Active Low Pass Filter and Active High Pass Filter Explained

Summary

This educational YouTube video from 'All About Electronics' delves into active low pass and high pass filters, contrasting them with passive RC filters. It highlights the limitations of passive filters, such as reduced output and load-dependent cut-off frequencies. The video then explores how active filters, using operational amplifiers (Op-amps) and transistors, overcome these issues by providing signal gain and maintaining cut-off frequency stability. Detailed explanations and examples are given for designing active filters, including buffer configurations and non-inverting amplifier setups. The video concludes with an exercise for designing a high pass filter with a 5 kHz cut-off frequency, encouraging viewers to apply their learning.

Takeaways

• 🔍 The video discusses active low pass and high pass filters, which are designed using Op-amps and transistors to overcome limitations of passive RC filters.
• 📉 Passive filters have limitations such as reduced output signal strength and cut-off frequency dependence on load, which active filters can mitigate.
• 💡 Active filters not only pass certain frequency bands but also provide gain to the input signal, enhancing signal strength.
• 🔌 Op-amps are used in active filters due to their high input impedance and low output impedance, which helps isolate the load from the filter circuitry.
• 🔄 The video demonstrates how to configure an Op-amp as a buffer, acting as a voltage follower with a gain of 1.
• 📌 The gain of an Op-amp in a non-inverting amplifier configuration can be adjusted by varying the feedback resistance and input resistance.
• 📐 The transfer function of an active low pass filter is derived and shown to be Av/√(1+(f/fc)^2), where Av is the voltage gain provided by the Op-amp.
• 🔄 The video explains how to design active filters that can avoid loading effects from both the input and output stages.
• 🎓 An example is provided to calculate the cut-off frequency for an active low pass filter, demonstrating the application of the formula 1/2πRC.
• 🛠️ The video concludes with an exercise for designing a high pass filter with a specified cut-off frequency and gain, encouraging practical application of the concepts discussed.

Q & A

What are the limitations of passive RC low pass and high pass filters?

The limitations of passive RC filters include the output always being less than the input signal, and the cut-off frequency depending on the load, which can modify the effective resistance and hence the cut-off frequency.

How do active filters overcome the limitations of passive filters?

Active filters overcome these limitations by using active components like Op-amps and transistors, which provide gain to the input signal and do not have their cut-off frequency affected by the load.

What is the main advantage of using an Op-amp in filter design?

The main advantage of using an Op-amp is its high input impedance and low output impedance, which allows it to act as a buffer to isolate the load from the filter circuitry.

How is an Op-amp configured as a buffer?

An Op-amp is configured as a buffer, or a voltage follower, by connecting the input to the non-inverting end and shorting the output to the inverting end, resulting in an output equal to the input with a gain of 1.

What is the formula for the gain of a non-inverting amplifier Op-amp configuration?

The gain of a non-inverting amplifier Op-amp configuration is given by 1 + (Rf/R1), where Rf is the feedback resistor and R1 is the input resistor.

What is the transfer function of an active low pass filter?

The transfer function of an active low pass filter is given by Av/√(1+(f/fc)^2), where Av is the voltage gain provided by the Op-amp, which is 1 + Rf/R1.

How is the cut-off frequency of an active low pass filter determined?

The cut-off frequency (fc) of an active low pass filter is determined by the expression 1/2πRC, where R is the resistor and C is the capacitor in the filter circuit.

What is the difference between an active low pass filter and a passive one in terms of frequency response?

While both active and passive low pass filters have a cut-off frequency where the output is 0.707 times the maximum value, active filters can also provide gain to the input signal, which passive filters cannot.

How can the effect of loading from the input stage be avoided in an active low pass filter?

The effect of loading from the input stage can be avoided by connecting the capacitor in the feedback path of the Op-amp, which changes the cut-off frequency to 1/2πRfC, with Rf being the feedback resistor.

What is the transfer function of an active high pass filter?

The transfer function of an active high pass filter is given by Av * (f/fc)/√(1+(f/fc)^2), where Av is the voltage gain provided by the Op-amp, which is 1 + Rf/R1.

How can higher order active filters be designed?

Higher order active filters can be designed by cascading first order active filters, which will be discussed in more detail in upcoming videos.

Outlines

00:00

🔌 Introduction to Active Filters

The video begins by introducing the topic of active low pass and active high pass filters. It contrasts these with passive RC filters, highlighting the limitations of passive filters such as reduced output signal strength and dependence of cut-off frequency on load impedance. The video then explains the advantages of active filters, which use op-amps and transistors to overcome these limitations, and provide gain to the input signal. The characteristics of op-amps, such as high input impedance and low output impedance, are discussed, and their use as a buffer to isolate the load from the filter circuitry is explained. The concept of using an op-amp as a voltage follower is introduced, demonstrating how it can act as a buffer with a gain of 1.

05:01

🔍 Active Low Pass Filter Configuration and Transfer Function

This section delves into the configuration of an active low pass filter using an op-amp. It explains how the op-amp can be set up as a non-inverting amplifier to amplify the filter output, with the gain determined by the feedback and input resistors. The video derives the transfer function for the active low pass filter, which includes both the voltage gain provided by the op-amp and the frequency-dependent response of the low pass filter. The cut-off frequency for the active low pass filter is shown to be the same as for a passive low pass filter, dependent on the resistor and capacitor values. Additionally, the video discusses how to modify the circuit to avoid loading effects from the input stage by moving the capacitor to the feedback path, which slightly alters the cut-off frequency.

10:07

🎚️ Active High Pass Filter Design and Frequency Response

The video then moves on to the design of an active high pass filter, starting with a unity gain buffer configuration using an op-amp. It explains how to amplify the filter output by adjusting the resistor values and derives the transfer function for the active high pass filter. This function includes the op-amp gain and the frequency-dependent response characteristic of a high pass filter. The video also discusses the frequency response of the active high pass filter, noting that while it theoretically passes high frequencies, practical limitations of the op-amp's gain characteristics may affect the response at very high frequencies. The video concludes this section by suggesting that active filters can be designed with input at the inverting end of the op-amp, leading to a different configuration with specific gain and phase characteristics.

15:13

🛠️ Designing Higher Order Active Filters and Exercise

The final part of the video discusses the possibility of cascading first-order active filters to create higher order filters, with more details to be provided in future videos. An exercise is presented to the viewers, challenging them to design a high pass filter with a specific cut-off frequency and gain requirements. The video concludes with a recap of the key points covered regarding active low pass and high pass filters, encouraging viewers to apply their understanding in the exercise and to share their designs in the comments section.

Keywords

💡Active Filter

An active filter is an electronic filter that uses active components such as operational amplifiers (op-amps) and transistors to provide gain to the input signal, in contrast to passive filters which do not require a power source. In the context of the video, active filters overcome limitations of passive filters by not only selectively passing certain frequencies but also amplifying the input signal. The video discusses active low pass and high pass filters designed using op-amps, highlighting their ability to maintain signal strength and adjust the cut-off frequency independently of the load.

💡Op-Amp

An operational amplifier, or op-amp, is a key component in active filters due to its high input impedance and low output impedance. The video explains how op-amps can be used as buffers to isolate the load from the filter circuitry, ensuring that the filter's performance is not affected by the load's impedance. The script also describes how op-amps can be configured as non-inverting amplifiers to amplify the filter output, with the gain determined by the ratio of feedback resistance to input resistance.

💡Passive Filter

A passive filter is a type of electronic filter that uses passive components like resistors (R) and capacitors (C) to filter signals. The video script contrasts passive filters with active filters, noting that passive filters have limitations such as reduced output signal strength and cut-off frequencies that can be affected by the load. Passive filters are simpler and do not require a power source, but they are less flexible and less powerful than their active counterparts.

💡Cut-off Frequency

The cut-off frequency in a filter is the point at which the filter starts to significantly attenuate frequencies. For low pass filters, it's the frequency below which signals are passed, and for high pass filters, it's the frequency above which signals are passed. In the video, the cut-off frequency is calculated using the formula 1/(2πRC) for both passive and active filters, with the script emphasizing how active filters can maintain a consistent cut-off frequency regardless of load.

💡Buffer

A buffer in electronics is a circuit that isolates parts of a system from each other, preventing signal degradation due to loading effects. The video script describes how an op-amp configured as a voltage follower can act as a buffer, maintaining the input signal's strength and phase at the output. Buffers are crucial in filter design to ensure that the filter's performance is not compromised by the input or output stages.

💡Non-inverting Amplifier

A non-inverting amplifier is a configuration of an op-amp where the input is applied to the non-inverting input and the output is taken from the same terminal, resulting in an output that is in phase with the input. The video explains how this configuration can be used to amplify the output of a filter, with the gain determined by the ratio of the feedback resistor to the input resistor. This is an important concept in the design of active filters where signal amplification is necessary.

💡Voltage Follower

A voltage follower is a specific configuration of an op-amp where the input is connected to the non-inverting terminal and the output is taken from the inverting terminal, resulting in an output that is equal to the input. The video script uses the voltage follower as an example of how an op-amp can act as a buffer, with a gain of 1, meaning the output signal's amplitude is the same as the input.

💡Transfer Function

The transfer function of a filter is a mathematical representation of the filter's response to input signals of different frequencies. It is typically expressed in terms of the output-to-input ratio as a function of frequency. The video script derives the transfer functions for both active low pass and high pass filters, showing how they incorporate both the voltage gain provided by the op-amp and the frequency-dependent response of the filter.

💡Unity Gain

Unity gain in the context of an amplifier or filter refers to a gain of 1, meaning the output signal has the same amplitude as the input signal. The video script mentions unity gain in the context of a high pass filter configuration where the op-amp is used as a buffer to isolate the load without changing the signal's amplitude.

💡Inverting Configuration

An inverting configuration of an op-amp is where the input is applied to the inverting input and the output is taken from the same terminal, resulting in an output that is 180 degrees out of phase with the input. The video script discusses how active filters can also be designed using this configuration, which results in a phase inversion and a gain that is the negative ratio of the feedback resistor to the input resistor.

Highlights

Introduction to active low pass and active high pass filters.

Limitations of passive filters, including reduced output signal and load-dependent cut-off frequency.

Active filters overcome passive filter limitations by providing gain to the input signal.

Active filters are designed using active components like Op-amps and transistors.

Op-amps have high input impedance and low output impedance, making them ideal for buffering.

Configuring Op-amps as voltage followers acts as a buffer in filter circuits.

Non-inverting amplifier configuration of Op-amps allows for adjustable gain.

Derivation of the transfer function for active low pass filters.

Explanation of how the cut-off frequency remains the same for active low pass filters as for passive ones.

Active low pass filter example calculation for determining cut-off frequency.

Active high pass filters can also be designed with unity gain using Op-amps.

Transfer function for active high pass filters includes both Op-amp gain and filter response.

Derivation of the transfer function for active high pass filters.

Frequency response characteristics of active high pass filters and their limitations.

Inverting configuration of Op-amps for designing active filters and its effects on gain and phase.

Cascading first-order active filters to design higher order filters.

Exercise for designing a high pass filter with a specified cut-off frequency and gain.

Summary of active low pass and high pass filter concepts covered in the video.

Transcripts

Hey friends, welcome to the YouTube channel ALL ABOUT ELECTRONICS.

So, in this video, we will learn about the active low pass and active high pass filter.

So, in the last couple of videos, we had seen that how by just using the resistor and capacitor

we can design the passive RC low pass and high pass filters.

But these passive filters have some limitations. The first limitation is that the output of

this passive filter will be always less than the input signal.

And when you cascade many of such filters to design the order filter, the output will

be even much lesser than the input. And not only that the cut-off frequency of

such passive filters will also depend upon the load.

So, depending upon the load value the cut-off frequency of such passive filters will get

modified. Like as you can see in this high pass passive

filter, depending upon the load value the effective resistance of this filter will get

modified, and hence the cut-off frequency will also get modified.

So, these problems can be overcome by using the active filter.

So, this active filter not only selectively passes the certain band of frequencies, but

it also provides the gain to the input signal. And as its name suggests, these active filters

are designed using the active components like Op-amp and transistors.

So, in this video, we will see the active low pass and the high pass filters which are

designed using the Op-amp. Now, the main advantage of Op-amp is, it has

very high input impedance and very low output impedance.

So, because of these characteristics, we can use Op-amp ass buffer to isolate the load

from the filter circuitry. Or may be we can use it to isolate the different

stages of the filter. So, now let's see how we can use this Op-amp

as a buffer. So, when we configure Op-amp as voltage follower

circuit, then it will act as a buffer. So, in that case, we are providing input to

this non-inverting end of this Op-amp and output is getting shorted with the inverting

end of the op-amp. So, in this configuration, the output will

be equal to the input. So, we can say that the gain of the gain of

the Op-amp is 1. So, in this configuration suppose if we connect

our filter circuit at this non-inverting end and if we take the output at this end then

this Op-amp will act as a buffer between the load and the filter circuit.

But in this configuration, the gain of the Op-amp will be 1.

So, now suppose if we want to amplify the filter output, then we can configure this

Op-amp in this configuration. So, this is known as the Non-inverting amplifier

configuration of the Op-amp, in which we are providing input at the non-inverting end and

we are taking output over here. So, in this configuration, the gain or DC

gain of this Op-amp will be 1+ (Rf/R1) So, by changing the value of this feedback

resistance, and the value of R1, we can change the gain of this Op-amp.

So, in this configuration, suppose if we connect our filter circuit at this end, then the output

of the filter will get amplified by this factor. And the circuit will look like this.

So, here will be the input to the filter and here we will take the output of this filter.

And let's say the intermediate stage which is the input to this Non-inverting end will

be Vx. So, for the low- frequencies, the gain which

is being provided by this Op-amp will be (1+Rf/R1) And let's denote that gain by symbol Av.

That is Voltage gain that is provided by this Op-amp.

Now, in this configuration, the cut-off frequency will be fc that is equal to 1/2πRC, which

is the same expression that we got for the passive low pass filter.

So, now earlier in the case of passive low pass filter, we had seen that the ratio of

output divided by the input is known as the transfer function of this filter.

So, let's see how we can write the transfer function for this active low pass filter.

So, the transfer function of this active low pass filter can be given by the equation

Av/√(1+〖(f/fc)〗^2 ) Where Av is nothing but 1+ Rf/R1

That is the gain that is provided by the Op-amp. So, in this expression, there are two components.

The first is the voltage gain of the Op-amp, that is Av.

And the second component is this expression. That is 1/√(1+〖(f/fc)〗^2 )

And that is the response of low pass filter. And if you are wondering how we have arrived

at this expression, so let's derive this expression. So, in the case of passive low pass filter,

we had seen that the output can be given by the expression Xc*Vin/(Xc+R)

Or we can write this expression as |Vout/Vin| = |Xc|/√(R^2+Xc^2 )

Or we can write it as (1/wc)/√(R^2+(1/wc)^2 )

Now, suppose if we multiply numerator and denominator by the term wc, then we will get

1/√((Rwc)^2+1 ) Now, we know that for the low pass filter,

the cut-off frequency wc can be given by the equation 1/RC

So, we can write this expression

as |Vout/Vin| = 1/√(1+(w/wc)^2), where w is nothing but 1/RC

And if we write this expression in terms of the frequency then we can write it as

1/√(1+(f/fc)^2) So, in this way, we got the expression for

the output over input for the passive low pass filter.

And if we multiply this expression by the op-amp gain then that will be multiplied by

the expression 1+(Rf/R1) So, this will be the transfer function of

Active Low- Pass Filter. And if we see the frequency response of the

active low pass filter, it will be very similar to the passive low pass filter.

So, this filter have a cut-off frequency of fc, where the output will be 0.707 times the

maximum value. So, now so far we had seen that by using the

op-amp, we can isolate the load and the filter circuit.

But what if my input that is coming to this filter is also coming from the another circuitry.

So, in that case, it is quite possible that depending upon the impedance of that circuit,

the cut-off frequency of this filter will get changed.

And to avoid that what we can do, we can provide that input to this filter by using the one

buffer circuit. But in that case, we will require one more

buffer. And if we want to eliminate one more buffer,

then what we can do, we can connect this capacitor in the feedback path.

And that circuit will look like this. So, in this case, we are applying the input

at the non-inverting end and instead of connecting the capacitor at this end, we have shifted

that capacitor in the feedback path. So, now let's understand how this circuit

will also act as low pass filter. So, at low frequencies or let's take the extream

case at zero frequency, the value of Xc will be infinity.

And hence, the parallel impedance of this Xc and Rf will be Rf.

So, at low frequencies, the gain that is provided by this Op-amp will be 1+ Rf/R1

And as we move towards the higher frequencies, or let's take the case at f is equal to infinity,

the value of this reactance will be zero. and in that case, this op-amp will act as

a voltage follower. So, at that time the output will follow the

input. And hence the gain will be equal to 1.

So, in this way, this circuit will also act as a low pass filter.

And by using this configuration, we can avoid the effect of loading from the input stage.

But the cut-off frequency for this filter can be given by the expression 1/2πRfC.

So, as you can see, our cut-off frequency has been slightly modified.

Because now, the resistance which decides the characteristics of the filter is not R

but this feedback resistor Rf. And the gain of this op-amp will be given

by the expression 1+ Rf/R1 Alright, so now let's take one example based

on this active low pass filter. So, in this example, we have been given to

find the cut-off frequency for the given filter. So, as you can see here, this filter is used

in the non-inverting configuration. And we know that the cut-off frequency expression

for this filter will be 1/2πRC. Now, here the value of R is 10-kilo ohm and

value of the capacitor is 0.1 micro Faraday. So, now if we put all the value of resistance

and capacitance, then the cut-off frequency will be approximately equal to 159 Hz.

And if you see here, the gain of this filter will be 1+Rf/R1, that is nothing but 5.

so, in this way, suppose if you are applying the signal of 1V, with 1Hz frequency, then

at the output, you will get output signal of 5V, with 1Hz frequency.

So, now like we have designed the active low pass filter, similarly, we can design the

active high pass filter. And here is the circuit of active high pass

filter with unity gain. So, here this Op-amp will be used as a buffer

to isolate the load and the filter circuitry. And suppose if we want to amplify the filter

output, then we can configure this high pass filter in this configuration.

Which is very similar to the equation we had seen for the active low pass filter.

So, the gain of this filter will be 1+Rf/R1 And the cut-off frequency fc can be given

by the expression 1/2πRC So, in this filter, we are applying input

at this end and we are taking output over here.

So, now let's see the expression for the transfer function for this active high pass filter.

So, the transfer function for this active high pass filter can be given by the expression

Av* (f/fc)/√(1+〖(f/fc)〗^2 ) So, here Av is nothing but 1+Rf/R1

That is the gain which is provided by the Op-amp.

So, again here as you can see this expression has two components.

One is the gain that is provided by the Op-amp and one is the response of high pass filter.

So, now let's derive this expression. So, in the last video, we had seen that for

the high pass filter, the ratio of output over input can be given by the expression

R/√(R^2 + Xc^2) Or, we can say that R/√[R^2 + (1/wc)^2]

So, now if we multiply numerator and denominator by the term wc, then we will get Rwc/√[(Rwc)^2+

1] And we know that for the high pass filter,

the cut-off frequency will be 1/RC. So, we can write this expression as (w/wc)/√(1+〖(w/wc)〗^2

) And

if we write in term of the frequency then we can say that (f/fc)/√(1+〖(f/fc)〗^2

) So, this will be the expression of the transfer

function for the passive high pass filter. And if we multiply this expression by the

gain of Op-amp, then we will get an expression for the Active high pass filter.

So, now if we see the frequency response of this active low pass filter, it should look

very similar to the passive high pass filter.

That means, it rejects the low-frequency components and it passes all the high-frequency components

up to the infinity. But if you see the actual filter, it will

not pass all the frequency components up to the infinity.

And the frequency response is limited by the electrical components that are used in the

design, particularly in this case, if you see, the response is limited by the gain characteristic

of the op-amp. So, if you see the gain characteristic of

the Op-amp, it will look like this. So, this op-amp provides the flat response

for frequencies let's say up to the 100 kHz or may be 1 MHz.

And if you go beyond this frequencies, then you will see the reduction in the gain.

So, now if we see the combined response, then the combined response of this active high

pass filter will look like this. So, this will be the response of our active

high pass filter. So, now so far, what ever active filters we

have designed, we have provided the input at the non-inverting end of this Op-amp.

But we can also design this active filters by providing the input at this inverting end.

And if you see the active low pass filter in the inverting configuration, it will look

like this. So, here in this inverting configuration,

the gain of the op-amp will be -Rf/R1. So, as you can see, the gain will be -Rf/R1,

so the output will be 180 out of phase with the input.

And the cut-off frequency fc can be given by the expression 1/2πRfC

Similarly, we can design the active high pass filter in the inverting configuration.

That means we are providing the input at this inverting end of the Op-amp.

So, now suppose, if you want to design the higher order filters, then we can cascade

this first order active filters, and we can design the higher order filters.

And we will see more about it in the upcoming videos.

So, before I end up this video, here I am giving you one exercise, which is very simple.

So, as you can see in this example you have to design the high pass filter which is having

a cut-off frequency of 5 kHz. And not only that for this filter, when ever

you are applying input signal let's say of 100 mV with the frequency of 10 kHz, then

at the output you should get an output of 1V with 10 kHz.

So, you have to select the value of this Rf, R1, C, and R in a such a way that all these

criteria will be fulfilled. And do let me know your designed values in

the comment section below. So, I hope in this video you understood about

the active low pass and the active high pass filters.