Frequency Response Video Lecture - Electrical Engineering (EE)

our topic today is frequency response
and this is a common topic in signals
and systems so if you remember from that
class this will be very familiar so the
idea is that we have a system G of s
we're calling it and we want to see how
the system reacts to specific
frequencies before when we do it steps
response you know we have an input it's
just a step we're looking at all the
frequencies at once but when we we want
to actually isolate each frequency and
see how it reacts individually so we're
going to set up a problem so say we have
so Valerie we all know Valerie she's
actually a really great singer and you
wouldn't know it but she's tiny but she
can sing opera it's really amazing
so say she can sing a perfect pitch a
perfect frequency and we're going to put
that into some system so it's some sound
modulation systems and she's going to
put that input just gonna sing a
frequency into it and we're going to get
some sort of signal out so first let's
look at her input signal so the sound
that she's singing so there's a we're
going to put on a time domain so she's
singing some frequency and we're going
to say that it maybe it starts we're
going to start here and it's some
amplitude here I'm not very good at
drawing these sine waves but go with it
okay so we have this input signal and
we're going to use the idea of a phaser
so we're going to look at the magnitude
of our system so we can break this as a
sign or a sum of a sine a cosine but
we're going to change it into a
magnitude and a phase shift so the
magnitude is simply going to be this
amplitude from the peak to zero so that
would be we call that M and we call mi
for the input and so this is going to be
mi is our frequency sorry is our
magnitude and then in phaser notation
you have a magnitude and an angle and
here the
angle is going to be so it's going to be
this phase shift so say we're going to
start off the stay our start starting
point is from here we have some phase
shift of that so this is our input so
this is V I and Phi B Phi one of those
so this is our phase shift our input and
then this is our magnitude okay so we
put that into our system and we will get
out some system so say so here's our I'm
going to put on the time domain again
this is time this is the amplitude of
the signal and this time it's going to
this is going to amplify our signal so
we're going to say it's amplified I'm
not very good at drawing these okay
let's do one more you can you can go
ahead use your imagination and pretend
it's a nice sine wave but the point I
want a thing I want to show here is that
we have should be the same amplitude we
have some amplitude out we call it M 0
and o output and then we have some phase
shift as well so here it's a little bit
different phase shift it's changed a
little bit and we're going to call that
V out so here's M I signal here is mo vo
so this is our input phasor this is our
output phasor and in each of these when
we do justice just individual
frequencies we can model how this system
will affect our input versus output so
we can essentially model this only in
this situation as a magnitude of this
transfer function and a phase shift that
it will cause such that when you
multiply these two together you will get
this output so essentially I'll write it
out so yeah
I see I multiplied by M G V G is equal
to mo 0 so this is essentially our
transfer function but only for an input
of frequency and an output frequency so
we call this a frequency response and
without going through all of the math I
can tell you that actually so I'll
rewrite this let's just move it over
here so if we want to think about this
like frequency response remember it's
the output of the input so we move this
over will it'll get this alright so we
can now get rid of that essentially this
is our frequency response so the next
question is how do we find this without
going through all of the math I'm just
going to tell you the answer so what we
can do is we actually know that we can
look at how the system reacts when you
put in a frequency signal so what we do
is we make s equal J Omega in this case
so and if you think about this on the
imaginary and real axis that is starting
from so this is real and imaginary we
are starting from if anything
essentially on this this area it says on
the imaginary axis which if we remember
that's where our marginally stable
occurrences can happen and we can
associate these points with a frequency
so in short we can put if we make s
equals J Omega and put that into our
transfer function here and it turns out
that so G of J Omega we put that into
our transfer function we get the
magnitude of that that is going to be
equal to our G mg here so the magnitude
of our transfer function and we can do
the same thing so now instead if we take
the angle
of G Omega J we will get this angle this
shift so this would be fee G oh hi so
and one more thing that this Omega
remember is 2pi frequency this frequency
is in Hertz so you can put in whatever
frequency your input is here and you can
figure out how this system will affect
so how the effects on the magnitude and
the phase at that given frequency okay
so we're going to look at how to use
this and draw it out in a bode plot and
hopefully that will be a little bit
clearer but to find the frequency
response you have to take your actual G
of s here you put in J Omega and you can
take the magnitude of that and the angle
of that to figure out how the input
versus output will be affected okay so
we'll stop here for now