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Welcome back to Linear Circuits. 
This lesson is a wrap up for module four, 

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which is the module on frequency 
analysis. 

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So, looking at our five modules, the 
frequency analysis module has been the 

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fourth one. 
It relates to the previous one in that 

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the reactive circuit module we pulled 
forward the ideas of RC and RLC circuits. 

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From the resistive circuit module, we 
pulled forward all the concepts and the 

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techniques that we've used to analyze 
resistive circuits. 

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So, mesh analysis, node analysis. 
Ohm's law, KCL, KVL, everything that we 

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use to analyze resistive circuits, we can 
use to analyze complex circuits, or 

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circuits with impedances in them. 
We treat impedances as if it was a 

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complex resistor, and then we can use all 
the those same methods. 

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So the particular topics we've covered 
here include phasors, impedance, AC 

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circuit analysis, transfer functions, 
frequency response and filters. 

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One of the main concepts that I want you 
to understand about this module is that, 

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how a system responds to sinusoids of 
different frequencies. 

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We've made this point before, that a 
resistive circuit is different from a 

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reactive circuit, in that a resistive 
circuit passes through the sine wave at 

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the same phase. 
It doesn't change the phase. 

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So, the signal, the sign wave, if you 
look at this particular case, if the 

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input is in green and the output of the 
circuit is in blue, the frequencies match 

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up, but more than that, the phases match 
up. 

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They lay on top of one another. 
I may change the amplitude, but I don't 

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change that phase. 
The difference in a reactive circuit is 

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that I change the amplitude, but I, I 
also change the phase. 

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So the output generally has a phase lag, 
compared to the input. 

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And we've used a lot of tools in this 
particular module to determine well, what 

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kind phase lag am I going to have? 
And what kind of amplitude change am I 

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going to have? 
And remember, one of the fundamental 

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points of a linear circuit is that if I 
input a sine wave at a given frequency, 

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I'm going to get out that same sine wave 
at that same frequency. 

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But I may change the amplitude, and I may 
change the phase. 

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And the transfer function is a way for us 
to understand how I change the amplitude 

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and how I change the phase. 
So looking at the, in particular details 

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of the important concepts and skills. 
Since we're looking at sine waves into 

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our circuit, we want to be able to 
understand sine waves, and treat them, 

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analyze the sine waves, and look at their 
amplitude and phases. 

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being able to look at a particular sine 
wave. 

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Look at the the period of it, the phase, 
amplitude, and so on. 

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And represent that as phasors. 
So I want you to be able to represent 

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them as phasors and be able to add sine 
waves using phasors. 

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Understand also the properties sine waves 
in capacitors and inductors. 

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Impedance is, I consider impedance as 
being a complex resistance. 

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I want you to understand what impedance 
is. 

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An impedance is going to be a function of 
the sine wave. 

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Impedance is this tool that we use to 
analayze circuits with sinusodial inputs 

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to them. 
So, the frequency of that input signal 

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determines what the value of the 
impedance is going to be. 

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You should be able to calculate the 
impedance of resistors, capacitors and 

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inductors. 
And you should identify the relationship 

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between voltage and current, based on the 
impedance value. 

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Being voltage or current through a 
particular element, based on the 

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impedance of that element. 
We've used impedance to help us analyze 

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AC circuit analysis. 
And again, when I say AC circuit 

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analysis, I'm talking about a circuit 
that has a sine wave input to it. 

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A sine wave at a given frequency. 
So given that frequency, given that 

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source frequency, you should be able to 
convert the RLC circuits into equivalent 

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circuits with impedances. 
To be able to replace the R, the L, and 

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the C with their equivalent impedance. 
And given resistors in series or 

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capacitors in parallel. 
Given these impedances in the device, I 

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want you to be able simplify it down to 
equivalent impedance. 

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Solve for voltages and currents using 
resistor analysis methods. 

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So again, treat impedance as if, as if it 
was a resistor, then you can apply Ohm's 

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Law, KCL, KVL, Mesh and everything else 
to be able to solve for particular 

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voltages and currents that we're 
interested in. 

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A transfer function is a way of 
representing the input to output behavior 

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of a circuit. 
So you should know the definition of a 

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transfer function. 
Know how to find it, using the impedance 

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method. 
We want to be able to understand how a 

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linear system responds to sine wave and 
steady state. 

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I've already mentioned this. 
A sine wave interlinear system gives you 

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a sine wave out at the same frequency. 
But the amplitude and the phase may 

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change, and the transfer function is 
exactly how we find out how the amplitude 

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and the phase changes. 
So you should be able to calculate what 

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the output amplitude should be, and you 
should also understand if I plot the 

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transfer function, understand the meaning 
of that plot. 

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In terms of finding an output amplitude 
given a particular input amplitude. 

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Input frequency. 
You should be able to find the transfer 

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functions of simple RL, RC and RLC 
circuits, again using the impedance 

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method. 
You should sketch the magnitude and angle 

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of the transfer function. 
Over first order system, given a linear 

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scale. 
Going on from transfer functions, we 

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looked at the frequency spectrum. 
The frequency spectrum is to be able to 

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determine what is a frequency content of 
signals? 

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You should be able to plot the frequency 
spectrum of sum of sine waves. 

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And recognize high and low frequency 
content in a signal both in the time 

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domain and in the frequency domain. 
So in the time domain, high frequency 

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means we've got a lot of fast changes in 
our signal. 

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In the frequency domain, frequency 
content has to do with amplitude. 

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If I plot the amplitude, I'll be given 
frequency component. 

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It's, if it, if a high frequency 
component dominates, that means I've got 

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a high, a large amplitude on the high 
frequency components. 

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So understand what it looks like in the 
time domain and in the frequency domain. 

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So the frequency response lesson, pull 
together the frequency spectrum lesson as 

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well as the transfer function lesson. 
Because the frequency response is nothing 

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more than the transfer function where 
we're analyzing that transfer function 

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versus frequency, or [INAUDIBLE], or 
perhaps F. 

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And in particular, we tend to start 
plotting it. 

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So in the frequency response we looked at 
a lot of plots. 

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Both in a linear scale, as well as in the 
logarithmic scale, which was the Bode 

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plot. 
And in particular, frequency response 

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tells us how that system processes 
signals of different frequencies. 

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So if my signal had a particular 
frequency spectrum and a particular 

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transfer function, then I use a frequency 
response method to tell me what the 

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output signal's going to look like. 
And we looked in particular about RC and 

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RLC circuits, and examined their 
frequency response. 

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So, understand those characteristics of 
those particular types of circuits. 

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You should also be able to sketch the 
frequency response from a transfer 

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function on a linear scale. 
You should understand the Bode plot 

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scales. 
And be able to match the time domain and 

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frequency domain inputs and corresponding 
outputs for a circuit with the known 

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frequency response. 
To know if I have a frequency response 

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where I attenuate certain frequency 
ranges so those frequency ranges should 

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be missing in my output. 
So again, the frequency response just 

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tells us how this circuit is going to 
process signals, input signals at 

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different frequencies. 
And we use the frequency response to 

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design filters. 
So, knowing that the frequency response 

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processes signals of different 
frequencies, I say, well, all right, I 

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want to get rid of my high-frequency 
content. 

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So I contour my frequency response to 
attenuate all frequency at high, at high 

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content, high frequency content, so that 
I end up with a low pass filter, for 

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example. 
And we looked at RC and RLC circuits to 

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be able to say, well, how can I redesign 
this circuit so that I get a certain 

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frequency response characteristics? 
And we look at particular types of 

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filters. 
Those being lowpass, highpass, bandpass, 

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and notch filters. 
So given that, those basic concepts, you 

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should be able to identify RC and RLC 
circuits as being lowpass, bandpass, 

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highpass, or notch filters from their 
schematics, as well as from their 

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frequency responses. 
So given a frequency response, you should 

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tell me, well is that highpass, lowpass 
and so on. 

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You should determine acceptable circuit 
parameters to achieve desired bandwidth, 

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corner frequencies or, in other words, 
the bandwidth as well as the center of 

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the pass band. 
And the pass band and rejection 

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frequencies. 
So in our, our case on filters, we looked 

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at samples where we looked at bandpass 
and notch filters. 

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And we wanted, went through specific 
examples of how to find the resistor 

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capacitor and inductor properties to give 
us the desired frequency kind, 

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characteristics that we needed. 
As a reminder, do all the homework for 

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this module, study for the quiz, and 
continue to visit the forum to ask and 

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answer questions. 
Thank you.