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.