Transfer (Gain) Function for AC Circuit

Transfer (Gain) Function for AC Circuit
John Matz
12/6/2020
George Mason University
Math 401: Mathematics Through 3D Printing

These two objects are graphs of the real an imaginary parts of the transfer function for a second order AC circuit. The transfer function (Vo/Vi) is 5s/(s^2+8s+5) where s = sqrt(-1)*(frequency), and in these examples the frequency is Pi rad/s. This is the answer to problem 14.3 from the fifth edition of Fundamentals of Electric Circuits by Charles K. Alexander and Matthew N. O. Sadiku, a picture of which can be seen in image #4, above.

While most circuits are modeled by differential equations, it is possible to convert these models into the phasor domain, which is easier to work with. By restricting inputs and outputs to sinusoids the differential equation becomes a polynomial. I believe this is similar to a Laplace Transform, but my experience is more in applications than the theory. This part of the aforementioned textbook and the accompanying proble