Finding the argument of a Transfer Function

[HairyScarecrow]

Homework Statement

How do I determine Arg{ H(ω) } of the transfer function H(ω)?

A = 1/RC

Both R and C are unknown.

Relevant Equations

H(ω) = (jAω)/((A^2)+(3jAω)-(ω^2))

 

[gneill]

What have you tried?

 

[scottdave]

In general, how would you go about finding the Arg (angle) of a transfer function?

 

[HairyScarecrow]

Arg{(jAω)/(A²+3jAω-ω²)} = Arg{jAω} - Arg{A²+3jAω-ω²} = arctan(Aω) - arctan(3Aω)

 

[Master1022]

Arg{(jAω)/(A²+3jAω-ω²)} = Arg{jAω} - Arg{A²+3jAω-ω²} = arctan(Aω) - arctan(3Aω)

I know this is a late reply, but there is an error there. When we have a complex number $z = x + j y$ and we want to find the argument, that means that we want to find the angle between the positive real axis and that complex number. There are plenty of youtube videos to watch/ articles to read that can give you a better graphical understanding, but basically for a 1st quadrant complex number ($x > 0 , y > 0$, we have that $arg(z) = \arctan \left( \frac{y}{x} \right)$. This should help you deal with the denominator of your transfer function (group the real and imaginary parts)

NOTE: do not just quote this formula without considering what quadrant we are dealing with.

It is sometimes helpful to think about this complex number as a 'vector' in terms of drawing a line from the origin to where it is.

As for the arg(jAw), try and draw a sketch of where jAw is located on an Argand diagram and think about the angle (a line connecting it to the origin) it makes with the positive real axis. HINT: what angle is the imaginary axis to the real axis?