This project is based on a project by Brian Winkel. https://www.simiode.org/resources/518
The goal of this scenario is to determine what the circuit shown above does. There is a voltage source on the left of the circuit. We will measure the gain of the circuit by finding the ratio of the amplitude of the voltage across the resistor labeled $R_{load}$ to the amplitude of the voltage source. The voltage across $R_{load}$ is $R_{load}$ times the current through the resistor. So, we will focus on the current.
Label the currents:
Enter these equations into a Matlab live scripts file.
Here are the basic steps:
When you find $i_3$ is should look something like: $$A\cos(\omega t) + B \sin(\omega t) +e^{- \text{something}}\cdot \text{a big mess}$$ The last term is transient: it goes to 0 as $t \rightarrow \infty$. One can use trig identities to show that the amplitude of this current is $\sqrt{A^2+B^2}$. Read the values of $A$ and $B$ from the Matlab output and have Matlab compute the amplitude of $i_3$. (Keep lots of decimal places.)
Everyone in class has been assigned a different value of $\omega$.
Come to class with your value of $\omega$ and your computed gain.
The Matlab file has the values of the resistors and capacitors entered. The voltage source is $v(t)=\sin(\omega t)$; this is also entered in the Matlab file.