# Determining the amplitude-phase characteristic from the transfer function

#### The Electrician

Joined Oct 9, 2007
2,900
Go have a look at: https://en.wikipedia.org/wiki/Complex_number

Scroll down to the topic heading: Modulus and argument

The absolute value or modulus of a complex number is the square root of the sum of the squares of the real and imaginary parts. For the square of the imaginary part, the "j" is eliminated before squaring; it's the coefficient of "j" that is squared.

#### neonstrobe

Joined May 15, 2009
181
Complex numbers is the first as The Electrician said. That is probably your biggest hurdle.

Then think about multiplying numerators and denominators by a constant.

#### MrAl

Joined Jun 17, 2014
9,158
I would appreciate any help with the following problem:
Edit: The final answer has 36omega^4 not 36omega^2 in the denominator.
View attachment 238856
As others have said, it's mostly about knowing how to handle complex numbers and complex expressions.

The general method is to compute the real and imaginary parts Re and Im, then finding the magnitude by taking the square root of the sum of the squares of the real and imaginary parts, then finding the angle using the two argument inverse tangent function. The phase angle is typically less than 360 degrees but there are cases when you have to figure out if it could be greater than 360 degrees.

The general method to find Re and Im is to convert the denominator into a purely real number and after that you will be left with a real and imaginary part in the numerator and then you can easily separate into Re and Im. To convert the denominator, multiply both the numerator and denominator by the complex conjugate of the denominator. Look up complex conjugate it is easy to calculate.
Actually all this is easy to calculate you just have to learn the procedure. The basic operations are like add, subtract, multiply, and divide you just are working with a "two part number" like 3+6j instead of a one part number like 6, 8, etc.

Do a couple you'll see how easy it gets.