Day 26 (No Lab)

We started the day by talking about the misleading term cutoff frequencies. The resonant frequency is the point where the current/voltage going through the circuit is the highest and the cutoff frequencies are where the clarity that a signal reciever starts to notice a decrease in quality. We did a derivation of what the output of the current would by when the circuit is at one of those cutoff frequencies.

We continued on the topic of frequencies by discussing bandwidth, which is the difference between the upper and lower cutoff frequencies, quality, which is the ratio between the resonant frequency and the bandwitdth. However formulas for the upper and lower cutoff frequencies change whether the circuit is a series or parallel RLC circuit but the relationships between the bandwidth, quality, and resonant frequency are the same for both and we did an example of calulating that for a parallel RLC circuit.

We then did an example where one of the three circuit elements have been set and we need to determine what the value of the other two elements should be in order for the circiut to work at the designated resonant frequency and cutoff frequencies.

Day 25 (Celebration)

Here is a picture of my grade during the celebration.

Day 24 (Signals with Multiple Frequency Components Lab)

We started the day by discussing transfer functions which are essentially seeing how the output of a certain circuit element compares to the input of the circuit element. However the output of elements in circuits with AC current is dependent on the frequency of the source so the transfer function is a function of omega (w). Another difficulty of expressing the transfer function comes with working with complex functions with j and w tied together so we replace it with s. In this example we are concerned at what points does the transfer function go to zero and where the asymptotes are.

The transfer function can also be used to find the impedance of the section that we are curious in relative to the input of the circuit source by have the voltage across the section being divided by the input current. Again the transfer function will be a function of the function of the source and again the complex components are easiest to handle when they are replaced with a variable like s. The interesting locations are when the function is zero and has an asymptote.

We did one last transfer function for a series RLC circuit and calculated the voltage output of the circuit across the inductor against the input voltage. Again the important sections are when the transfer function gives us zero and an asymptote.

We then did the Signals with Multiple Frequency Components Lab and we started with the pre-lab. The pre-lab was to calculate what the response of the circuit across the second resistor would be as a transfer function. We then calculated the values at the frequencies 500Hz, 1000Hz, 10kHz.

Here are images of the circuit that was built.

Here are images of the oscilliscope graphing the input versus the output voltages. The difference in the images are the time divisions used for the horizontal axis.

Day 23 (Apparent Power and Power Factor Lab)

We started the day by deriving the equation for the effective current from power.

We then went and derived what the effective voltage of a sinusoidal voltage source would be.

We then did an example of power with complex and real powers and a power factor that determines what is real and what is complex.

We did another example of complex and real power but this time instead of being given a circuit, we were given RMS polar values for the voltage and current.

We did one final example of apparent power.

We then started the Apparent Power and Power Factor Lab. Here is a picture of the pre-lab.

Here is a picture of the circuit we built.

Here is a picture of the window from the oscilliscope.

Here is a picture of the results of the experimental values.

Day 22 (Inverting Voltage Amplifier Lab)

We started by analyzing a circuit that has an op amp with capacitors and resistors and found the expression for the output voltage.

We then started the Inverting Voltage Amplifier Lab. Here are pictures of the circuit we built.

Here are pictures of the oscilliscope comparing the input voltage to the output voltage across the op amp.

Here is a picture of the final results.

Day 21 (Phasors: Passive RL Circuit Response Lab)

We started the day with doing nodal analysis on an AC circuit that is converted from the time domain to the phasor domain.

Next we analyzed an AC circuit using mesh analysis.

We then started the Phasors: Passive RL Circuit Response Lab. Here is a picture of the pre-lab.

Here are pictures of the circuit we built.

Here are pictures of the oscilliscope that showed the voltage across inductor versus the input voltage and the current across the circuit.

Here is a picture of the numerical results of the experiment as frequency changes.

We ended the day by doing an analysis of a circuit using super position.

Day 20 (Impedence Lab)

We started the day by analyzing an AC RC circuit using phasor analysis and find the current in the circuit.

We then did the same analysis for an AC RC circuit and find the voltage across the capacitor as a function of time.

We then started the Impedence Lab. Here are the pictures of the pre-lab.

Here is a picture of the input voltage versus the current in the circuit for the resistors.Under it are the results of changing frequency and seeing how the current gain and phase angle changes.

Here is a picture of the input voltage versus the current in the circuit for the inductor. Under it are the results of changing frequency and seeing how the current gain and phase angle changes.

Here is a picture of the input voltage versus the current in the circuit for the capacitor. Under it are the results of changing frequency and seeing how the current gain and phase angle changes.

Next we looked at adding impedences of different elements in AC circuits.

We then analyzed a voltage divider in AC using phasors.

Finally we analyzed the phase shift that an element would have, like a capacitor.