04-26-2016

04-26-2016

Lab: Introduction AC circuit, Inverting 

After the second exam, we are now back to inductor and capacitor with the introduction of frequency in voltage and current, which is known as the alternating current (and voltage).

Given the derivative graph, we have to integral the given ones to bring them back to the original shape. The square waves graph is the most intuitive one.

II. Lab:
For this lab, given a capacitor and a resistor with such values, we will apply sinusoids of various frequencies to the circuit and compare the output with our expectation based on analysis

Here is our derivation to find the V_o

Here is our setup. The oscilloscope wires had been taken out for brevity

The voltage of V_out(blue) is lagging the the current source, which was the correct, recalled ELI the ICE man.

When we changed to high frequency, the output displayed some strange peaks, we belived that due to such high frequency, small errors could greatly affect the graphs

With low frequency, the graphs were smoothed out

Here is our derivation for the pre-lab, each times we ran, the amplitude changed and also the frequency

II. Introduction to parametrized function:
Given the current sinusoidal voltage and current, we could used another two equations, with delta linked to u and u linked to r. We can use u and delta function to describe r function

Here we wrote the two definitions of u, delta, and r and their relationships

Given the function in terms of r and u, we can take derivative to bring them back to delta and u and plot them

derivation of voltage using u and r representation

Given circuit, we have to find the current across the capacitor over time.

use the nodal analysis to find the current across the inductor.

III. Conclusion:
Today, we were briefly introduced to the idea of AC circuit and their nearly representation of delta and u. We did the inverting differentiator lab, which gave us the idea of how output voltage with frequency varies. Last but not least, we reviewed some nodal and mesh analysis techniques to solve some voltage and current in the circuit.