RC Low Pass Filter Explained
Summary
TLDRThis video from the 'All About Electronics' YouTube channel delves into the fundamentals of passive electronics filters, specifically focusing on low-pass filters. It explains the concept of filters that allow low-frequency signals while attenuating higher ones. The script covers the types of filters, including low-pass, high-pass, band-pass, and band-reject, and emphasizes the distinction between active and passive filters. It then provides an in-depth look at the first-order RC low-pass filter, detailing its design, frequency response, and phase shift characteristics. The video also illustrates how to calculate the -3dB frequency and output voltage for a given input signal, offering practical insights into filter design and its applications.
Takeaways
- 🔧 Passive electronic filters are circuits that pass certain frequency components while rejecting or attenuating others.
- ⚙️ Filters are classified into four types: Low Pass Filter, High Pass Filter, Band-Pass Filter, and Band-Reject Filter.
- 📉 A Low Pass Filter passes signals from 0 Hz up to a cutoff frequency and attenuates higher frequencies.
- 📈 A High Pass Filter allows signals above a cutoff frequency to pass, while attenuating lower frequencies.
- 🔊 A Band-Pass Filter passes frequencies within a specific range and rejects those outside of it.
- 🔇 A Band-Reject Filter does the opposite, rejecting frequencies within a specific range and passing others.
- 📏 The cutoff frequency for a first-order RC low pass filter is determined by the formula 1/(2πRC).
- 🔬 Active filters use active components like Op-Amps and transistors, providing gain, whereas passive filters use resistors, capacitors, and inductors, and output less than the input.
- 📉 The output of a low-pass filter decreases as frequency increases, with the output at the cutoff frequency being 0.707 times the input.
- 🎚️ Higher-order filters provide sharper roll-off, with attenuation increasing by 20 dB/decade for each order.
Q & A
What is an electronic filter and what does it do?
-An electronic filter is a circuit that allows certain frequency components to pass through while rejecting or attenuating all other frequency components. It processes the input signal by filtering out unwanted frequencies.
How many types of filters are mentioned in the script, and what are they?
-Four types of filters are mentioned: Low Pass Filter, High Pass Filter, Band Pass Filter, and Band Reject Filter. Each type is designed to pass or reject specific frequency bands.
What is the primary difference between an active filter and a passive filter?
-Active filters are designed using components like Op-Amp and transistors, which can provide gain to the input signal. Passive filters, on the other hand, are designed using components like resistors, capacitors, and inductors, and the output is always less than the input.
What is the formula for calculating the cut-off frequency of a first-order low-pass filter?
-The cut-off frequency (fc) of a first-order low-pass filter is given by the formula fc = 1/(2πRC), where R is the resistance and C is the capacitance in the filter circuit.
What is the significance of the -3dB frequency in the context of filters?
-The -3dB frequency, also known as the cut-off frequency, is the frequency at which the output is 0.707 times the input, indicating a 3dB reduction in amplitude. It is a key parameter in determining the filter's performance.
How does the phase of the output signal change as the input frequency increases in a low-pass filter?
-In a low-pass filter, as the input frequency increases, the phase of the output signal lags behind the input signal. At the cut-off frequency, the phase lag is -45 degrees, and it approaches -90 degrees at very high frequencies.
What is the output voltage of a 10 V, 2 kHz sinusoidal input signal applied to the given low-pass filter in the script?
-The output voltage for a 10 V, 2 kHz sinusoidal input signal applied to the given low-pass filter is 6.22 V, as calculated using the formula for output voltage in the script.
How does the attenuation rate change with the order of the filter?
-The attenuation rate increases with the order of the filter. For an nth order filter, the roll-off rate is -20*n dB/decade, meaning higher order filters provide a sharper roll-off and greater attenuation at higher frequencies.
What is the purpose of cascading first-order low-pass filters to create a higher order filter?
-Cascading first-order low-pass filters increases the overall order of the filter, which results in a sharper roll-off and greater attenuation at higher frequencies, thus improving the filter's performance.
Why is it important to consider loading effects when designing higher order filters by cascading first-order filters?
-Loading effects occur when the input impedance of the second stage affects the output impedance of the first stage, potentially degrading the filter performance. To minimize this, the value of R2 should be at least 10 times R1, or active filters can be used to provide buffering between stages.
Outlines
🔌 Introduction to Passive Electronics Filters
This paragraph introduces the concept of electronic filters, which are circuits designed to allow certain frequency components to pass while attenuating others. It explains that filters can be categorized into four types based on the frequency band they allow: Low Pass, High Pass, Band Pass, and Band Reject filters. The focus then shifts to the Low Pass Filter, which passes low-frequency signals up to a cut-off frequency and rejects higher frequencies. The paragraph also distinguishes between active and passive filters, with active filters providing gain to the input signal and passive filters having an output that is always less than the input. The RC low pass filter is highlighted as the main subject for the video, explaining its design and function.
📡 Understanding the RC Low Pass Filter's Operation and Characteristics
This paragraph delves into the workings of the first-order RC low-pass filter, describing its circuitry and how it acts to pass low-frequency signals while attenuating higher frequencies. The output voltage formula is provided, showing the relationship between the input voltage, the reactance of the capacitor, and the resistor. The behavior of the filter at different frequency ranges is explained, including how the output voltage decreases as frequency increases, approaching zero at very high frequencies. The paragraph also discusses the frequency response of the ideal low-pass filter and the actual response, introducing the concept of the cut-off frequency (-3dB frequency) and how it is derived from the filter's components.
📚 Example Calculation and Higher-Order Filter Considerations
The final paragraph presents an example calculation to determine the -3dB frequency for a given low-pass filter and to find the output voltage for a specific input signal. It provides the formula for the cut-off frequency and demonstrates its application using given values of resistance and capacitance. The example includes calculating the reactance at a specific frequency and using it to find the output voltage for a 10V, 2 kHz sinusoidal input signal. The paragraph concludes with a discussion on the benefits of higher-order filters for achieving a sharper roll-off and the considerations involved in designing them, such as minimizing loading effects and the use of active filters as buffers.
Mindmap
Keywords
💡Passive Electronics Filters
💡Low Pass Filter
💡High Pass Filter
💡Band-Pass Filter
💡Band-Reject Filter
💡Active Filter
💡Passive Filter
💡RC Low-Pass Filter
💡Cutoff Frequency
💡Reactance
💡Attenuation
💡Phase Shift
💡Higher-Order Filters
Highlights
Introduction to passive electronics filters and their function in passing certain frequency components while attenuating others.
Classification of filters into four types: Low Pass, High Pass, Band Pass, and Band Reject based on the frequency band passed.
Explanation of the ideal low-pass filter's frequency spectrum and its characteristics.
Description of the High Pass Filter, its function, and ideal frequency response.
Introduction to Band Pass and Band Reject filters, their purposes, and how they manage frequency bands.
Focus on the Low Pass Filter and its further classification into active and passive types.
Differentiation between active and passive filters based on the components used in their design.
Advantage of active filters providing gain to the input signal, unlike passive filters.
Examples of passive low pass filters and the introduction of the RC low pass filter.
Design of a first-order RC low-pass filter using resistor and capacitor and its function.
Explanation of how the RC low-pass filter operates at different frequency ranges.
Derivation of the cut-off frequency formula for a first-order low pass filter.
Phase response of the low pass filter and its variation with frequency.
Example problem solving to find the -3dB frequency and output voltage for a given low pass filter.
Calculation of the cut-off frequency using the provided R and C values.
Determination of output voltage for a 10 V, 2 kHz sinusoidal input signal.
Discussion on the use of higher-order filters for sharper roll-off and attenuation of signals.
Comparison of the roll-off rates for different orders of filters and the concept of cascading filters.
Technical considerations for designing higher-order filters to minimize loading effects.
Advantages of using active filters in minimizing loading effects and providing gain.
Conclusion summarizing the understanding of passive RC low pass filters covered in the video.
Transcripts
Hey friends, welcome to the YouTube channel ALL ABOUT ELECTRONICS.
So, in the next couple of videos, we will learn about the passive electronics filters.
So, the electronics filter is the circuit which passes some frequency components in
the circuit and rejects or attenuates all other frequency components.
So, now based on the frequency band which is being passed by this filter, the filters
can be classified into four different types. The first is Low Pass Filter. So, this low
pass filter passes the low-frequency signals starting from 0 Hz up to the cut off frequency
fc. And beyond this cut-off frequency, it rejects
all other frequency components. So, if you see the frequency spectrum of the
ideal low-pass filter it will look like this. So, now the second type of filter is High
Pass Filter. So, this high pass filter passes all the high-frequency
components starting from the cut off frequency. And it rejects all the frequencies which are
lesser than this cut off frequency. And if you see the frequency response of ideal
high pass filter, it will look like this. So, the third type of filter is a band-pass
filter. So, this band pass filter passes the frequencies
which are in the certain band. And it rejects all the frequencies which are
outside this band. Then the fourth type of filter is the band
rejects filter. So, this band reject filter, rejects all the frequency components which
are under certain band and it passes all the frequencies out of this particular band.
So, in this video, we will focus on low pass filter.
So, now this low-pass filter further can be classified into two different types.
That is an active filter and passive filter. And this classification is based on the components
which are used for the design. So, now if the filter is designed using the
active components like Op-Amp and transistors then such filters are known as the active
low pass filters. While if the filters which are designed using
the passive components like resistor, capacitor, and inductor then such filters are known as
passive low pass filter. So, the advantage of the active filter is
that it also provides the gain to the input signal.
While in the case of passive low pass filter, or in general passive filters, the output
is always less than the input. So, the following are the examples of passive
low pass filters. So, in this particular video, we will concentrate
on the RC low pass filter. So, now the first-order RC low-pass filter
can be designed by connecting resistor and capacitor in this fashion.
So, now in this circuit, the input is provided at this end and output is taken across this
capacitor. So, now let's understand how this circuit
acts as a low-pass filter. So, now if you see, the output can be given
as Xc*Vin/(Xc +R)
where Xc is the reactance of this capacitor. And we know that Xc can be written as 1/wc.
So, now at lower frequencies, if you see, the reactance of this capacitor will be much
larger. So, the output will be approximately equal
to input. While if you go at higher frequencies, the
value of this capacitive reactance will reduce. And hence, the output will also reduce.
And at very high frequencies, the output will tend to zero.
So, in this way, this circuit will act as low pass filter.
So, it passes the low-frequency components in the input signal and rejects or attenuates
higher frequency components. So, now earlier we had seen that frequency
response of the ideal low-pass filter. But if you see the actual response, the actual
response will look like this. So, at lower frequencies, this filter provides
the zero attenuation or minimum attenuation and as the frequency increases the attenuation
will also increase. And the frequency at which the output is 0.707
times the input, that frequency is known as the cut-off frequency or (-3dB) frequency.
So, at this frequency, the output will be 1/√2 times the maximum value of the output
value. And after this cut off frequency, the output
will reduce at the rate of -20 dB/decade That means, if you increase the frequency
by 10 fold, then the output will reduce by the factor of 10.
So, this cut off frequency fc can be given by this equation.
That is 1/2πRC. So, now let's derive the expression for this
cut off frequency for the first order low pass filter.
So, earlier we had seen that Vout can be given as
Xc*Vin/(Xc +R) And if we only consider the magnitude then
we can write it as Vout= |Xc|*Vin/|Xc+R|
That means, |Vout/Vin| = |Xc|/√(R^2 +Xc^2) Now, at the cut-off frequency, the output
will be 1/√2 times the input. That means the gain or attenuation of the
system will be 1/√2. That is equal to (1/wc)/√(R^2 + (1/wc)^2)
And if we take square at both the sides then we will get
1/2 =(1/wc)^2/(R^2 + (1/wc)^2) And if we further simplify it then we will
get w= 1/RC
Or we can say cut off frequency fc= 1/(2πRC) So, now in the case of low pass filter, as
we increase the input frequency, not only the output of the signal will reduce but phase
will also get changed. And this phase can be given as -tan^(-1)
(wcr). So, now at w=0, if you see the value of phase,
value of phase will be nothing but -tan^(-1) (0)= 0
So, at w=0, the output will be in-phase with the input.
Now at cut off frequency if you see, the phase phi can be given as -tan^(-1) (1). As at cut
off frequency the value of w is equal to1/RC. So, at cutoff frequency, the value of phase
will be -45 degree. And now, if you look at w is equal to infinity,
phi in nothing but -tan^(-1) (∞)= -90 degree. So, now if you plot the phase vs frequency
curve, it will look like this. So, at zero frequency the phase will be 0
degrees and at cut off frequency, the phase will be -45 degrees.
That means output signal lags the input signal by 45 degrees.
And as we move away from the cut off frequency, the phase will move towards the -90 degree.
So, now as we know about the phase and frequency response of this low pass filter, now let's
take one example based on this low pass filter. So, in this example, we have been given one
low-pass filter. And in this example, we have been asked to find the -3dB frequency for
the given filter. And apart from that, we have been asked to
find the output voltage for the given applied input signal.
So, to this filter at the input side, 10 V sinusoidal signal of 2 kHz has been applied.
And we have been asked to find the output voltage for the given input signal.
So, now, first of all, let's find the cut-off frequency for the given low-pass filter.
So, as we know, the cut-off frequency can be given as
1/2πRC. And if we put the value of R and C, then we
will get the value of cut-off frequency as 1.59 kHz.
So, now we have been asked to find the value of output voltage at the 2KHz frequency.
So, earlier we had seen that the output voltage can be given as
|Xc|*Vin/√(R^2 + Xc^2) So, first of all, we need to find the value
of reactance at 2 KHz frequency. And we know that the capacitive reactance
can be given as 1/2fRC And now if put the value of frequency and
capacitance in this equation, then we will get the value of Xc as 796.
And if w put the value of Xc into this equation then we will get vout as
796*vin/√[(796)^2 + (1000)^2] Now, here Vin is nothing but 10V sinusoidal
input signal. So, if we further simplify it then we will
get Vout as 6.22 V. That means at the input side if we apply 10
V sinusoidal signal of 2 kHz frequency, then at the output, you will get 6.22 V of the
sinusoaidal signal. So, now if you plot the frequency response
for the given low-pass filter, then it will look like this.
And the cut-off frequency which we have found is nothing but 1.59 kHz.
And 2 kHz frequency will be around somewhere here.
So, at this frequency, we have found the output value as 6.22 V.
Now, suppose in your design if you want that, this 2 kHz signal should be attenuated as
much as possible then we should go for the higher-order filters.
And as we go for higher order filters, the slope of the decay will increase gradually.
So, now suppose let's say if you go for the second order filter, then at the second order
filter, the amplitude at 2 kHz will be lesser than the first order filter.
And similarly, if you go for the higher order filters, the amplitude at 2 kHz frequency
will reduce drastically. So, in this way using higher order filters,
we can achieve the much sharper roll-off. So, let's say if you are using the second
order filter, then the roll-off will be -40 dB/decade.
Or in general, we can say that if you are designing the nth order filter then decay
will be -20*n dB/decade. That means suppose if you are designing the
fourth order filter, then the roll-off will be -80 dB/decade.
And this higher order filters can be designed by cascading the first order low pass filters.
So, now let's see the second order low-pass filter.
So, here two first order low pass filters are cascaded.
And let's assume that the cut-off frequency of the first filter is fc1 and the cut-off
frequency of the second filter is fc2. So, the cut-off frequency of the overall second
order filter can be given as 1/2π√(R1C1R2C2)
So, now suppose R1=R2 and C1=C2, then the cut-off frequency can be given as 1/2πR1C1
So, now as we go for the higher order filters, the attenuation at the cutoff frequency will
also increase. So, for the first order filter, as we had
seen, the output is 1/√2 times the input at cut-off frequency.
So, now if you go to the second order filter then output is
1/√2 *1/√2 times of the input. That means the output is 0.5 times the input.
So, we can say that if we cascade the n number of filters with same cutoff frequency, then
the output will be reduced by the factor of (1/√2)^n *Vin
So, in this way, you will get sharp and sharp roll-off.
But designing this higher order filter is not as simple as it looks like.
Suppose you are designing the second-order low-pass filter, by cascading the two first
order low pass filters, so you should make sure that second stage of this low pass filter
should not get loaded by the first stage. And to minimise this loading effect, you should
choose the value of resistance R2 and C2 in such way that the impact of the first stage
will be minimised. And to minimise loading effect the value of
R2 should be at least 10 times the R1. And best way to minimise the effect of loading
is to use the active filters. because this active filters not only provides
the gain, but they also act as a buffer between the two stages.
So, we will see more about this active filter, once we complete all the passive filters.
So, I hope in this video you understood about the passive RC low pass filters.
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