Bode phase plots and initial angles of transfer functions

[vysero]

Hello everyone. So I have a test coming up and I am struggling with the concept of figure out what the initial phase or angle of a transfer function is. For instance, consider the following transfer function:

L(s) = 4/s(.4s+1)(s+2)

So the initial angle for L(s) is -90 degrees. Is there a simple trick for figuring that out given any transfer function? I have heard that if there is a negative in the numerator then you add 180 degrees of phase or depending on the degree of the denominator you would subtract phase.

Can someone help me sort this out?

 

[milesyoung]

Is there a simple trick for figuring that out given any transfer function?

I assume you mean this function:
L(s) = 4/(s(.4s+1)(s+2))

Some thoughts to help you get to the answer:

Say you have two complex numbers z1 and z2, what is arg(z1 z2) and arg(z1/z2) in terms of arg(z1) and arg(z2)?

What happens to the angle of each factor in the denominator as s = jω, ω → 0?