Quick question regarding some algebra?

[papasmurf]

The gain of an internally compensated op amp may be expressed by

Equation 1) A(s) = A0 / ( 1 + s/$\omega$b) where $\omega$b is the 3dB frequency or "break frequency" and A0 is the dc gain.

Plugging in s=j$\omega$ and $\omega$ = 2*pi*f gives

Equation 2) A= A0 / (1 + j*f / fb) where fb is still the "break frequency"

I understand how all of that works.

What I don't understand is how you can go from Equation 2 to this:

Equation 3) A = A0 / sqrt( 1 + (f/fb)^2).

I hope all of this makes sense and someone can help me. Thank you.

 

[berkeman]

The gain of an internally compensated op amp may be expressed by

Equation 1) A(s) = A0 / ( 1 + s/$\omega$b) where $\omega$b is the 3dB frequency or "break frequency" and A0 is the dc gain.

Plugging in s=j$\omega$ and $\omega$ = 2*pi*f gives

Equation 2) A= A0 / (1 + j*f / fb) where fb is still the "break frequency"

I understand how all of that works.

What I don't understand is how you can go from Equation 2 to this:

Equation 3) A = A0 / sqrt( 1 + (f/fb)^2).

I hope all of this makes sense and someone can help me. Thank you.

That's the magnitude of the complex gain... See Equation #9 here for example:

http://cheme.eng.wayne.edu/neuron/auth/ece3310/experiment_12.htm

.