How to get |Vo/Vs| after finding Vo/Vs

CoolDude420 · Dec 10, 2017

Homework Statement

This is probably a stupid question, but I'm not too sure how to obtain the "Voltage gain |Vo/Vs| after finding Vo/Vs which I think is called the transfer function".

I'm doing a question where I found the Vo/Vs but I'm not sure how to turn that into |Vo/Vs|

Homework Equations

The Attempt at a Solution

Handwritten derivation on lined paper: Vo/Vs = jwL / (jwL + R(1-w^2LC)), followed by the question 'how do I get |Vo/Vs| now?'

The correct answer given to us is below

Handwritten answer: magnitude of Vo/Vs equals wL divided by the square root of (1 - w^2 LC)^2 R^2 + w^2 L^2.

The answer seems to have squared top and bottom and taken the square root of the bottom? Not entirely sure what's the general method for this.

NascentOxygen · Dec 10, 2017

Consider first the denominator. It is a complex number, and has a Real component and an Imaginary component. You can sketch it. To find the magnitude of a complex number, use Pythagoras.

The numerator is also a complex number ...

CoolDude420 · Dec 10, 2017

NascentOxygen said:

Consider first the denominator. It is a complex number, and has a Real component and an Imaginary component. You can sketch it. To find the magnitude of a complex number, use Pythagoras.

The numerator is also a complex number ...

Ah. Got it! Took the magnitude of the top and the bottom. Thank you!

How to get |Vo/Vs| after finding Vo/Vs

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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