Welcome back to Linear Circuits. 
This lesson is a wrap up for module four, 
which is the module on frequency 
analysis. 
So, looking at our five modules, the 
frequency analysis module has been the 
fourth one. 
It relates to the previous one in that 
the reactive circuit module we pulled 
forward the ideas of RC and RLC circuits. 
From the resistive circuit module, we 
pulled forward all the concepts and the 
techniques that we've used to analyze 
resistive circuits. 
So, mesh analysis, node analysis. 
Ohm's law, KCL, KVL, everything that we 
use to analyze resistive circuits, we can 
use to analyze complex circuits, or 
circuits with impedances in them. 
We treat impedances as if it was a 
complex resistor, and then we can use all 
the those same methods. 
So the particular topics we've covered 
here include phasors, impedance, AC 
circuit analysis, transfer functions, 
frequency response and filters. 
One of the main concepts that I want you 
to understand about this module is that, 
how a system responds to sinusoids of 
different frequencies. 
We've made this point before, that a 
resistive circuit is different from a 
reactive circuit, in that a resistive 
circuit passes through the sine wave at 
the same phase. 
It doesn't change the phase. 
So, the signal, the sign wave, if you 
look at this particular case, if the 
input is in green and the output of the 
circuit is in blue, the frequencies match 
up, but more than that, the phases match 
up. 
They lay on top of one another. 
I may change the amplitude, but I don't 
change that phase. 
The difference in a reactive circuit is 
that I change the amplitude, but I, I 
also change the phase. 
So the output generally has a phase lag, 
compared to the input. 
And we've used a lot of tools in this 
particular module to determine well, what 
kind phase lag am I going to have? 
And what kind of amplitude change am I 
going to have? 
And remember, one of the fundamental 
points of a linear circuit is that if I 
input a sine wave at a given frequency, 
I'm going to get out that same sine wave 
at that same frequency. 
But I may change the amplitude, and I may 
change the phase. 
And the transfer function is a way for us 
to understand how I change the amplitude 
and how I change the phase. 
So looking at the, in particular details 
of the important concepts and skills. 
Since we're looking at sine waves into 
our circuit, we want to be able to 
understand sine waves, and treat them, 
analyze the sine waves, and look at their 
amplitude and phases. 
being able to look at a particular sine 
wave. 
Look at the the period of it, the phase, 
amplitude, and so on. 
And represent that as phasors. 
So I want you to be able to represent 
them as phasors and be able to add sine 
waves using phasors. 
Understand also the properties sine waves 
in capacitors and inductors. 
Impedance is, I consider impedance as 
being a complex resistance. 
I want you to understand what impedance 
is. 
An impedance is going to be a function of 
the sine wave. 
Impedance is this tool that we use to 
analayze circuits with sinusodial inputs 
to them. 
So, the frequency of that input signal 
determines what the value of the 
impedance is going to be. 
You should be able to calculate the 
impedance of resistors, capacitors and 
inductors. 
And you should identify the relationship 
between voltage and current, based on the 
impedance value. 
Being voltage or current through a 
particular element, based on the 
impedance of that element. 
We've used impedance to help us analyze 
AC circuit analysis. 
And again, when I say AC circuit 
analysis, I'm talking about a circuit 
that has a sine wave input to it. 
A sine wave at a given frequency. 
So given that frequency, given that 
source frequency, you should be able to 
convert the RLC circuits into equivalent 
circuits with impedances. 
To be able to replace the R, the L, and 
the C with their equivalent impedance. 
And given resistors in series or 
capacitors in parallel. 
Given these impedances in the device, I 
want you to be able simplify it down to 
equivalent impedance. 
Solve for voltages and currents using 
resistor analysis methods. 
So again, treat impedance as if, as if it 
was a resistor, then you can apply Ohm's 
Law, KCL, KVL, Mesh and everything else 
to be able to solve for particular 
voltages and currents that we're 
interested in. 
A transfer function is a way of 
representing the input to output behavior 
of a circuit. 
So you should know the definition of a 
transfer function. 
Know how to find it, using the impedance 
method. 
We want to be able to understand how a 
linear system responds to sine wave and 
steady state. 
I've already mentioned this. 
A sine wave interlinear system gives you 
a sine wave out at the same frequency. 
But the amplitude and the phase may 
change, and the transfer function is 
exactly how we find out how the amplitude 
and the phase changes. 
So you should be able to calculate what 
the output amplitude should be, and you 
should also understand if I plot the 
transfer function, understand the meaning 
of that plot. 
In terms of finding an output amplitude 
given a particular input amplitude. 
Input frequency. 
You should be able to find the transfer 
functions of simple RL, RC and RLC 
circuits, again using the impedance 
method. 
You should sketch the magnitude and angle 
of the transfer function. 
Over first order system, given a linear 
scale. 
Going on from transfer functions, we 
looked at the frequency spectrum. 
The frequency spectrum is to be able to 
determine what is a frequency content of 
signals? 
You should be able to plot the frequency 
spectrum of sum of sine waves. 
And recognize high and low frequency 
content in a signal both in the time 
domain and in the frequency domain. 
So in the time domain, high frequency 
means we've got a lot of fast changes in 
our signal. 
In the frequency domain, frequency 
content has to do with amplitude. 
If I plot the amplitude, I'll be given 
frequency component. 
It's, if it, if a high frequency 
component dominates, that means I've got 
a high, a large amplitude on the high 
frequency components. 
So understand what it looks like in the 
time domain and in the frequency domain. 
So the frequency response lesson, pull 
together the frequency spectrum lesson as 
well as the transfer function lesson. 
Because the frequency response is nothing 
more than the transfer function where 
we're analyzing that transfer function 
versus frequency, or [INAUDIBLE], or 
perhaps F. 
And in particular, we tend to start 
plotting it. 
So in the frequency response we looked at 
a lot of plots. 
Both in a linear scale, as well as in the 
logarithmic scale, which was the Bode 
plot. 
And in particular, frequency response 
tells us how that system processes 
signals of different frequencies. 
So if my signal had a particular 
frequency spectrum and a particular 
transfer function, then I use a frequency 
response method to tell me what the 
output signal's going to look like. 
And we looked in particular about RC and 
RLC circuits, and examined their 
frequency response. 
So, understand those characteristics of 
those particular types of circuits. 
You should also be able to sketch the 
frequency response from a transfer 
function on a linear scale. 
You should understand the Bode plot 
scales. 
And be able to match the time domain and 
frequency domain inputs and corresponding 
outputs for a circuit with the known 
frequency response. 
To know if I have a frequency response 
where I attenuate certain frequency 
ranges so those frequency ranges should 
be missing in my output. 
So again, the frequency response just 
tells us how this circuit is going to 
process signals, input signals at 
different frequencies. 
And we use the frequency response to 
design filters. 
So, knowing that the frequency response 
processes signals of different 
frequencies, I say, well, all right, I 
want to get rid of my high-frequency 
content. 
So I contour my frequency response to 
attenuate all frequency at high, at high 
content, high frequency content, so that 
I end up with a low pass filter, for 
example. 
And we looked at RC and RLC circuits to 
be able to say, well, how can I redesign 
this circuit so that I get a certain 
frequency response characteristics? 
And we look at particular types of 
filters. 
Those being lowpass, highpass, bandpass, 
and notch filters. 
So given that, those basic concepts, you 
should be able to identify RC and RLC 
circuits as being lowpass, bandpass, 
highpass, or notch filters from their 
schematics, as well as from their 
frequency responses. 
So given a frequency response, you should 
tell me, well is that highpass, lowpass 
and so on. 
You should determine acceptable circuit 
parameters to achieve desired bandwidth, 
corner frequencies or, in other words, 
the bandwidth as well as the center of 
the pass band. 
And the pass band and rejection 
frequencies. 
So in our, our case on filters, we looked 
at samples where we looked at bandpass 
and notch filters. 
And we wanted, went through specific 
examples of how to find the resistor 
capacitor and inductor properties to give 
us the desired frequency kind, 
characteristics that we needed. 
As a reminder, do all the homework for 
this module, study for the quiz, and 
continue to visit the forum to ask and 
answer questions. 
Thank you.