Non Inverting Operational Amplifier

[theuniverse]

Derive an expression for the gain Vout/Vin. Express your answer in the form of A+jB.

I know that If C is the capacitor in series with R1, gain = 1 + R2/[R1 + 1/(jwC)]. It says to express it in the form of A (real)+ jB (imaginary), but I'm not sure how to make the conversion from my solution of gain to the form of A+jB.
Any help is appreciated.

 

[Nathaniel]

Putting that on Wolfram Alpha we get:
(K R)/(1/(C^2 w^2)+K^2)+1+(i R)/(C w (1/(C^2 w^2)+K^2))

Where K = R1 and R=R2


(K R)/(1/(C^2 w^2)+K^2)+1 = A
(R)/(C w (1/(C^2 w^2)+K^2)) = B

The other way is to do it with algebra.

 

[MrAl]

Derive an expression for the gain Vout/Vin. Express your answer in the form of A+jB.

I know that If C is the capacitor in series with R1, gain = 1 + R2/[R1 + 1/(jwC)]. It says to express it in the form of A (real)+ jB (imaginary), but I'm not sure how to make the conversion from my solution of gain to the form of A+jB.
Any help is appreciated.

Hi,

When you have it in a form that includes a complex quantity (which is just about every case) you take the absolute value, also known as "norm".
This is calculated as follows:
abs(a+b*j)=sqrt(a^2+b^2)
This gives the magnitude.