Question

Highpass filter output solved in freq and time, Show these 2 equations are saying the same thing by showing it with a known frequency input
http://prntscr.com/d40hw5 @kainui

Answer 1

Just plug in some value for omega and show you get the same response

Answer 2

Or, you could do it with just using your general cos(wt) input, integrating; and looking at the result

Answer 3

You can just show that the transfer function V_o/V_i is the same...

Answer 4

@inkyvoyd what is cos(wt) in the s domain

Answer 5

Well first of all, what's your context? I'm a EE major so I have a lot of tools in my toolbox that I"m not sure what you're allowed to use. What class is this problem for?

Answer 6

high pass filter

Answer 7

freq and time response

Answer 8

Is this really Hayz?

Answer 9

yes

Answer 10

Well, what's the laplace transform of cos(wt)?

Answer 11

s/(s^2+w^2)

Answer 12

Ok, let's start over. We can derive the impedances of the capacitor relatively easily, especially with the aid of online resources.

Answer 13

Here is a good example on wikipedia: https://en.wikipedia.org/wiki/Electrical_impedance#Deriving_the_device-specific_impedances

Answer 14

Essentially an easier way to look at these things is that capacitors resist a change in voltage, but can't really "keep up" at high frequencies, so they behave like shorts at high frequencies. Hence, 1/(jwC) becomes small for big omega, i.e. at high frequencies capacitor impedance decreases.

Answer 15

The reason the impedance is IMAGINARY and not real is because the voltage and current are out of phase. the perfect 90 degree difference means we're looking at a purely imaginary component, with no real resistance so no power is consumed.

Answer 16

Thanks, let me read wikipedia a bit more

Answer 17

Sounds good. Note that you're looking at a LOT of things... laplace, fourier, and phasors are all slightly different ways of mathematically representing a related concept

Answer 18

@inkyvoyd so instead of jw i can just use s and solve it like in laplace straight forward

Answer 19

or even rewrite cos(at) in s and then change to phasic domain by just saying s = jw?

Answer 20

is that really the only change between laplace and phasor

Answer 21

mm well, phasor is not directly the same as fourier/laplace. Fourier is a specific form of laplace.

Answer 22

In your case tho, yes, you can

Answer 23

well actually fourier and laplace are different they are specific forms of orthogonal function set

Answer 24

but okay cool that makes things so much more clear ughh why do ppl use phasor

Answer 25

thanks bby

Answer 26

fourier is a special case of laplace... namely when sigma equals o

Answer 27

*0... phasors for are EE techs that don't know higher math probably