Active Low Pass Filter - EXPERIMENT
Summary
TLDRThis video tutorial demonstrates the operation of an active low-pass filter, which allows signals below a certain frequency to pass through. The presenter uses a circuit with an operational amplifier (op-amp) in inverting mode, with R2 and C components to create the filter. The critical frequency formula is provided as 1/(2πR2C). The video includes a practical setup, input signal testing at various frequencies, and a visual comparison of the input and output signals. The presenter also discusses the Butterworth filter characteristics and the expected gain at the cutoff frequency, concluding with a graph plotting the gain versus frequency to verify the filter's performance.
Takeaways
- 🎛️ The video demonstrates the working of an active low-pass filter, which only allows signals with frequencies lower than a certain cutoff frequency to pass through.
- 🔌 The active low-pass filter in the video uses an operational amplifier (op-amp) in an inverting configuration.
- 🛠️ The circuit shown uses a 741 C operational amplifier IC, with the input signal given through the inverting terminal (pin 2).
- 🧮 The formula for the cutoff frequency (critical frequency) of an active low-pass filter is given by 1 / (2πR2C).
- 📊 The video discusses the characteristics of a first-order active low-pass filter, also known as a Butterworth filter.
- 📉 The Butterworth filter has a flat response in the passband and falls off at a rate of 20 dB per decade after the cutoff frequency.
- 🔍 At the cutoff frequency, the gain is approximately -3 dB, which corresponds to about 70.7% of the input voltage.
- 🔄 The video shows a practical demonstration, where the input signal is compared to the output signal using a digital storage oscilloscope (DSO).
- 🔧 The experiment involves varying the input frequency and measuring the corresponding output signal to plot a gain vs. frequency graph.
- 📈 The video emphasizes the importance of taking multiple readings at different frequencies to get a smooth and accurate gain vs. frequency curve.
Q & A
What is the primary function of a low pass filter?
-A low pass filter allows signals with frequencies lower than a certain critical frequency to pass through while blocking higher frequencies.
What distinguishes an active low pass filter from a passive one?
-An active low pass filter contains active components such as an operational amplifier, which amplifies the input signal, in contrast to a passive filter that does not use active components.
What is the significance of the operational amplifier being used in inverting mode in the given circuit?
-The operational amplifier in inverting mode inverts the phase of the input signal, which is a characteristic of the active low pass filter design demonstrated in the script.
What is the formula for calculating the critical or cutoff frequency of an active low pass filter?
-The formula for calculating the cutoff frequency is \( \frac{1}{2\pi R_2C} \), where \( R_2 \) is the resistance and \( C \) is the capacitance in the filter circuit.
What type of filter is the demonstrated circuit known as, and what are its characteristics?
-The demonstrated circuit is known as a first-order active low pass filter or Butterworth filter, characterized by a flat response region and a roll-off rate of 20 decibels per decade after the cutoff frequency.
At what frequency does the gain of the filter drop to about minus 3 decibels?
-The gain of the filter drops to about minus 3 decibels at the cutoff frequency.
What is the practical significance of the cutoff frequency in the context of the experiment?
-The cutoff frequency is the point at which the filter's output voltage is approximately 70.7% of the input voltage, marking the transition from the passband to the stopband.
What are the values of R2 and C used in the circuit for the experiment?
-The R2 resistance used in the circuit is 1 kilo-ohm, and the capacitance C is 0.01 microfarads.
How does the output voltage of the filter change as the input frequency increases beyond the cutoff frequency?
-As the input frequency increases beyond the cutoff frequency, the output voltage decreases, indicating the filter's effectiveness in attenuating higher frequencies.
What is the recommended approach for verifying the performance of the active low pass filter?
-The recommended approach is to take multiple readings of the output voltage at various frequencies, both below and above the cutoff frequency, and then plot the gain versus frequency or output voltage versus frequency to verify the filter's performance.
How can viewers with questions or doubts about the experiment get assistance?
-Viewers can leave their questions or doubts in the comment section of the video, and the presenter will get back to them.
Outlines
🔧 Demonstration of an Active Low Pass Filter
The video begins with an introduction to the concept of an active low pass filter, which allows signals below a certain frequency to pass through and is distinguished by the presence of active components like an operational amplifier. The presenter uses a specific circuit diagram that includes an op-amp in inverting mode, with R2 and C components to form the filter. The critical frequency, or cutoff frequency, is calculated using the formula \( \frac{1}{2\pi R2C} \). The video also explains that this type of filter is known as a first-order active low pass filter or a Butterworth filter, characterized by a flat response and a 20 dB per decade roll-off after the cutoff frequency. The presenter mentions a previous tutorial for more theoretical details and proceeds to a practical demonstration of the filter's operation.
📊 Testing the Active Low Pass Filter with Various Frequencies
The presenter tests the active low pass filter by applying a 20 Hz input signal and observing the output on a digital storage oscilloscope (DSO). The output signal is in phase opposition to the input due to the inverting configuration of the op-amp. The video continues with testing at various frequencies, including the critical frequency of approximately 16 kHz, where the output voltage is expected to be 70.7% of the input. The presenter measures the output voltage at different frequencies, noting the expected behavior around the cutoff frequency. The goal is to collect data points to plot a gain versus frequency graph, which will later be used to verify the filter's performance.
📈 Plotting the Gain vs. Frequency Graph and Conclusion
After collecting numerous readings of output voltage at frequencies below and above the critical frequency, the presenter plots the gain in decibels against the logarithm of frequency on a graph. The resulting curve is smooth and closely matches the theoretical plot, demonstrating the effectiveness of the active low pass filter. The video concludes with a reminder to ensure that the output voltage at the cutoff frequency is approximately 70.7% of the input, which is confirmed by the experiment. The presenter invites viewers to ask questions or share doubts in the comments section and thanks them for watching.
Mindmap
Keywords
💡Active Low Pass Filter
💡Operational Amplifier (Op-Amp)
💡Critical Frequency
💡Inverting Configuration
💡First-Order Active Low Pass Filter
💡Butterworth Filter
💡Gain
💡Decibels (dB)
💡Frequency Response
💡Digital Storage Oscilloscope (DSO)
💡Cutoff Frequency
Highlights
Introduction to the concept of an active low pass filter, which allows signals below a certain critical frequency to pass through.
Explanation of the active low pass filter circuit using an operational amplifier in inverting mode.
Description of the circuit components, including R2 resistance and C capacitance, which form the active low pass filter.
Presentation of the formula for calculating the critical or cutoff frequency of an active low-pass filter.
Identification of the filter as a first-order active low pass filter or Butterworth filter due to its specific frequency response characteristics.
Demonstration of the filter's response with a graph showing a flat region and a 20 decibels per decade falloff after the cutoff frequency.
Mention of the gain at the cutoff frequency being about minus 3 decibels with potential for slight experimental error.
Recommendation to watch another tutorial for a deeper understanding of the formula and frequency response graph.
Overview of the experimental setup for the active low pass filter circuit with a power supply for the operational amplifier.
Comparison of the experimental setup with the circuit diagram for clarity.
Application of a 20 Hertz input signal to the filter and observation of the output on a digital storage oscilloscope.
Observation of the phase difference between input and output signals due to the inverting configuration of the operational amplifier.
Process of measuring the output signal amplitude at various frequencies to plot the gain versus frequency graph.
Disclosure of the values of R2 resistance and C capacitance used in the circuit for reference.
Calculation of the theoretical cutoff frequency using the provided formula and comparison with experimental results.
Demonstration of the output voltage at the cutoff frequency and its comparison with the theoretical 70.7% of the input voltage.
Incremental increase of input frequency to observe the decrease in output voltage, illustrating the filter's behavior beyond the cutoff frequency.
Instruction to take multiple readings to plot a smooth curve of gain in decibels versus log of frequency.
Presentation of the final plotted curve matching the theoretical plot, demonstrating the successful experiment.
Invitation for viewers to ask questions or share doubts in the comment section for further clarification.
Transcripts
hey guys how's it going and in this
video I'm going to demonstrate the
working of an active low pass filter now
by definition a low pass filter only
allows signals with frequencies lower
than a certain critical frequency to
pass through it and if the filter
contains any active components such as
an op-amp that is an operational
amplifier then there is known as an
active low pass filter now to make the
active low pass filter I use this
particular circuit that you are seeing
on your screen now and the peculiar
thing about this circuit diagram is that
it uses the operational amplifier right
here in an inverting mode as you can see
that the input is given through the
inverting terminal that is the second
terminal of the 741 C operational
amplifier IC and free it's pretty basic
actually it's just a low-pass filter
circuit and using the R 2 and C and then
they have added an operational amplifier
to just amplify the input signal and
thus making the low pass filter
containing r2 resistance and the C
capacitance as an active low pass filter
now the formula for the critical
frequency or the cutoff frequency of an
active low-pass filter is given by 1 by
2 PI R 2 C and you can see that R 2 is
the resistance right here and sees this
capacitance right here so you can use
this formula to calculate what your trip
theoretical cutoff frequency should be
and then after you design
active low-pass filter and you can
verify if you are getting the same
results as I'm going to be doing in a
few moments from now now this particular
low-pass filter that I'm showing you is
also known as a first-order active low
pass filter or Butterworth filter
because if you take the input for a
variety of frequency and plot the key
versus those frequencies on a graph then
you get a graph of somewhat this kind
and a Butterworth filter has the
characteristic that this graph is almost
flat in this region and it falls off at
the rate of 20 decibels per decade after
the cutoff frequency which is being
shown by the screen line right here and
another thing to note is that at the
growl frequency the gain is about minus
3 decibels and we arrive at this result
quite erratically so you can have a
slight error when you perform this
experiment and since this is only a
practical demonstration so I will not be
going into any theory of the the this
graph or the low-pass filter however I
would recommend that you check out my
another tutorial on the active low pass
filter in which I explain how we arrive
at the formula for the cutoff frequency
and I also explain this graph right here
but if you only want the practical
demonstration then you can continue
watching this video and this is my
experimental setup for this circuit and
my power supply for the operation
amplifier let me just pull this frame
right here so that we can compare it
with the circuit diagram so this wire
right here is my input signal then this
resistance is r1 resistance which is
going into the second terminal after or
the second pin or two seven four once
the operational amplifier and as you can
see it with the circuit diagram there is
another resistance r2 popping over
towards our sixth pin of two seven four
one CIC and another capacitance that is
C as compared to the circuit diagram
which is going from the second terminal
or the second pin of the CERN for one C
is e to the sixth pin of the operational
amplifier since the sixth pin is for the
output and then there is another yellow
wire in this sixth then connected to the
six pin of the operational amplifier on
to the output of the operational
amplifier which will be would be of
observing on the DSO that is the digital
storage oscilloscope let me just get
them zoom in into towards the pins so
that you can see them even more clearly
okay so that's better and also note that
the seventh pin of this operational
amplifier is connected to the positive
terminal of the battery that is to our
to the 50 plus 15 volts and the fourth
terminal the yellow wire right here is
going towards the negative terminal of
the power supply
now I'm giving a 20 Hertz input signal
to this active low-pass filter and I'm
observing the output on the DSL let me
just hold this frame right here for a
moment now as you can see that the
yellow curve is for the input signal and
the blue curve is the output signal that
I'm getting from the active low-pass
filter now as you can see since we used
the operational amplifier in an
inverting configuration therefore both
the signals are out of phase now that we
can see that our low-pass filter is
working what we are going to do is we
are going to observe the output signal
for a variety of frequencies and then we
are going to plot the gain versus
frequency graph so I just set the
frequency generator at a particular
frequency let's say I said it at
approximately 40 Earth's 41 Hertz or 42
Hertz
and then go over to your DSO and observe
the input as well as output signal now I
have already measured my input signal to
be at around three point five two bowls
so what I'm going to do is I'm just
going to measure the the amplitude of my
output signal
okay so just turn on the cursor mode of
my DSO ad measure the amplitude of the
output signal and I'm getting somewhat
three point six zero volts as the output
voltage at 42 Hertz as can be seen from
the DSO so just no doubt that reading on
your observation file and change the
frequency again and note down that
reading too now I'm sorry I forgot to
tell you the values of the resistances
and the capacitances that I use in the
circuit before so let me just tell you
that the r2 resistance that I'm using is
of one pillow and the capacitance is of
point zero 1 micro farad and if you
calculate the cutoff frequency using the
former that I showed you before that was
one by two PI R 2 C then you get the
real frequency at about fifteen thousand
923 Hertz that is approximately sixteen
clothes so theoretically or as we will
also experiment leave my output voltage
will remain about somewhere between
three point five to three point 6 volts
up till I reach the cutoff frequency
since the input voltage that is a yellow
go right there is of three point six
zero volts or somewhere near that so the
cutoff frequency
I'm sorry so that output voltage will
also be somewhat and somewhere near that
up till I reach the critical frequency
and as you can see I am getting the same
voltage again and again now let's see
what we get at the cutoff frequency that
is 16 kilo Hertz as you can see I have
given 16 kilo Hertz input signal and I
am getting approximately two point six
two volts which is almost correct as at
the cutoff frequency I should be getting
70 point seven percent of the input
voltage and since the input voltage
three point 6 volts its 70.7% comes out
and about something two point five four
volts now let's increase the frequency a
little further and observe the output
voltage and just turn on the measuring
mode of your DSO I am just adjusting the
curve a little bit okay so if you
measure the output voltage now it would
be about two point five six volts or
five eight volts which is good and now I
have increased input frequency to about
twenty five kilo Hertz and the output
voltage is now two point one four volts
so just keep taking the readings of the
output voltage at various frequencies at
least I would say that you take at least
twenty five readings with below the
cutoff or the critical frequency and
then another twenty five readings above
the cutoff frequencies so that you have
approximately like at least fifty values
to plot a good curve between the output
voltage and the frequency or even you
can plot a curve between the gain and
frequencies so take a lot of readings
and make sure that you and the output
voltage at the cutoff frequency is at
about 70 point seven percent of the
input
and this is the curve that I got when I
plotted the gain in decibels on the
y-axis and log of the frequency along
the x-axis and as you can see I took a
lot of readings that's why I have gotten
a pretty smooth curve and it also
matches the theoretical plot in a very
good manner so that's how you perform
this experiment if you have any
questions or doubts don't forget to drop
them in the comment section down below
and I will definitely get back to you
and that's it thanks for watching and
have a great day head
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