Magnitude calculation of filter

Electrical Engineering Asked by smake5730 on December 5, 2020

I am working on a problem for a given transfer function given below and am having trouble calculating the magnitude and phase of it. The problem is specifically that I do not know what method to use to seperate the imaginary value out of from the real to allow me to use their seperate values in calculating the magnitude and phase.


Ideally I’d like to end up with something like a+bi to allow me to do the srqt(a^2 + b^2) and the tan equation for the phase but I do not know how to do this.

Could anyone suggest a method to use or some mathematical identity to use?


So implementing what was in the first comment from ocrdu

It simplifies to


Then multiplying top and bottom by inverse of bottom gives:


But how does this help me?

3 Answers

So the solution was simply to take the square as follows:


j squared is j * j = -1



Correct answer by smake5730 on December 5, 2020

$$frac{Vout}{Vin}=frac{-0.579-j*1.25}{(-0.579+j*1.25)*(-0.579-j*1.25)}=$$ $$frac{-0.579-j*1.25}{0.335+0.724j-0.724j+1.563} = $$ $$frac{-0.579-j*1.25}{1.898} = -0.305-0.659j$$

Please check for errors (yours and mine), but you get the idea.

Multiplying top and bottom by the denominator's complex conjugate gives a real number in the denominator.

Answered by ocrdu on December 5, 2020

$(1 + ja)cdot(1 - ja) = 1 + a^2$

Answered by Andy aka on December 5, 2020

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