Finding a phase characteristic from a transfer function?

Given a transfer function:

Show that the phase characteristic is

My text book only briefly covers this subject so I really have no idea what to do.

I know the formula is:

So I have that:

So I assume I need to find the argument of this fraction?

Re: Finding a phase characteristic from a transfer function?

My attempt:

I looked at this Wikipedia article under the section "Computation" where it says that:

for

I'd assume this is the definition I need to look at because in the formula, it says that and the omega is the imaginary part.

So that leaves me with:

So I've figured out this much. I'm a bit confused as what to do next. What about ?

Re: Finding a phase characteristic from a transfer function?

Nevermind, I think I solved it on my own.

Arg(-1)=pi

Arg(ib+1)=arctan(b)

So subtracting them with each other gives the answer.

Re: Finding a phase characteristic from a transfer function?

Quote:

Originally Posted by

**MathIsOhSoHard** My attempt:

I looked at

this Wikipedia article under the section "Computation" where it says that:

for

I'd assume this is the definition I need to look at because in the formula, it says that

and the omega is the imaginary part.

So that leaves me with:

So I've figured out this much. I'm a bit confused as what to do next. What about

?

You can take the out of the denominator by multiplying the numerator and denominator of by to get,

Using the properties of arctan,

and

results in the answer.

EDIT:You've already done it. Well done