First-Order Transient Circuit Suppose we are to analyze the transient behavior of the circuit below. The switch in the network opens at t = 0. Our goal is to plot the output voltage Vo(t) for t > 0. At t = 0- the circuit is in steady state and the inductor acts like a short circuit. The initial current through the inductor can be found in many ways, however, I will not explicitly show how here. The network for t > 0 is not impacted by the 4-V independent source and the 2-ohm resistor in series with it. The KVL equation for the circuit is The solution to this equation is Solving the differential equation we get Now that we have solved for Vo(t), we can use Extrema to plot the transient curve of the circuit. First, we must enter in the range of time to plot for. In the Extrema command line, type the following code segment. t=[0:5:0.1] This code specifies the time to be 0 to 5 seconds at 0.1 second intervals. Next we will input the equation for the output voltage Vo. Vo=6-(10/3)*exp(-2*t) Lastly, some simple commands to create a labeled plot of the transient. set xlabel 'time(seconds)' set ylabel 'Vo (V)' graph t,Vo In your visualization window you should see We can add a title to the plot by using the "draw a text string" utility. Click the abc button in the visualization window as shown below. The draw character string window should now appear. Type in the desired title for the plot in the 'Character String' text box. Make sure the checkbox for "position string with the cursor" is checked and have the String alignment at center center. Click the draw button at the bottom and a new window should pop up telling you to click in the visualization window to place the string. Click along the top edge of the plot to insert the text string where normal titles go. Your end result should look something similar to this: Congratulations, you have just created the transient response of the above circuit using Extrema.
Created by Andy Liang		Email Me