To define a rheostat, we need to know what is Resistor or Resistance. Resistors are electrical devices that are to controls the flow of current. A formal rheostat’s definition will be –
“Rheostat is an element of an electrical circuit whose resistance value can be changed whenever needed, that means a variable resistor.”
It is a three-terminal device, of which two are usable. There is a slider as a moving terminal, and only one is usable out of two fixed terminals. A typical rheostat also consists of a resistive material and a slider.
What does a rheostat do
The basic principle of this device is simple. In electrical circuits, whenever we need to change the resistance value, a rheostat comes into action. If we need to increase the flow of current – we will increase the resistance of the device. When we need to decrease the current flow in the circuit, we will raise the resistance value.
How does a rheostat work
Rheostat works on the property of resistance. The resistance of a material (let’s say wire) depends linearly with the length and inversely with the cross-section area.
R∝L/A
R=?L/A,
?is the resistivity of the material
Thus, if we keep the cross-section area constant, increasing the length will increase the resistance. As shown in the figure, the slider- is moved through the resistive element for linear rheostats. It moves either from input to output or vice-versa. The effective length changes accordingly. While moving the wiper towards the output port, the effective length decreases, causing a fall in resistance, increasing the current.
Working of a Rheostat
Rheostat symbol
Institute of Electrical and Electronics Engineers(IEEE) and the International Electrotechnical Commission(IEC), has defined two different rheostat’s symbols.
The IEEE standard Rheostat symbol
The IEC standard Rheostat symbol
Rheostat Switch
Rheostats control current of a circuit by controlling the resistance of the circuit. A rheostat, thus, can be used as as switch to vary the resistance as well as the current of the circuit. That is why a rheostat is used as switch.
RheostatsApplications
A rheostat has its application in an electrical circuit. When there’s a need to control the flow of current with a change of time. Based on the property of current controlling, some of the purpose of rheostat is given below.
Why is a rheostat connected in series?
To connect rheostat in the circuit, we must place it in series, not in parallel. The flow of current is much in a lesser resistive path. Thus, when it finds an option between a less resistive path and a more resistive path, it always chooses the lesser one.
Now, a rheostat is a device that has some variable resistance value. If we connect it to the parallel path, that path gains some more resistance than the other way available. When current flows in the circuit, electrons will never choose the parallel-path instead- they will flow straight through the series path. So, the rheostat will not function at all. It needs the current flow to work as a rheostat.
Series Connection
Type of Rheostat
Though there are several types of rheostat available, three main types are –
Linear Rheostats
Rotary Rheostats
Preset Rheostats
A. Linear Rheostats:
This type of rheostat consists of a cylindrical resistive element. The slider is moved linearly along the resistive element. It has two fixed terminals; one- is used, and another connects the slider. This type of rheostats is mostly used – in laboratories and experiment purposes.
This type of rheostat has a resistive element, which is circular. To use it, one needs to move the slider in a rotary way. They find applications in power electronics and also, they are used widely because of their smaller size than linear types. As the wiper needs to rotate to change the value, that’s why it is called a rotary rheostat.
When it is needed to implement a rheostat in a PCB (Printed Circuit Board), one should use preset rheostats or trimmers. It provides fine-tuning, that’s why they have found application in calibration circuits. This types of rheostats are suitable for industrial uses.
Differences between rheostat and potentiometer
There is a misconception that a rheostats and potentiometer are the same things, but there are some differences. Let us discuss some of them –
Rheostats are rated – in Amperes and Watts. There is also a resistance value. For example – 50W – 0.15 A, 100k Ohm. It means the maximum amount of current that can be measured is 0.15A. The resistance offered by the rheostat will be in the range of 0 to 100k Ohm.
2. How to select a rheostat based on rating?
While selecting a rheostat, the current rating is more important than the power rating.
It is the current that limits what power the device will generate provided for any resistance value. One should select rheostats with a current rating more than or equal to the actual need of current in the circuit.
3. What are the differences between resistors and rheostats?
A resistor is a passive electronic component that reduces the flow of current by providing resistance. On the other hand, rheostats are – variable resistors, which gives different values of resistances as per the need.
4. What is the function of a rheostat in the circuit?
A. It decreases the current
B. It increases the current
C. It limits the current
D. It makes the current constant in the circuit
E. All of the above
The correct option will be E. All of the above. Using Ohm’s law, we can find the answer to the question. As the ohm law states, V = IR, where V is the applied voltage, I is current, and R is the resistance. Rheostat provides variable resistances value; thus, it can increase, decrease, and limits the current. Keeping the resistance value constant will keep the current steady. So, all the options are correct.
5. Can rheostats be used as a potentiometer?
The answer is no, but there is some way to do this. A rheostat is a two-terminal device, while a potentiometer is a three-terminal device, so it seems impossible. But if a rheostat has inbuilt three terminals, the unused terminal can be joined to the circuit to use it as a potentiometer.
6. Can potentiometers be used as a rheostat?
Yes, a potentiometer is usable as a rheostat. A potentiometer controls voltage in a circuit. A potentiometer has three terminals. One terminal should connect the wiper while another should leave unconnected.
7. What are the drawbacks of using a rheostat?
There are few drawbacks of using this device. Some of them are –
A. The main drawback of this device is that it produces excessive heat causing loss of power.
B. It is bigger & does not fit into modern devices. That’s why rheostats are not used – in modern technologies. Though in rotors and various laboratory experiments, they are irreplaceable. Some of the replacements of rheostats are – triacs, SRCs, etc.
8. What type of taper a rheostat has?
Rheostat has linear types of taper. A taper is a relationship between resistance and sliding position. It is one of the most important parts of the device.
9. What is the use of a rheostat in a Wheatstone Bridge?
A Wheatstone bridge is used in labs to measure mean value resistances. Rheostats find its application in a Wheatstone Bridge to determine the value of unknown resistance in imbalanced conditions. The maximum resistance a rheostat can offer is the maximum resistance that a mounted Wheatstone Bridge can measure.
10. Why is choke of a coil preferred over a rheostat in AC circuits?
A rheostat is a resistive element. It provides resistance and produces an excessive amount of heat. So it causes a loss of electricity. On the other hand, a choke coil is an inductive element by nature. It maintains the same power but changes voltage according to Faraday’s Law. That is why a choke coil is preferred more.
11. Does a Rheostat change voltage?
No, a rheostat doesn’t change the voltage of the circuit. One of the conditions for working of a Rheostat is to keep the voltage constant. As the Ohm’s law states- V= IR, where V is the voltage, I is current, R is resistance. Using a rheostat, we change the current. One of the conditions for working of a Rheostat is to keep the voltage constant. Then only it can change the current of the circuit.
12. Does a rheostat’s terminal have polarity?
A rheostat is a three-terminal device of which two are fixed, and one is a moving terminal. The terminals have no polarity. So, any terminal can be connected.
“Band reject filter is combined of low pass and high pass filter which eliminates frequencies or stop a particular band of frequencies.”
Band rejection is obtained by the parallel connection of a high pass section with a low pass section. Now, the general rule is that, the cutoff frequency should be higher than the cut-off frequency of the low-pass area.
There is another way to create it. If a multiple feedback system is incorporated with an adder, then that functions like the desired operation. It is called as notch.
The Frequency response of a bandstop filter is calculated by considering the frequency and gain.
The bandwidth is chosen through the lesser and greater cut-off frequency. Notch filter is used to remove the single frequency. From this frequency response, we can also obtain Passband ripple and stopband ripple.
Where ∂p= magnitude response of the passband filter
∂s= magnitude response of the stopband filter
The frequency response of a band-stop filter
Why It is called band stop filter ?
Bandstop filter rejects a certain band of frequency and allows another frequency component of the primary signal. If the band of the frequency is narrow, the stopband filter is known as Notch Filter. The filter attenuates the specific band. The filter has several applications.
For example, a band-stop filter is designed to reject frequencies between 2.5 GHz to 3.5 GHz. The filter will allow frequency components lower than 2.5 GHz and above 3.5 GHz. The filter will We will explore the filter in the below sections.
Passband and stopband of a filter
Before diving into a band-reject or bandpass details, let us understand what pass band and stop band means. A passband is the frequency bandwidth that is allowed by a filter. On the other hand, a stopband is the band of frequency which one filter hasn’t allowed to pass. For a bandstop filter, there are two passbands and one stopband.
What does a band-stop filter do?
As the name suggests, a band-stop filter simply ‘stops band.’ That means a band-stop filter resistor doesn’t allow a certain band of frequency to pass through the
What is a band-stop filter used for
When there is a need to attenuate a certain band of frequency and pass other frequency components, a band-stop filter is used. Bandstop filters are useful in various applications.
Band stop filter applications
Being a very important type of filter, bandstop filters has several applications. Let us find out some of the applications.
Medical Engineering: Bandstop filters are used in medical engineering. Like – in ECG machine. 60 Hz bandstop filters are used to remove the supply frequency from the output.
Audio Engineering: Bandstop filters have huge applications in audio engineering. They remove the unwanted spikes and noises from the score and provides a good quality of audio.
Telecommunication: Bandstop filters are used in telephonic connections to remove the internal noise from the lines.
Radio communication: Band rejects filters are widely used in radio stations to transmit a better audio quality.
Optical filters: Band-stop filters are used to block certain wavelengths of light in an optical communication system.
Digital Image Processing: Bandstop filters are also used in digital image processing to remove certain periodic noises.
Miscellaneous: Whenever there is a need to remove the noise of a certain frequency, a band-stop filter is used.
Band stop filter diagram
This article explains the bandstop filter with various circuit diagrams, block diagrams, and graphs. This article includes a block diagram, band reject-with op-amp, frequency response of band stop, passive circuits, bode plots.
Circuit diagram of band-stop filter
The bandstop filter can be designed in several ways. It can be active types (which has op-amp). It can be for passive kinds (without op-amp). Active types have several varieties, too as well as passive filters have different styles too. That is why there are several circuits available also. In this article, almost all possible courses are given below. Check out the needed one.
Band stop filter block diagram
The bandstop filter is a combination of both high pass filters as well as low pass filters and another amplification factor for the filter. The block diagram is given below.
Narrow band stop filter
If the freq. of the bandstop filter is narrowed than general, the filter is often known as a Notch filter(hyperlink) or narrow bandstop filter.
Simple band stop filter
Unlike notch filter or higher-order filters, the simple bandstop filter is a basic filter which attenuates certain band of frequency allowing other bands.
Band stop filter using op-amp
Active bandstop filters are designed using operational amplifiers. Op-amp is one of the most important devices in making a filter. In passive filters, as there is no op-amp, there is no amplification. Thus, using the op-amp as a circuit element gives amplification.
Bandstop filter circuit using op-amp
This filter consists of a high-pass filter, a low-pass filter, and a summing amplifier to summation the lpf and hpf’s o/p, The circuit is shown below.
Band pass filter vs Band stop filter
There are fundamental differences between bandpass and bandstop filter.
The main principle of a bandpass filter is that it allows a certain band of frequency. At the same time, the main tenet of the bandstop filter is that it blocks a certain band of frequency.
Let us take an example to demonstrate. Let us say there is a lower cutoff frequency of Flow and a higher cutoff frequency high. Now, for a bandpass filter, the frequency in between the lower cutoff and higher cutoff will only pass, and other components below the Flow and above the fhigh will not pass.
Now, for a band-stop filter, the frequency band lower Flow, and above fhigh will pass. But the band in between the frequency limit will not pass.
Band stop filter vs notch filter
A notch filter is one type of bandstop filter. The main difference between them is that a notch filter attenuates a narrower band of frequency than a bandstop filter. In other words, bandstop filters have a wider band of frequency to attenuate.
Band stop filter RLC circuit
The band stop filter can be designed using basic components like resistor, capacitor, and inductor. There are two ways of developing the filter – 1. RLC parallel band-reject filter or Parallel resonant band-reject filter, & 2. RLC series resonant band-reject filter. As we are using passive elements, so both the filters will be of passive types.
Parallel RLC band stop filter
As mentioned earlier, a bandstop filter can be designed with basic components like – resistor, capacitor, and inductor. There are two ways of developing the circuits. The methods are discussed below.
Parallel RLC band stop filter
A Parallel RLC bandstop filter is a tank circuit. It also works fine as a frequency attenuator as the tank circuit is providing a lot of impedance. The below image shows the circuit diagram of a parallel rlc bandstop filter.
The parallel resonant band stop filter
The parallel resonant bandstop filter is also known as the parallel rlc bandstop filter. The details of the circuit and filter are given previously.
Series resonant bandstop filter
The main instruments for this filter are – capacitor and inductor. As the name suggests, the inductor and capacitor are kept in series. This part is the filter. At resonance, the circuit can attenuate certain frequencies before reaching the load. The below image shows the circuit diagram of the series resonant circuit.
Passive bandstop filter circuit
The passive bandstop filter is made of passive components, such as – resistor, inductor, and capacitor etc. Previously given circuits are an example of such filters. These filters do not have any operational amplifiers. Thus, there is no amplification process. A passive band stop filter consists of both passive hpf and passive lpf.
Active band stop filter
Unlike passive bandstop filters, active band-reject filters come with active components. The most important active part is the operational amplifier which also introduces amplification. Circuit using op-amp or the functional bandstop filter diagrams are given previously in this article.
Active bandstop filter design
Let us design a band stop filter. The center frequency will be 2 KHz. The bandwidth will be -3 dB of 200 Hz. Take capacitor value as one uF.
The depth in decibel comes as: 20log (0.1) = -20 db.
Band stop filter transfer function
The transfer function of a device refers to a mathematical function that provides output for every input. The transfer function of a band-stop filter is given below.
The second-order band-stop filter transfer function
The transfer function expression for the second-order band-stop filter transfer function is given below.
Band stop filter graph
The phase response stands for the phase output of the bandstop filter, bottom one represented the phase response.
The bandwidth of the bandstop filter depends on the requirement. The band-width is the range of freq. in which the filter will attenuate. In general, the bandwidth is referred to as the specification of a filter.
The impulse response of band-stop filter
Bandstop or band-reject filter can be designed digitally. There are two types of digital band-reject filters, They are – Infinite Impulse Response(IIR) and Finite Impulse Response(FIR). FIR method is more popular.
There are two design methods of FIR filter. They are also known as non-recursive filters. The methods are – 1. Window method & 2. Weighted-Chebyshev method.
Sallen key band stop filter
Low pass filters allow the lower frequency components of a filter and reject the higher frequency components. So, for the low pass filter, the stopband is the high-frequency component.
Sallen key is another topology of designing filters. The bandstop filter can also be created using the topology. Sallen key topology is designed using operational amplifiers for creating higher-order filters. Thus, we can understand this topology is for active filters.
Basic Sallen Key topology comes with one non-inverting op-amp and two resisters. It creates a Voltage Control Voltage Source or VCVS circuit. The circuit provides high input impedance and low output impedance which useful for filter analogy.
This Sallen Key topology also provides good stability of the system, which is highly suggested. The circuit is also very simple. They are connected one after another to achieve the higher-order filters. The circuit diagram of the band-reject filter using Sallen key topology is given below.
Band stop filter formula
There are some important equations for designing a band stop filter. Using these equations, we can find out important parameters. But one of the values of the parameter should be supplied as it is needed to design the filter.
The Normal Frequency Equation:
The Lower Frequency Cut-off:
The Higher Frequency Cutoff:
Here, the RL is lower resistance, and RH is higher resistance.
The center frequency:
The bandwidth: fBW = fH – fL
The Q Factor of the filter: Q = fC/fBW
Band stop filter example
The bandstop filter is an important concept that has several applications. That is why there are several examples as well. There is a band stop filter for blocking certain frequencies. Like – 2.4 GHz Band Stop filter. There is a band-reject filter for blocking narrower frequency bands, like the Notch filter, which has several applications. Audio bandstop filters, optical band-reject filters, digital-analog filters are some of its examples.
60 Hz band stop filter
From the filter’s name, we can understand that this bandstop filter is designed for attenuate frequency bands of 60 Hz. Now, the question comes why the 60 Hz band reject filter is so popular. It is because, in the USA, their supply frequency is 60 Hz. So, in most cases, when there is an interference of the supply frequency with the working signal, a 60 Hz bandstop filter is used to remove the frequency band from the output.
Band stop filter bode plot
At first, let us understand what the abode plot means. Abode plot refers to the graph of the frequency response of a device. The freq. response of the band-reject filter is presented below.
The cutoff frequency of a band-reject filter refers to the frequency of the band to be attenuated. There are formulas for lower frequency cutoff and higher frequency cutoff.
The lower cutoff frequency: fL = 1 / 2π RL C
The higher cutoff frequency: fH = 1 / 2π RH C
Band stop filter image processing
The bandstop filter is used in image processing. There are some different kinds of noises. The noises are repetitive. They have certain frequencies. A band-stop filter omits such noises. At first, the frequency is matched with the noise frequency. Then the bandstop filter removes the noises and makes the image a better one.
Band stop filter pole-zero plot
A band-reject filter can be designed using two zeros placed at ±jω0. These types of designs don’t have a unity gain at zero frequency. A notch filter can be developed by putting two poles close to the zeros.
Bandstop filter using op-amp 741
As mentioned earlier, band-reject filters can be designed using operational amplifiers. That is known as creating active band-reject filters. The band-reject filters consist of both low pass and high pass filters. Both these filters require operational amplifiers to design. Op-amp 741 is used here. Another summing op-amp is also necessary to sum the outputs of the previous filters and provide amplification. Op-amp 741 can be used in all those cases.
Band stop notch filter
A bandstop notch filter is just a special type of band-reject filter. Bandstop notch filter has a narrower bandwidth than usual band-reject filters. To know more about the notch filter, check out my article on Notch filter.
Band stop vs. Bandpass filter
The name of both the filters explains the difference between them. Here band means the range of frequency. Bandpass filter allows the specific band to pass through the filter and attenuates other components. At the same time, band-reject filters attenuate the particular band of frequency while it will enable other parts.
Characteristics of band stop filter
The bandstop filter has several characteristics. Some of them are listed below.
It has two passbands and one stopband.
It comes with a combination of lpf and a hpf.
If the bandstop filter has a narrow bandwidth, it is a notch filter that has great depth.
Bandstop filters are also known as band-reject filters as it ‘rejects’ the specified band.
Constant k band stop filter
Constant k filter is another topology of designing a filter. It is quite a simple topology, but it has a shortcoming. Here, the ‘k’ is referred to as the impedance level of the filter. It is also known as the nominal impedance. The terminating resistance is also considered as ‘k’ ohms (Rk2 = k2). The bandstop filter using constant k topology is shown below.
Design Procedure: At first, the center frequency, the bandwidth, and the intended characteristic impedance should be specified. Then follow the steps.
Calculate C2 using wH -wL = RkC2w02/2.
Calculate L2 using L2 = 1/w02C2.
Calculate L1 using L1 = k2C2, as L1/C2= k2.
Calculate C1 using C1 = 1/w02L1.
FIR band stop filter
FIR or Finite Impulse Response Filter is a digital bandstop filter. The formula for an FIR bandstop filter is given below.
N signifies the dimension of the filter. F1 and F0 are the cut off freq and Fs is the sampling freq.
lC band stop filter
A passive band-reject filter can be designed with an LC circuit. The working of the LC filter is quite simple. Inductors come with a reactance as well as capacitors also come with capacitive reactance. Now an increase in the frequency causes the decrease in capacitive reactance and increase in inductive reactance. This is the primary principle behind LC bandstop filter.
Notch band stop filter
As mentioned earlier, the notch bandstop filter is a normal bandstop filter that has a narrower bandwidth. It has several applications as it has great depth and performance than a band-reject filter. To know more about notch band-reject filters, check here. <link>.
Optical band stop filter
Optical band-reject filters block a certain wavelength of light and allow other components to pass. Just like normal band-reject filters, an optical filter rejects a certain wavelength. For example, there is a 532nm optical bandstop filter. Now, it will block the light, which has a wavelength of 532 nanometers.
RC band stop filter
The bandstop filter can also be designed using resistance and capacitors. Such band-reject filters are known as RC band top Filter. The circuit is shown below. It is a first-order filter. The resistors and capacitors are connected in parallel at first; then, they are connected in series. The frequency components are trapped in between them.
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RF band stop filter
The bandstop filter has several applications in Radio Frequency Domain. For example, during the measurement of non-linearities of a power amplifier. Also, when radio signals are transmitted from stations, band-reject filters are used to remove interfering noises.
Twin-t band stop filter
It is another method of implementing a higher-order filter and provide great depth and accuracy in performance. That is why this method is popular for notch filters. The twin t filter is made of two T networks, there is an RCR circuit, and another is the CRC network
Mathematical Expression for a Band Stop Filter:
Band Reject Filter can also be obtained by using the multiple -feedback bandpass filter with an adder. A notch filter is created using a circuit which eliminates the output of a bandpass filter from the unmodified signal.
Characteristics of a Band Reject Filter:
A band-stop filter works a frequency remover which is not within a specific range, reason it is called a rejection filter.
A band-stop filter passes frequencies of a particular bandwidth with maximum attenuation.
Different types of band-stop filters produce a maximum rate of roll-off rate for a given order and flat frequency response in the passband.
Applications of a Band Stop Filter:
An active Band Pass filter is used in the public addressing system and speakers for enhancing the quality.
A bandstop filter is also used in telecommunication technology as a noise reducer from different channels.
BSF is used in radio signals to remove static on the radio devices for better and clear communications.
Besides radios and amplification, this filter is also used in many other electronic devices to decrease a specific range of frequencies, known as ‘noise.’
In the medical field, BSF is used in making many useful devices like ECG machines, etc.
It also plays a vital role in image processing.
What is a Notch filter?
Notch filters find applications when there is a need to attenuate the undesirable frequencies while passing the necessary frequencies.
Advantages & Disadvantages of a band stop filter:
A bandstop filter attenuates the frequencies that are below the cut off range, so key advantage of using this filter is, it eliminates the external and unwanted noise or signals as well as gives us a stable output.
On the other hand, due to some certain limitations a band stop filter does not function properly under sustainable conditions. The parallel arrangement between the high pass and low pass filter my vary about the change of frequencies.
Frequently Asked Questions :
What is the Q factor or ‘Quality Factor’?
Q is given by the ratio between the resonant frequency to the bandwidth. It is an important parameter and it helps us to calculate the selectivity.
The higher the value Q, the more selective is the filter, i.e., narrower is the bandwidth.
How do a Band stop filter work?
A band stop or band reject filter always cuts or rejects frequencies that are not within a certain range, as the name implies. Besides this, it also gives easy passage to the frequencies to pass which are not in the range. These types of filters are often termed as ‘Band Elimination Filters’.
How to design a Band Reject Filter?
To make a Band Stop/reject filter we always need a Low Pass Filter(LPF) & a High Pass Filter(HPF). Therefore we combine them and make a ‘parallel’ connection with both the filters to create a band reject filter.
What does a Notch Filter do?
Notch Filter is also band reject filter. They can be used to fix frequency noise sources which are from the line frequency within a certain limit. Notch filter is also used to remove resonances from a system. Like a Low pass filter, notch filter creates less phase lag in a control loop.
Find out the differences between between a band reject filter & a notch filter?
A band reject filter or band stop filter is a filter that carries or passes the frequencies without altering and attenuates them in a specific range to low level. This is the opposite of a band pass filter.
On other hand, a notch filter is a bandstop filter which has a narrow stop band and has good high ‘Quality factor’(Q-factor).
What is Ideal Filter & Real Filter?
Sometimes, for the reason of simplification, we often use the active filters to approximate ways. We upgrade them into an ideal and theoretical model, which is called ‘Ideal Filter.’
The use of these standards is insufficient, leading to errors; then, the filter should be treated based on accurate real behaviour, For example, the Real filters.
The characteristics of an ideal filter are:
The response transits between zones in a sudden way.
It does not create any distortion when the signal passes through the transit zone.
Comparison between Active Band Pass Filter & Active Band Stop Filter
Short note on All-Pass Filter
Definition of bandpass filter:
“A Band Pass Filter (BPF) is an electronic filter or device which passes frequencies within a certain range and rejects or attenuates frequency outside the particular range.”
Now an Active Band Pass Filter is a filter, consists of active components and has a passband between two cut-off frequencies, fce(lower cut-off frequency), and fcu (upper cut-off frequency) such that fcu>fce. All the other frequencies outside the passbandare attenuated.
Passband – “Pass-band is the particular range of frequencies which a filter pass through inside it.”
Stopband – “A filter always carries filters within a given band, and rejects the frequencies which are below the given range. This particular range is known as a Stopband”.
Working principle of an Active Band Pass Filter:
Active Bandpass Filter
Bandwidth:
In an active bandpass filter, the range of frequency between two cut-off frequencies, fce, and fcu, is called the bandwidth.
BW=(fcu-fcl)
The bandwidth of this filter is not mainly centered on the resonant frequency, i.e., fr.
We can easily calculate the resonant frequency(fr) if we know the value of fcu and fcl
If the bandwidth and ‘fr‘ are known, the cut-off frequencies can be obtained from,
fcu = (fcl+BW)
There are two types of Band Pass Filter exist, they are –
Wide Band Pass Filter:
A Wide Bandpass filter has a bandwidth, double or fourth, of its resonant frequency.
This filter is made by cascading a low-pass and a high-pass filter circuit.
A wide bandpass filter provides a cut-off frequency of the low pass section, which is greater than that of the high-pass area.
Circuit Diagram of Wide bandpass filter
Characteristics of a wide bandpass filter-
In a wide bandpass filter, a low pass filter’s cut-off frequency should be ten or more times than the high pass filter’s cut-off frequency present in the circuit.
Each section of the filter(LPF & HPF) present in wide BPF should have the same passband gain.
The high pass filter determines the lower cut-off frequency fcl.
The low pass filter determines the higher cut-off frequency fcu.
The gain is always maximum at the resonant frequency, fr, and equal to the passband gain for both filters.
Frequency Response of an Active Band Pass Filter:
The frequency response of wide BPF
Here,
The voltage gain magnitude of the bandpass filter equals the voltage gain magnitudes of the high pass and the low pass filter.
Where,
AFL,AFH= pass band gain of the low pass and high pass filter,
f= frequency of the input signal(Hz);
fCL= lower cut-off frequency(Hz);
fCU= higher cut-off frequency(Hz);
Center Frequency =
NARROW BAND PASS FILTER: In general, a narrow bandpass filter is made of multiple feedback circuit with a single op-amp.
Narrow BPF circuit diagram
Characteristics of a narrow bandpass filter:
A narrow bandpass filter consists of two different blocks, i.e., two feedback paths; hence, it is known as ‘Multiple Feedback Filter.’
An inverted op-amp is used here.
We can change the center frequency without changing the gain or the bandwidth of this filter.
The gain of the filter-
Bandwidth-
Transfer function of Active Band Pass Filter:
What is a Transfer Function?
“Transfer function is a complex number that has both magnitude and phase. In the case of filters, the transfer function helps to introduce a phase difference between input and output.”
A bandpass filter need is made of at least two energy-saving elements, which are capacitor and inductor. So a first-order bandpass filter is not possible. The transfer function of a second- bandpass filter can be derived as;
Where T1=R1C1, T2=R2C2 T3=R3C3
Applications of an Active Band Pass Filter:
An active bandpass filter is used in optics like LASER.
Bandpass filters are widely used in the audio amplifier circuits.
Bandpass filters are used to choose signals with particular bandwidth in the communication system.
In audio signal processing, this filter is used.
BPF is used to detect signal to noise ratio and sensitivity of a receiver.
Advantage of using a bandpass filter:
An active bandpass mainly controls the narrowband and passbands. It also removes distortion and has a sharp selectivity. Due to excellent electrical performance and mechanical reliability, BPF is used widely is the communication field.
Difference between Band Pass Filter & Band Stop Filter:
A bandpass filter carries frequencies within a given band and attenuates all the other frequencies below the range. In contrast, a band-stop filter does precisely the opposite and attenuates all the frequencies above the given frequency range.
Apart from that, a bandpass filter removes the energies outside of the passband, but a band-stop filter does not remove all the powers outside the passband at all.
What is an All-Pass Filter?
An active all-pass filter passes all frequency components of the input signal without attenuation and provides some phase shifts between the input and output signal.
Circuit diagram of an active all-pass filter
All pass filter is generally used in digital reverberators. When signals are transmitted over transmission lines from one end to another, they undergo some phase changes. To avoid such phase changes and loss, the all-pass filters are used.
The frequency response of the all-pass filter
The capacitor creates an inverting amplifier at high frequencies, which is in a short circuit.
The capacitor is an open circuit when the frequency is low, and it creates a unity gain voltage buffer, i.e., there will be no phase shift.
At the corner frequency ω=1/RC, the circuit generates a 90˚ shift. That implies the output appears to be delayed by a quarter from the input.
Comparison between active low-pass and passive low-pass filter
Why do we use active LPF
Advantages of an active LPF
FAQs
What is an Active Low Pass Filter?
First things first, let’s discuss what a simple Low Pass Filter is-
“Low Pass Filter is a type of filter which mainly passes signals with a frequency lower than the particular cut-off frequency and attenuates all the frequency higher than the cut-off range ”.
Now, an Active Low Pass Filter is made of active components like Op-amp, resistors, and it also carries lower frequency signals with lessresistance and has a constant output gain from zero to a cut-off frequency.
Components of Low Pass Active Filter:
Active filters consist of active components as the name implies such as Operational amplifier, transistors or FET within the circuitry.
An active filter typically consists of amplifiers, capacitors and resistances.
So generally, Low Pass Active Filter is any filter using an Op-amp to improve the performance and predictability in such a low cost.
How does an Active Low Pass Filter work
Active Low Pass Filter
In the above figure, it’s a commonly used low pass active filter.
Frequency Response of Low Pass Filter:
Characteristic Curve of an active LPF
Active Low Pass Filter Design:
Resistance R =
Fc = cut-off frequency
Ωc = cut-off frequency
C = capacitance
A cut-off frequency can be varied by multiplying it with RC or C.
Transfer Function of a First Order Active Low Pass Filter:
Differential Equation for the filter –
Second-Order Active LPF:
What is a second-order LPFs?
To build a second-order filter, we usually use an op-amp, and therefore the second-order filter can also be called as a VCVS filter; where VCVS is referred to ‘Voltage Control Voltage Source’ amplifier. We design a second-order filter along with a first-order active RC filter.
As it is a low pass filter, it only allows the lower frequency signals to pass, and it attenuates all the higher frequencies above the specified frequency range.
A second-order low pass filter attenuates the higher frequency signals more precisely. The gain reduces at the rate of 12 dB per octave. In other way it is 40 dB/decade.
Second order LPF diagram
In a second order filter,
When the resistor and capacitor values are different,
When the resistor and capacitor values are same,
Transfer Function of a Second Order Active Low Pass filter:
The Transfer Function is denoted as,
The magnitude of the Transfer function –
Where ωc is the cut-off frequency.
Frequency-responses of second-order low-pass active filters is given.
The frequency response of 2nd order LPF
Design of a second-order active low pass filter
First, we choose a value of the cut-off frequency, ωc (or fc).
Find R,
Rf comes as –
Rf = K(2R) = 3.172 R.
Find R1 while K = 1.586
Differences between Active Low Pass Filter & Passive Low Pass Filter:
Active components are effectively costlier, that’s why the active filters are expensive as well, whereas the cost of passive filters is lower due to the presence of the passive components.
Active Low Pass filter circuit is a complex one, while a passive low pass filter circuit has less complexity.
To operate an active LPF, we need an external power supply for operating it. But passive filters do not require external power because it drives the energy for its operation from the applied input signal.
Passive filters contain more components than an active low pass filter; that’s why they are heavier in weight.
Active LPF is more sensitive during temperature change, but the passive ones show less sensitivity with the growth of temperature.
Why to use Active LPF?
Due to the less complex circuitry and lower price than the other active filters, we use Active LPF in many fields.
In this article, we will discuss about few basic concept related to active high pass filter and try to answer few questions in following sections and we will try to learn about some important application of active high pass filters with advantage.
What is an active high pass filter?
Working Principle of an active HPF
Time Response & Frequency Response
Cut-off Frequency of an active HPF
What is a transfer function for an active HPF
Design a first order active order HPF
Second order active HPF
Transfer Function for second order HPF
Advantages of active High Pass Filter
Applications of a HPF
FAQS
Active high pass filter definition:
An active high pass filter is nothing but a circuit contains an active component such as a transistor, an operational amplifier(op-amp), etc. These components are mainly used for better performance or better amplification.
What are the components of an active high pass filter?
We can make an active high pass filter by adding an op-amp across a passive high pass filter.
To imply simplicity, time effectiveness and due to growing technologies an op-amp designing, generally, an op-amp is used for an Active High Pass Filter design.
In an active high pass filter, the limitation we have is the op-amp bandwidth. It means that the op-amp will pass the frequency according to its gain and the open-loop characteristics of the op-amp.
Circuit Diagram of active high pass filter:
Active High Pass Filter
In the above figure, the CR network does the filtering, and the op-amp is connected as a unity-gain follower. The feedback resistor, Rf, is included to minimize the dc off-set.
Since op-amp gain is infinite, we can therefore derive.
Where
= Passband gain of the high pass filter,
f = Frequency of the input signal (Hz),
= cut-off frequency of the high pass filter (Hz)
The Gain Magnitude,
And phase angle (in degree),
Working Principle of an active high pass filter:
First-order filters are the simplest form of any filters that contain only one reactive component, i.e., capacitor, as it is also used in passive filters. To transform it into an active filter, an op-amp is used to the output of a passive filter.
Now, the op-amp is used for different configurations. Each configuration has additional attributes to the performance of the filter.
The main thing to be remembered is a first-order filter’s roll-off rate. The roll-off rate is the rate of change in the gain of a filter in its desired stopband. It shows us the steepness in the curve and how fast the growth tends to increase with frequency.
First-order filters have a roll-off rate of 20dB/decade or 6dB/octave.
Roll Off Rate = -20n dB/decade = -6n dB/octave
Time Response & Frequency Response of an active HPF
To operate a high pass filter, the verification can be done from the gain-magnitude equation as follows:
At very low frequency, i.e., f<fc,
At f=fc,
At f>>fc,
The bandwidth of the active high pass filter shows the value of frequency from which signals are allowed to pass. As an example, if the bandwidth of that high pass filter is given as 50 kHz, that means the only frequencies from 50 kHz to infinity are allowed to pass the range of bandwidth.
The phase angle of the output signal is +450 at the cut-off frequency. The formula to calculate the phase shift of an active high pass filter is
Ø= arctan (1/2πfRC)
Active High Pass Filter Transfer Function
The impedance of the capacitor keeps frequently changing, so electronic filters have a frequency-dependent response.
The form of a T.F is derived from the ratio of Output Voltage to Input Voltage
The standard form of the transfer function is :
Where,
a1 = Amplitude of signal
ω0 = Angular cut-off frequency
Cut-off Frequency:
What do we mean by cut-off frequency ?
By cut-off frequency, we define the useful or essential part of a spectrum. It is simply a frequency level above or below a device or filter cannot response or can be operated properly.
The Cut-off frequency for an active high pass filter is the particular frequency at which the load(output) voltage equals 70.7% of the source(input) voltage. The origin or output voltage is more significant than 70.7% of the input or load voltage and vice versa.
The cut-off frequency also indicates the frequencies at which the power of the output path falls to half its maximum value. These half-power points correspond to a fall in the gain of 3dB(0.7071) relative to the maximum dB value.
Filter Designing of Active High Pass Filter:
To construct an active high pass filter, we need to implement the following steps-
A value of the cut-off frequency,
is chosen.
A value of the capacitance C, usually between 0.001 and 0.1µF, is selected.
The value of the resistance R is calculated using the relation,
Now, the values of R1 and Rf are selected depending on the desired pass-band gain, using the relation,
Second-Order Active High Pass Filter:
What is a second-order filter?
The maximum delay in each sample used in generating each output sample is called the order of that particular filter.
Second-order filters mostly consist of two RC filter, which is connected together to provide a –40dB/decade roll-off rate.
Second-Order Active High Pass Filter
Where DC gain of the amplifier =
The Transfer Function of a second-order active high pass filter can be obtained from the transfer function of the low pass filter by the transformation,
Substituting s=jω, the transfer function is,
In the above equation, when ωà0, |H(jω)|=0. Thus the low-frequency gain of the filter is zero.
If we compare it with Butterworth filter transfer function, we get
Characteristic curve of a second order HPF
The Frequency response of a second-order active high pass filter is shown in the above diagram. It is noted that the filter has a very sharp roll-off response.
The design procedure for a high pass will be as same as low pass.
The frequency response will be a maximally flat one, i.e., having a very sharp roll-off response.
Whenever there is a small signal is present, an active High pass Filter is used to increase the amplification factor, which also increases the amplitude of those small signals.
Due to very high input impedance, active high pass filters can transfer efficient signals without any loss in any preceding circuit.
Active filters usually have very low output impedance, which is perfect for transferring efficient signals to its next stage, mostly when they are used in different multistage filters.
This type of filters gives us smooth frequencies.
They have a sharp roll-off response.
Strong broadcasting power to receivers to select desired channel frequency.
Best for audio processing in any electrical or electronic device.
Active HPF prevents amplification from DC etc.
Application of Active High Pass Filter:
To transmit higher frequency in case of video related filters.
We use HPF as a treble equalizer.
We often use HPF as a treble boost filter.
We are changing the frequency depending on different waveforms.
Active High Pass filters are also used in oscilloscopes.
In the generator, these filters are used.
Frequently Asked Questions
Where are high pass filters used?
The high pass filters are used in all audio sources to remove unwanted noise that lurks below the important frequencies.
Many unwanted sounds can be hidden by some louder core of a high pitch signal and can be overlooked. We don’t get to hear the rumble due to the limits of hearing as the lowest parts of the spectrums are around 20-40 Hz. High pass filters also eliminate those noises or reduce it that makes them nearly silent.
Can I get the output of a high pass filter as a power source?
A high pass filter is an electronic filter that passes signals with higher frequencies which are above the cut-off frequency range and also attenuates the frequencies which are below the cut-off range.
Now, the output of the specific high pass filter has no DC(0Hz) voltage due to its specified cut-off frequency(fc). The lower cut-off frequency of an active high pass filter is 70.7% or -3dB(dB= -20log Vout/Vin) of the voltage gain which it allows to pass can be used as a power supply as well.
What does corner frequency mean in regards to high pass filter?
The corner frequency, which is also called as cut-off frequency, defines a specific frequency at which the transfer attenuation reaches -3dB below(50%) the magnitude from the 0dB or pass-band level.
“Low pass filter carries lower frequency signals with less resistance and has a constant output gain from zero to a cut-off frequency.”
Generally, a low pass filter does attenuation of frequencies above cut-off points.
Circuit Diagram of a Low Pass Filter:
There are two types of active filter exist, they are-
Active Low Pass Filter – consists of mostly active components like op-amp, a transistor.
figure 1.1 Active Low Pass Filter
Passive Low Pass Filter – consists of mostly passive components like capacitors, resistors, etc.
figure 1.2 Passive Low Pass Filter
How does a Low Pass Filter Work?
What does a low pass filter do?
In figure 1.1, it’s a commonly used low-pass active filter.
The filtering is commonly done by the RC network, and the op-amp is used as a unity gain amplifier. The resistor RF(= R) is included for Dc offset.
At DC, the capacitive reactance is infinite, and the dc resistive path to ground for both terminals should be equal.
Here, all the voltages Vi, Vx, Vy, V0 are measured concerning ground.
The input impedance of the op-amp is always infinite; no current will flow into the input terminals.
According to the voltage divider-rule, the voltage across the capacitor,
Since the op-amp gain is infinite,
Where,
= pass-band gain of the filter
f = frequency of the input signal
= cut-off frequency of the signal
AcL
= closed-loop gain of the filter as a function of the frequency.
The Gain Magnitude,
And Phase Angle (in degree),
Operation of a Low Pass Filter:
The operation of the low-pass filter can be verified from the gain magnitude equation as follows-
At very low frequencies, i.e., f>>fc,
At f=fc,
At f>fc,
|AcL|<AF
Thus the filter has a constant gain of AF from 0 Hz to the cut-off frequency fc. At fc, the growth is 0.707AF, and after fc, it decreases at a steady rate with an increase in frequency.
Here, the actual response deviates from the linear dashed-line approximation at the vicinity of ‘fc.’
Frequency Response of Low Pass Filter:
Low pass filter characteristics
How to make a Low Pass Filter?
Low pass filter design:
A value of the cut-off frequency ωc is chosen.
Capacitance C is selected with a certain value; usually, the value is between 0.001 and 0.1µF. Mylar or tantalum capacitors are recommended for better performance.
The value of R is calculated from the relation,
Fc = cut-off frequency in hertz
Ωc = cut-off frequency is in radian second.
C = in Farad
Finally, the values of R1 and RF are selected depending on the desired pass-band gain by using the relation,
Frequency Scaling:- Once a filter is designed, there may be a need to change its cut-off frequency. The method of converting an original cut-off frequency fc to a new cut-off frequency is called ‘frequency scaling.’
To change a cut-off frequency, multiply R or C, but not both by the ratio:-
Corner frequency & Cut-Off Frequency of a Low Pass Filter:
The transition of a low pass filter is always swift and smooth from the pass-band to stopband. Also, a cut-off frequency is not any parameter to measure the goodness or badness in a range of frequency. The cut-off frequency is more accurately referred to as the -3dB frequency, i.e., it is the frequency at which the magnitude response is 3dB lower than the value at 0 Hz.
What is Pass-band?
“Pass-band is the particular range of frequencies which a filter pass through inside it.”
For low pass filters, the frequencies that move towards the end of the pass-band cannot have any significant gain or attention.
What is Stopband?
“A filter always carries filters within a given band, and rejects the frequencies which are below the given range. This particular range is known as a Stopband”.
As the limitations are there for low pass filters, the stopband attenuates at a particular frequency, which moves near the cut-off frequency closer to 0 Hz.
The transfer function of a Low pass Filter:
What is a Transfer Function?
“Transfer function is a complex number that has both magnitude and phase. In the case of filters, transfer function helps to introduce a phase difference between input and output.”
Since low pass filter allows low-frequency AC signals to pass through it, the output gets attenuated. We use different active and passive components to make a filter, which eventually has other characteristics. The transfer function tells us how one input is related to an output depending on the component’s characteristics. The transfer function can easily be determined from a graph of the output signal at various frequencies. We can also calculate the transfer function using Kirchoff’s Laws to derive the filter’s differential equation.
As more signal passes through it, the filter will apply a phase shift to the output signal for the input signal. Hence, the transfer function of a filter is a complex function of frequency. It also contains all the vital information we need to determine the magnitude of the output signal and its phase.
Ideal Filter & Real Filter:
Sometimes, for the reason of simplification, we often use the active filters to approximate ways. We upgrade them into an ideal and theoretical model, which is called ‘Ideal Filter.’
The use of these standards is insufficient, leading to errors; then, the filter should be treated based on accurate real behavior, i.e., as a ‘Real filter.’
The main key terms of an ideal filter are
A gain unit
Complete degradation of the input signal across the bands.
The transition of response from one zone to another is quite abrupt.
It does not create any distortion when the signal passes through the transit zone.
What are the differences between the Low pass filter & High pass filter?
What are the advantages of a Low Pass Filter?
Low-Pass filters can easily remove aliasing effects from a circuit, which makes the circuit working smoothly.
Low-Pass Filters are cost-effective so that it can be used easily.
Low-Pass Filters have low output impedance; thus, it prevents the filters cut-off frequency from being affected because of the load.
Applications of a Low Pass Filter:
A low-pass filter is used in ‘hiss’ filters.
LPF is used in audio speakers to reduce high frequency.
LPF can be used as an audio amplifier and an equalizer.
LPF is also used in radio transmitters to block harmonic emissions.
These filters are used in music systems to filter the high-frequency sounds, causing echo at higher sounds.
What is a passive low pass filter?
A passive low pass filter is a filter made of all passive components like capacitors, resistors, etc. It causes a lesser output level compared to the input level.
What is an RC low pass circuit?
An RC low pass circuit is made of only Resistors and Capacitors, as the name implies. It is an essential passive filter, as well. In this filter, the reactance of a capacitor varies inversely with frequency, and the value of the resistor remains constant as the frequency changes.
What is a Butterworth Low pass Filter?
A Butterworth filter is that type of filter where the frequency response is flat over the pass-band region. A Low-Pass Butterworth filter provides a constant output from DC source to a particular cut-off frequency and rejects the higher level frequencies.
How can a second order low pass filter be constructed?
We know that a first-order low-pass filter can be made by connecting a single resistor and capacitor whose single pole can give us a roll-off slope -20dB/decade. To make a second-order passive low pass filter, we connect or cascade two passive filters (first-order). It is also a two-pole network.
Write down the corner frequency of a second-order filter.
In a second-order low pass filter, we observe a -3dB corner frequency point and therefore, the pass-band frequency changes from its original value as calculated in the equation:
As the titles suggest, these types are made using active components. Some of the active transistors are – transistors (BJT, FETs), any other electronics devices which are capable of amplifying a signal or can produce powers.
If there is a need to increase the characteristics, various stages are joined in a certain or specific ways.
How to design an active low pass filter?
To design an active types, we may use IC741, an Op-amp, configured with 8 pins. The op-amp is to be supplied with DC power along with resistors and capacitors of different values.
An active type may have an advantage, increasing the signal power available in comparison with the input. Whereas a passive one dissipates energy from the signal. For various ranges of frequencies, such as at sound frequencies and under, an active type may realize a specified transfer function with no use inductors, that are comparatively big and costly components in contrast to resistors and capacitors, and that are more costly to create with the essential high quality and precise values.
Numerous stages may be cascaded when wanted to enhance attributes. By comparison, the layout of multiple-stage passive blockers needs to take into consideration every phase’s frequency-dependent loading of the previous stage. Since inductors aren’t utilized, they can be reached in really compact dimensions.
Passive type suffers from attenuation of signals. There are various ways; one popular method of control or restoration is by using amplification through the Active type applications. The major point of conflict between the active and passive types is the ‘amplification’.
Compared to a passive one, active type are composed of active components in operational amplifiers, transistors, or FET’s within their circuit design, as described in earlier sections. These components draw power from the external power source, use it for amplification of output. That’s an added advantage compared to a passive one.
Why is an active filter needed at low frequencies?
An active type is needed at lower frequencies because it helps achieve low output impedance while providing high input impedance. It also stabilizes different frequency ranges as multiple stages can be cascaded with it.
These can be categorized and sub-categorized from several points of view. The most common divisions and sub-divisions are- active or passive type; high-pass type low-pass type, bandpass type, band-reject/notch type or all-pass type; digital or analog type discrete-time or continuous-time type; linear or non-linear type; infinite impulse response (IIR) or finite impulse response (FIR) and so on.
Examples:
Active types and Passive types are designed to modify certain band of frequency in a desired way. They have different types according to their needs. The categories are given below.
Low pass types (LPF)
High pass types (HPF)
A bandpass types (BPF)
Band reject/stop types (BSF)
Applications:
They are nowadays used in many purposes of the electronic circuit, and its applications are immense. Moreover, it’s possible to improve the circuit gain by using different filters in different ways, either active or passive types, especially in active types. Active types use amplifiers, and we know that it helps increase gain. This article will discuss two type, such as Low pass type, High pass type with appropriate diagrams and simulated wave shapes for both active and passive condition in the following sections with the importance of using higher-order in the HPF and LPF.
In electronics, some applications are as follows:
In Radio communication System for Radio tuning to a specific frequency: They are used to enable radio receivers to only “see” or “detect” the desired signal and reject all the other signals by assuming their different signal frequency. So noise-free signals can be received. The high-frequency bandpass types are used for channel selection in central telephone offices.
Power Supply Design: They are used to remove noise or high frequencies usually present on AC input lines. These are also applied to decrease the ripple.
Modify digital images: It can be used to modify digital images also.
Data analysis: They are also very helpful to remove specific frequencies in data analysis.
Frequency Response & Time Response:
Time-domain refers to the change of signal’s amplitude with respect to time. In contrast, in the frequency domain, Frequency refers to the occurrence of an event in a given period.
A Frequency Response of different type Image credit:SpinningSpark real life identity: SHA-1 commitment ba62ca25da3fee2f8f36c101994f571c151abee7, Bandform template, CC BY-SA 3.0
What is Bandwidth (BW)?
For filters, bandwidth is the difference between the upper and low -3dB points.
For example, if a bandpass filter has -3dB cut-off points and set to 200Hz and 600Hz, then the filter bandwidth will be = (BW) = 600-200 = 400Hz.
What do you mean by the Q Factor?
Q factor is given by the ratio of resonant frequency to the BW.
Q = 2 * π * (Maximum Amount of Energy Stored) / (Energy Dissipated per Cycle)
A greater Q value represents the filter is more selective as Q factor is a parameter which judges the selectivity.
Resonant Frequency
Resonant frequency is simply given by the frequency of the given resonant circuitry. A Resonant circuit is also popularly known as the tank circuit or the LC circuit. A resonant circuit is designed using parallelly placed inductors and capacitors and resistors.
A parallel Resonant Circuit
Oscillation of a system is given by the following equation –
Where,
f= frequency in Hertz
L= Inductance in Henry
C= Capacitance in Farads
Orders of Filters
Higher-order filters provided more excellent roll-off rates between passband and stopband.Higher-order filters are also required to achieve required levels of attenuation or sharpness of cut-offs.
Active type and Passive typealso have variation in different types of orders, such as:
First Order Low pass active types, First Order High pass active types, First-order Bandpass active types, First-order Band stops active types.
Second order Low pass active types, Second order High pass active types, Second-order Bandpass active types, Second-order Band stops active types.
The frequency response of second-order are shown below –
Frequency response of Second-order
Ideal type & Real type:
Sometimes, for the reason of simplification, we often use the active filters to approximate ways. Later they are modified and termed as ‘ideal filter’. Filters, which operate in reality considering all the possible factors, are real ones.
“High pass filter is a circuit that attenuates all signals of frequencies which belong to the below cut-off frequency and gives a constant output or gain above this particular frequency.”
First-order type
In the above figure, the CR circuit does the ‘filtering’ work. The op amp is linked with a voltage follower. Now, the feedback system is also incorporated to cancel out the offset voltage according to the property of the operational amplifier.
Here,
The equation can be calculated using the property of ideal operational amplifier which states that an operational amplifier has infinite gain. Here, f represents input signal’s frequency.
Where= HPF’s passband gain,
f=Input signal’s frequency (It is also the cut-off freq.),
Operation of a High pass filter:
Here, the gain-magnitude equation does the job of verification at a lower level of frequency.
An active high pass filter is nothing but a circuit contains an active component such as a transistor, an operational amplifier(op-amp), etc. Using these devices gives us more efficiency.
2. Efficient transmission of signal (with minimal loss),
3. Efficient performance when used in a multistage filter.
Working of high pass filter.
The most straightforward and simple type of filter is the First order Filter. It has a single reactive component. The transforming process is quite simple. You have to add just an op-amp.
Operational amplifiers have several configurations. Different configurations have different attributes and impact in the filter’s performance.
Now, note of the roll off rate of a first order filter. Roll off rate is defined as the rate at which the gain of a filter changes in the operational stop band. The rate represents the steepness of the curve and it also help us to find out the increase rate of the growth.
The first order filters come up with a growth rate 20 dB/decade or in other terms, it can be said the growth rate is 6db/Octave.
High Pass Filter Transfer Function
We know that the capacitor’s impedance varies with the frequency. That is why electronic-filters comes up with response which are dependent on frequencies.
The impedance of a capacitor is typically given by the following equation.
The transfer Function is derived using some basic theorems of network theory.
The Transfer Function is given by ratio of output to the supplied input. The typical representation of transfer function is given as follow.
The typical transfer function is :
Where,
a1 represents Amplitudes of signals
ω0 represents Angular cut-off frequencies
Application of Active High Pass Filter:
To transmit higher frequency in case of video related filters.
The frequency is changed based upon various waveforms.
The active ones finds application in the CROs, generators.
Passive High Pass Filters:
Why are passive high pass filters used?
A filter is called passive when there won’t be any external power, and the input signal also remains unamplified due to the passive components present in the Filter. The passive components may be the same as low pass, but the overall connection is always reversed. The passive components are Resistor(R) and Capacitor(C), so it is an RC filter combination.
The name “passive,” “high,” “pass,” and “filter” suggest that the Filter will only pass the higher frequency, i.e., it will block the low frequencies.
Passive High Pass Filter (RC)
In the above circuit, the output voltage is determined across the resistor(R); when the frequency increases, the reactance of the capacitor decreases, so the output and gain increases simultaneously.
The formula to calculate the frequency of the RC circuit is,
f=1/2πRC
How to build an RC High Pass Filter:
To build an RC HPF, the components we need are as follows,
(0.00000001F) = 15,293 Hz, the greater the output, the more signal gets attenuated.
If we give an AC signal input to the circuit from a function generator and sets the signal to a low frequency, the capacitor will block the voltage signal. So the low-frequency signals which get blocked do not reach past the capacitor. The high-frequency signals keep going and pass to the output.
Passive High Pass Filters are used in:
Audio amplifiers
In speaker systems
In different music control systems etc.
First Order High Pass Filter vs. Second Order High Pass Filter
The second-order high-pass filter comprises two different reactive components.
First-order HPF has a transfer function of the first order; on the other hand, second-order HPF has a transfer function of second order.
The first order filter differs from the second order filter on the basis of the stopband. The slope of the graph of a second order is typically the algebraic double of the first order.
Passive RL High Pass Filter:
Passive RL High Pass Filter
This circuit consists of a resistor and an inductor. The inductor in the circuit passes all the lower frequencies and reduce the voltages across it. It also keeps the output voltage closer to the input voltage.
There is a frequency response in dB below the circuit for a specific range of frequencies.
The lower cut-off frequency for an RL high-pass filter is determined by the inductor and the parallel combination of RF and RL, by the formula:
Where, REQ = RF||RL
How to build an RL High Pass Filter:
To build an RL HPF, we need,
A function Generator
A Resistor
An Inductor
Oscilloscope
For making the circuit, we may use a 470mH inductor and a 10KΩ resistor.
The circuit forms a high-pass filter and helps the high-frequency signals to pass through to the output. It also filters the low-frequency signals through the inductor.
Butterworth High Pass Filter:
What is a Butterworth Filter?
“Butterworth filter is probably the first and best-known filter approximation.”
The Butterworth filter is created to get a smooth frequency response graph in the passband.
Circuit Image –
The circuit diagram of Butterworth high pass filterand frequency response
The Butterworth filter is created to get a smooth frequency response graph in the passband. Filters can be classified into two categories. The categories are ‘Chebyshev Filter’ and ‘Inverse Chebyshev Filter’.
The filter response comes out to be response of a Butterworth filter, if the ripple value is fixed at 0%. Typically the ripple value is fixed at 0.5% for applications in digital filters.
In this article we will study about the Schmitt trigger Comparator and Oscillator circuitry with different related parameters in detail. As we have seen till now that an op-amp is used in various fields of applications and being such a versatile device its importance as a part of analog circuits is immense. One of the most convenient applications of the op-amp is as a multivibrator circuit. We will be studying in detail about types and working of multivibrator circuit constructed using op-amps (op-amp multivibrators) and other passive devices such as capacitors, diodes, resistors etc.
Contents
Introduction of Multivibrators
Positive feedback usage in multivibrator
What is Schmitt trigger ?
Schmitt trigger comparator closed-loop circuit or bistable multivibrator
Voltage transfer characteristics of Bistable multivibrator
Astable multivibrator or Schmitt trigger oscillator
Oscillator’s duty cycle
Introduction of Multivibrator and Schmitt trigger Circuitry
Multivibrator circuits are sequential logic circuits and are of many types depending on how they are created. Some multivibrators can be made using transistors and logic gates, whereas there are even dedicated chips available as multivibrators such as NE555 timer. The op-amp multivibrator circuit has a few advantages over other multivibrator circuits as they require much fewer components for their working, less biasing, and produces better symmetrical rectangular wave signals using comparatively fewer components.
Types of Multivibrators
There are mainly three types of multivibrator circuits present:
Astable multivibrator,
Monostable multivibrator
Bistable multivibrator.
The monostable multivibrator has single stable state, whereas the number of stable-states a bistable multivibrator has- is 2.
As we have learnt in the previous section about op-amp as a comparator, in the open-loop configuration the comparator can switch in an out of control manner between the positive saturation supply rail voltage and negative saturation supply rail voltage when an input voltage near to that of the reference voltage is applied. Hence, to have control on this uncontrollable switching between the two states, the op-amp is used in a feedback configuration (closed-loop circuit) which is particularly known as closed-loop Schmitt trigger circuit or bistable multivibrator.
Positive feedback usage in multivibrator and hysteresis effect
Till now, we have learnt about the negative feedback configuration in op-amps in the previous sections. There is also another type of feedback configuration known as positive feedback, which is also used for specific applications. In positive feedback configuration, the output voltage is fed back (connected) to the non-inverting (positive) input terminal unlike the negative feedback, where the output voltage was connected to the inverting (negative) input terminal.
An op-amp operated in a positive feedback configuration tends to stay in that particular output state in which it is present, i.e. either the saturated positive or saturated negative state. Technically, this latching behaviour in one of the two states is known as hysteresis.
If the input applied signal in the comparator consists of some additional harmonics or spikes (noise), then the output of the comparator might switch to the two saturated states unexpectedly and uncontrollably. In this case, we won’t get a regular symmetrical square wave output of the applied input sinusoidal waveform.
But if we add some positive feedback to the comparator input signal, i.e. use the comparator in a positive feedback configuration; we will be introducing a latching behaviour in the states, what we technically call as hysteresis into the output. Until and unless there is a major change in the magnitude of the input AC (sinusoidal) voltage signal, the hysteresis effect will continue to make the output of the circuit remain in its current state.
What is Schmitt trigger ?
The Schmitt trigger or bi-stable multi-vibrator operates in positive feedback configuration with a loop-gain greater than unity to perform as a bi-stable mode. Voltage V+ can be.
Schmitt trigger comparator or bistable multivibrator
The Voltage transfer characteristics of Schmitt trigger Comparator
The above figure represents the output voltage versus the input voltage curve (which is also known as the voltage transfer characteristics), particularly showing the hysteresis effect. The transfer characteristic curve has two specific regions, the curve as the input voltage increases and the part of the curve in which the input voltage decreases. The voltage V+ does not have a constant value, but instead, it is a function of the output voltage V0.
Voltage transfer characteristics
In the voltage transfer characteristics, Vo = VH, or in high state. Then,
Higher Cross-over voltage VTH
If signal is less than that of V+, the output stays at its high state. The cross-over voltage VTH occurs when Vi = V+ and expressed as follows:
When Vi > VTH, the voltage at the inverting terminal is more than at the non-inverting terminal. Voltage V+ then turn out to be
Lower Cross-over voltage VTL
Since VL < VH the input voltage Vi is still more than V+, and the output rests in its low state as Vi carry on to increase; If Vi decreases, as long as the input voltage Vi is larger than V+, the output remains at saturation state. The cross-over voltage here and now occurs when Vi = V+ and this VTL expressed as
As Vi continues to decrease, it remains less than V+; therefore, V0 remains in its high state. We can observe this transfer characteristic in the above figure. A hysteresis effect is shown in the net transfer characteristic diagram.
What is Schmitt trigger oscillator ?
Astable multivibrator or Schmitt trigger oscillator
Astable multivibrator accomplished by fixing an RC network to the Schmitt trigger circuit in –ve feedback. As we will advance through the section, we will see that the circuit has no stable states and therefore, it also known as the astable multivibrator circuit.
Astable Multivibrator circuit or Schmitt trigger Oscillator
As noticed in the figure, an RC network is set in the negative feedback path, and the inverting input terminal is connected to the ground through the capacitor while the non-inverting terminal is connected to the junction between the resistors R1 and R2 as shown in the figure.
At first, R1 and R2 is to be equal to R, and assume the output switches symmetrically about zero volts, with the high saturated output represented by VH = VP and low saturated output indicated by VL = -VP. If V0 is low, or V0 = -VP, then V+ = -(1/2)VP.
When Vx drops just slightly below V+, the output switches to high so that V0 = +VP and V+ = +(1/2)VP. The equation for the voltage across the capacitor in an RC network can be expressed as:
Where τx is the time constant which can be defined asτx= RxCx. The voltage Vx increases towards a final voltage VP in an exponential manner with respect to time. However, when Vx turn out to be slightly greater than V+ = +(1/2)VP, the output shifts to its low state of V0 = -VP and Vx = -(1/2)VP. The RxCx network gets triggered by a negative sharp transition of the voltages, and hence, the capacitor Cx start discharging, and the voltage Vx decreasing towards value of –VP. We can therefore express Vx as
Where t1 refers to the time instant when the output of the circuit switches to its low state. The capacitor discharge exponentially V+ = -(1/2)VP, the output again shifts to high. The process repeats itself continuously over time, which means a square-wave output signal is produced by the oscillations of this positive feedback circuit. The figure below shows the output voltage V0 and the capacitor voltage Vx with respect to time.
The Schmitt Trigger Oscillator: Plot of Output voltage and Capacitor Voltage with respect to time
Time t1 can be found by substituting t=t1 and Vx = VP/2 in the general equation for the voltage across the capacitor.
From the above equation when we solve for t1, we get
For time t2 (as observed in the above figure), we approach in a similar way, and, from a similar analysis using the above equation, it is evident that the difference between t2 and t1 is also 1.1RxCx. From this, we can infer that the time period of oscillation T can be defined as T = 2.2 RxCx
And the frequency thus can be expressed as
Duty cycle of Oscillator
The percentage of time the output voltage (V0) of the multi-vibrator is in its high state is particularly termed as the duty cycle of the oscillator.
The oscillator’s duty cycle is
As observed in the figure, depicting output voltage and capacitor voltage versus time, the duty cycle is 50%.
A comparator or a voltage comparator is a device used to compare two voltage levels. We can determine which voltage level is higher from the comparator’s output. It is an application of typical op-amps, and it has applications furthermore.
What does a comparator circuit do ?
A comparator compares two given input voltage and provides the output indicating which voltage has a more excellent value. The circuit takes input using inverting and non-inverting terminals and provides output from the output terminal. The output range lies between the positive saturation voltage and negative saturation voltage.
Op Amp comparator circuit
The below image represents a circuit diagram of the comparator circuit. As we can observe that the circuit comprises only an op-amp, and voltage inputs are supplied in it through the inverting and non-inverting terminals.
The comparator circuit is designed using an op amp. To make it ready for operation, input voltages are provided. There is no feedback system incorporated with it. A reference voltage and a voltage signal are provided through the op-amp. The positive and negative saturation voltage inputs are also provided. The indicative output is collected from the output of the op-amp.
How comparator circuit works ?
The working principle of the comparator is pretty simple. In general, it compares between two voltage sources and provides a greater output. Below mentioned two points state the working.
If the voltage in the non-inverting terminal is higher than the inverting terminal voltage, the output is switched to the op-amp’s positive saturation voltage.
If the inverting terminal’s voltage is higher than the voltage in the non-inverting terminal, the output is switched to the op-amp’s negative saturation voltage.
Voltage comparator circuit using op amp 741
Op-amp 741 is an integrated circuit containing an op amp. A voltage comparator can be created using op amp 741. The below image represents a non-inverting voltage comparator’s circuit diagram using op amp 741.
Comparator using op amp 741
Comparator block diagram
The operation of a comparator can be represented by using block diagrams. The following image represents a block diagram of a comparator,
Comparator Block Diagram
Comparator circuit relay
Relays are switches that can control a circuit. It can turn On or OFF a circuit and can connect and disconnect a circuit from another circuit. A comparator is broadly utilized as the utilization of the relays.
Comparator circuit uses
A comparator is a valuable and essential device. There are several applications of comparators. Some of the applications of the comparators are listed below.
Null Detector: If a value is zero, a null detector detects it. A comparator is typically a high-gain amplifier, and for controlled inputs, a comparator is suitable for detecting Null.
Level Shifter:A level shifter can be designed using a single op-amp. Using a suitable pull-up voltage, the circuit allows for a lot of versatility in selecting the voltages to be interpreted.
Analog-to-digital Converter (ADC):Comparators are used to create analog-to-digital converters. In a converter, the output indicates which voltage is higher. This operation is the same as a 1-bit quantization. That is why comparators are used in almost every analog-to-digital converter.
Other than the mentioned applications, there are many other comparators like – Relaxation Oscillator, in Absolute Value Detectors, in Zero-Crossing Detectors, in Window Detectors, etc.
Comparator fuzz circuit
Fuzz circuits can be developed using comparators. LM311 IC is such an example of comparator fuzz. We will discuss this later about LM311.
How to make a comparator ?
A comparator is a particular and straightforward electrical device to build. To build a comparator, we need an op amp and supply voltages. At first, the op-amp is provided with positive and negative saturation voltages. The output will vary in that range of voltages. Then inputs are provided in their inverting and non-inverting terminals. The reference voltage is provided in the non-inverting terminal, and the input voltage is provided in the inverting terminal. There is no feedback system associated with this circuit.
Voltage comparator circuit
A comparator circuit can detect the high-valued voltages between two voltages. Comparators, which typically compare to voltages, are known as a voltage comparator circuit.
Phase comparator circuit diagram
A phase comparator is an analog logic circuit capable of mixing and multiplying. It detects the differences in phases between two given signals by generating a voltage signal. The below image represents the phase comparator circuit diagram.
Ic comparator circuits
As mentioned earlier, a comparator compares two voltage signals and produces an indicative output. Comparators are incorporated inside an integrated circuit for better usability. The below image represents the circuits for comparator ic.
A typical Comparator IC
lM358 comparator circuit
lm358 is a comparator ic consisting of two comparators inside it. It has eight pins. This ic doesn’t require any independent external power supply for functioning each comparator. The circuit diagram of the ic is given below.
LM358 Comparator IC
Comparator internal circuit
The comparator is designed using an op amp—the op amp as further circuitry. The internal circuitry inside an ic is given below in the diagram. Observing the diagram, we can see that it consists mainly of transistors, diodes, and resistors. The internal diagram can be divided into three parts based on their operation. They are – input stage, gain stage, and output stage.
The schematic diagram of a comparator is given below. The internal schematic diagram is the same as an internal comparator circuit. It has diodes, transistors, and resistors. The internally connected components work as a comparator.
Schmitt trigger comparator circuit
Schmitt trigger is a viral circuit used to improve noise immunity and reduce the likelihood of multiple switching.
A schmitt trigger is a comparator circuit with separate input switching levels for changing the outputs. The schmitt trigger comparator circuit is depicted in the below diagram.
555 timer is an oscillator circuit. It is known as 555 timers as there are three resistors of 5 kilo-ohms that are internally connected to provide the reference voltages for both the timer circuits’ comparators. A555 timer ic is used in delay timers, LED flashers, pulse generations, etc. A basic block diagram of 555 timer ic is given below. There are two comparators, an NPN transistor, a flip-flop, three 5k resistors, and an output driver.
lm324 is a general-purpose op-amp IC that has four op-amps inside it. It can be used as a comparator also. The op-amps have properties of higher stability, wider bandwidth. LM324 has 14 pins. The pin diagram of lm324 is given below.
Pin No.
Description
1
First Comparator’s Output
2
First Comparator’s Inverting input
3
First Comparator’s Non-inverting input
4
5V supply voltage
5
Second Comparator’s Non-inverting input
6
Second Comparator’s Inverting input
7
Second Comparator’s Output
8
Third Comparator’s Output
9
Third Comparator’s Inverting input
10
Third Comparator’s non-inverting input
11
Ground PIN (GND)
12
Fourth Comparator’s non-inverting input
13
Fourth Comparator’s Inverting input
14
Fourth Comparator’s Output
The circuit diagram of the LM324 comparator is depicted in the below diagram.
lm139 comparator circuit
lm139 is another comparator ic. It has four separate precision comparators. The ic is designed to function under a single power supply. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic. The ic comes with a propagation delay of 0.7 microseconds.
The below image depicts the internal circuit diagram of the lm139 comparator.
lm319 is another comparator ic having 14 pins. It has two separate precision comparators. The ic is designed to function under a wide range of supply voltages. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic, RTL, DTL. The ic comes with a propagation delay of 0.025 microseconds.
lm311 voltage comparator circuit
lm311 is another comparator ic having eight pins. It has a single comparator. The ic comes with a response time of a minimum of 0.200 nanoseconds and a typical voltage gain of 200.
The below image depicts the internal circuit diagram of the lm311 comparator.
LM 311 Comparators
lm339 comparator circuit
lm339 is another comparator ic. It has four separate precision comparators. The ic is designed to function under a single power supply and for a wide range of voltages. It is specially developed for directly interacting with Transistor-Transistor Logic and Complementary MOS logic and DTL, ECL, MOS logic. The ic comes with a propagation delay of 0.7 microseconds.
Op amp comparator circuit example
Op-amp comparator circuits are used in various applications. For example – to ensure if an input value has reached the peak or the specific value or not, or for quantization in an ADC, also in window detectors, zero-crossing detectors, etc.
Voltage window comparator circuit
A window comparator refers to the circuit that works only in a particular frame or window or voltage. And a voltage comparator compares two signals and provides the output. For a window comparator circuit, there is something called the sandwich effect: if the input voltage goes higher than the low-level reference voltage. The circuit is ON, and if the input voltage gets higher than the high-level reference voltage, then the circuit is OFF.
Components required for a voltage window comparator:
LM741 op-amps (2)
4049 Inverter Chip (1)
A resistor of 470 ohms (1)
1N4006 Diodes (2)
LED
The voltage window comparator circuit is given in the below image.
<image: vol-win1>
Latching comparator circuit
A latched comparator is developed using a StrongArm latch. The StrongArm latch is considered the primary decision amplification stage. The next stage is processed out with a latching element to carry the output load.
Op amp comparator circuit with hysteresis
The difference between Upper Trip Point and Lower Trip Point is Hysteresis. Hysteresis comes with the concept of Schmitt Trigger. If a typical comparator is designed with positive feedback, that circuit causes hysteresis. The below image depicts the circuit diagram.
Regenerative comparator circuit
A Schmitt trigger circuit is also called regenerative comparator circuits. They are used to improve noise immunity and reduce the likelihood of multiple switching Regenerative comparator circuits to design other complex circuits. They are used in ADCs, slicer circuits, memory sensing, etc. The Schmitt Trigger circuit diagram is referred to as the regenerative comparator circuit’s circuit diagram.
Temperature comparator circuit
A temperature circuit is a digital electronic circuit that measures whether the input temperature is below the specified reference temperature. It is one of the primary examples of a comparator circuit. Temperature sensors include a comparator.
Frequently Asked Questions
1. How does a comparator circuit work ?
Answer:The working principle of the comparator is pretty simple. In general, it compares between two voltage sources and provides a greater output. Below mentioned two points state the working.
If the voltage in the non-inverting terminal is higher than the inverting terminal voltage, the output is switched to the op-amp’s positive saturation voltage.
If the inverting terminal’s voltage is higher than the voltage in the non-inverting terminal, the output is switched to the op-amp’s negative saturation voltage.
2. Comparator circuit types
Answer: There are several types of comparators. Some of the widely used amplifiers are listed below.
3. Why is the output voltage in the comparator circuit of an op amp equal to the saturation voltage ?
Answer: Comparator circuits do not have any feedback associated with them. The op-amp thus has an open-loop gain. For an ideal op-amp, the open-loop gain is infinite, and for a practical op-amp, the gain is very high. Now, the saturation voltage of typical op-amps is +- 15 V. The op-amp gets saturated at +13 or -13 V. Now, the op-amp gets quickly saturated for a small input voltage. That is why the output voltage in the comparator circuit equal to the saturation voltage.
4. In an op amp comparator circuit, why is a reference voltage used
Answer:Comparison is made between two or more quantities. To indicate which is more significant, we need a reference to decide. We need to determine which voltage is more significant for a comparator. That is why a reference voltage is used to make the decision.
5. How does the digital comparator circuit distinguishes between a lesser and more significant number
Answer:A digital comparator compares two binary numbers. The comparator first finds out the equivalent voltage of the binary numbers and then determines which number is less, which number is significant.
