are further playing with the differential equations to relate V(out) with V(in) for the circuit. Many calculations were performed such as damping ratio, natural frequency, damped natural frequency, DC gain, and any frequency of oscillations we would expect to see in the step response of the circuit.

This is the output of the under damped circuit. As you can see it has a forced response which limits the amplitude and we can see it dip off gradually as it reaches zero. This is the graph you would expect to see by adding the cosine function and sine function together.

Once again, we have some more sexy circuit pics

Overall, this lab wasn't too difficult where we saw the behavior of a simple RLC circuit in a series and were able to see how it function depending on the ratios between alpha and omega.