Engineering

Mutual inductance is a fundamental concept in the field of electromagnetism. It refers to the phenomenon where a changing current in one coil induces a voltage in another nearby coil. This occurs due to the magnetic field produced by the first coil, which cuts across the turns of the second coil, resulting in the generation of an electromotive force. Mutual inductance plays a crucial role in various applications, including transformers, inductors, and wireless power transfer systems. Understanding mutual inductance is essential for designing efficient and reliable electrical circuits.

Key Takeaways

Mutual Inductance
– Induced voltage in one coil due to a changing current in another coil
– Occurs due to the magnetic field produced by the first coil
– Essential for transformers, inductors, and wireless power transfer systems

Understanding Mutual Inductance

Mutual inductance is a fundamental concept in the field of electromagnetic induction, which is governed by Faraday’s law. It describes the interaction between two coils or inductors that are in close proximity to each other. This phenomenon occurs when the magnetic field generated by one coil induces a voltage in the other coil. Mutual inductance plays a crucial role in various electrical circuits and devices, such as transformers and inductive coupling.

What is Self and Mutual Inductance?

Before delving into mutual inductance, it is essential to understand the concept of self-inductance. Self-inductance refers to the ability of a coil or inductor to generate an electromotive force (EMF) in itself when the current flowing through it changes. This self-induced EMF opposes any change in the current, following the principles of electromagnetic induction.

On the other hand, mutual inductance occurs when the changing magnetic field produced by one coil induces a voltage in another nearby coil. The induced voltage in the second coil depends on the rate of change of the magnetic field and the number of turns in the coil. The mutual inductance between two coils is influenced by their physical proximity and the alignment of their magnetic fields.

Mutual Inductance Formula

The mutual inductance between two coils can be calculated using the following formula:

Where:
– M represents the mutual inductance
– V2 is the induced voltage in the second coil
– ΔI1 is the change in current in the first coil

The unit of mutual inductance is the Henry (H), named after Joseph Henry, a pioneer in the field of electromagnetism.

Mutual Inductance of Two Solenoids

When considering the mutual inductance between two solenoids, several factors come into play. The mutual inductance depends on the number of turns in each solenoid, the radius of the solenoids, and their separation distance. By adjusting these parameters, the mutual inductance can be increased or decreased.

Reciprocity Properties of Mutual Inductance

One of the interesting properties of mutual inductance is reciprocity. This means that the mutual inductance between two coils remains the same regardless of which coil is considered the primary and which is considered the secondary. In other words, the induced voltage in one coil due to the magnetic field of the other coil is the same as the induced voltage in the second coil due to the magnetic field of the first coil.

Mutual Inductance Equivalent Circuit

In electrical circuits, mutual inductance can be represented using an equivalent circuit. This circuit includes inductors that account for the mutual inductance between different parts of the circuit. By incorporating mutual inductance into the circuit analysis, engineers can accurately predict the behavior of complex electrical systems.

Understanding the physics of inductance and the role of mutual inductance is crucial in the field of electrical engineering. It allows engineers to design efficient transformers, analyze the reactance and impedance of circuits, and explore the concept of resonance. Moreover, inductance calculations and the understanding of electromagnetic energy transfer are essential for various applications in electrical engineering.

In summary, mutual inductance is a fundamental concept in electromagnetism that describes the interaction between two coils or inductors. It plays a vital role in the functioning of electrical circuits and devices, and its understanding is crucial for engineers in the field of electrical engineering.

Mutual Inductance in Transformers

Mutual inductance is a fundamental concept in the field of electrical engineering, particularly in the study of transformers. It is based on the principle of electromagnetic induction, which was first discovered by Michael Faraday in the early 19th century. Mutual inductance refers to the phenomenon where the magnetic field produced by one coil induces a voltage in another nearby coil.

How is Mutual Inductance Used in a Transformer?

In a transformer, mutual inductance plays a crucial role in the transfer of electrical energy from one circuit to another. A transformer consists of two or more coils, known as windings, which are wound around a common magnetic core. When an alternating current flows through the primary winding, it creates a changing magnetic field. This changing magnetic field induces a voltage in the secondary winding, allowing for the transfer of electrical power.

Mutual Inductance Transformer Formula

The mutual inductance between two coils can be calculated using the following formula:

M = k * √(L1 * L2)

Where M is the mutual inductance, k is the coefficient of coupling (ranging from 0 to 1), L1 is the self-inductance of the first coil, and L2 is the self-inductance of the second coil. This formula quantifies the extent to which the magnetic field of one coil links with the other coil.

Self-Inductance and Mutual Inductance of an Ideal Transformer

In an ideal transformer, the primary and secondary windings have perfect mutual inductance, meaning that all the magnetic flux produced by the primary winding is linked with the secondary winding. Additionally, each winding has self-inductance, which is a measure of the coil’s ability to store energy in its magnetic field. The self-inductance of a coil is determined by its physical properties, such as the number of turns and the core material.

Single-Phase and Three-Phase Transformer

Transformers can be categorized based on the number of phases they handle. A single-phase transformer is designed to transfer power between two single-phase alternating current systems. On the other hand, a three-phase transformer is used in three-phase power systems, which are commonly found in industrial and commercial applications. Three-phase transformers are more efficient and compact compared to single-phase transformers.

Auto-Transformer Definition

An auto-transformer is a type of transformer that has a single winding, which serves as both the primary and secondary winding. It is designed to step up or step down the voltage in electrical circuits. Auto-transformers are commonly used in applications where a small voltage adjustment is required, such as in voltage regulators and variable speed drives.

In conclusion, mutual inductance is a fundamental concept in transformers, enabling the efficient transfer of electrical energy between circuits. Understanding the principles of mutual inductance and its application in transformers is essential in the field of electrical engineering.

Practical Applications and Problems

Electromagnetic induction, based on Faraday’s law, is a fundamental concept in physics and electrical engineering. It has numerous practical applications and can also pose certain challenges. Let’s explore some of the practical applications and problems related to electromagnetic induction.

Mutual Inductance Circuit Problem

One common problem encountered in electrical circuits is the issue of mutual inductance. Mutual inductance occurs when two or more coils are placed close to each other, resulting in the magnetic field generated by one coil inducing a voltage in the other coil. This can lead to unwanted effects such as crosstalk or interference between circuits.

To solve mutual inductance circuit problems, the mutual inductance formula is often used. This formula calculates the mutual inductance between two coils based on their geometrical arrangement and the magnetic flux linking them. By understanding the principles of mutual inductance, engineers can design circuits that minimize or eliminate these unwanted effects.

Numerical Problems on Mutual Inductance

To further understand and apply the concept of mutual inductance, numerical problems can be solved. These problems involve calculating the mutual inductance between coils of different shapes and sizes. By solving these problems, engineers can gain a deeper understanding of the factors that affect mutual inductance and how to manipulate them to achieve desired outcomes in circuit design.

How to Insulate Two Coils to Prevent Mutual Inductance?

In certain situations, it may be necessary to insulate two coils to prevent mutual inductance. This can be achieved by using materials with high magnetic permeability, such as mu-metal, to shield the coils from each other’s magnetic fields. Additionally, physically separating the coils or using non-magnetic materials between them can also help reduce mutual inductance.

How to Achieve Zero Inductance?

While it is not possible to achieve zero inductance in a practical sense, it is possible to minimize its effects. This can be done by designing circuits with low inductance values or by using techniques such as inductive coupling, where the magnetic fields of two coils are intentionally coupled to transfer energy between them. By carefully controlling the parameters of the circuit, engineers can achieve a near-zero inductance effect.

Can Mutual Inductance be Negative?

Mutual inductance is a positive quantity that represents the coupling between two coils. It is not possible for mutual inductance to be negative. However, it is important to note that the induced voltage in the secondary coil can have a polarity opposite to that of the primary coil, depending on the direction of the magnetic field and the relative orientation of the coils.

In conclusion, understanding and managing mutual inductance is crucial in the design and operation of electrical circuits. By applying the principles of electromagnetic induction and utilizing techniques to minimize its effects, engineers can ensure the efficient and reliable functioning of various electrical systems.

Advanced Concepts

In the field of electrical engineering, there are several advanced concepts related to electromagnetic induction and coil inductance that are worth exploring. These concepts include mutual inductance of parallel wires, methods to reduce mutual inductance, mutual inductance coupling coefficient, derivation of mutual inductance, and the formula for calculating mutual inductance of two coils. Let’s delve into each of these concepts in more detail.

Mutual Inductance of Parallel Wires

Mutual inductance refers to the phenomenon where the magnetic field produced by one coil induces a voltage in another coil. When two parallel wires carry electrical currents, they generate magnetic fields that interact with each other. The mutual inductance of parallel wires describes the extent to which these magnetic fields influence each other. It plays a crucial role in understanding the behavior of electrical circuits and is governed by Faraday’s law of electromagnetic induction.

How to Reduce Mutual Inductance?

In certain situations, it may be desirable to reduce the mutual inductance between two parallel wires. This can be achieved through various methods. One approach is to increase the distance between the wires, as the magnetic field strength decreases with distance. Another method involves twisting the wires together, which helps to cancel out the magnetic fields generated by each wire. Additionally, using shielding materials can effectively reduce the mutual inductance by confining the magnetic fields within the wires.

Mutual Inductance Coupling Coefficient

The mutual inductance coupling coefficient is a measure of the coupling efficiency between two coils. It quantifies the extent to which the magnetic field produced by one coil links with the other coil. The coupling coefficient ranges from 0 to 1, where 0 indicates no coupling and 1 represents perfect coupling. It is an important parameter in the design and analysis of transformers and inductive coupling systems.

Mutual Inductance Derivation

The derivation of mutual inductance involves mathematical calculations based on the principles of electromagnetic induction. It takes into account factors such as the number of turns in the coils, the magnetic flux linking the coils, and the geometry of the coils. By understanding the derivation of mutual inductance, one can gain insights into the physics of inductance and its role in electrical circuits.

Mutual Inductance of Two Coils Formula

The mutual inductance between two coils can be calculated using a formula that takes into account various parameters. The formula involves the number of turns in each coil, the magnetic flux linking the coils, and the geometrical arrangement of the coils. This formula is widely used in the design and analysis of transformers, where mutual inductance plays a crucial role in transferring electrical energy from one coil to another.

By understanding these advanced concepts related to mutual inductance, one can gain a deeper insight into the physics of inductance and its applications in electrical engineering. These concepts are fundamental to the study of electromagnetic fields, reactance, impedance, resonance, and the calculation of inductance in various electrical systems.

Frequently Asked Questions

Is Mutual Inductance Always Positive?

No, mutual inductance can be positive or negative depending on the orientation of the coils and the direction of the current. Mutual inductance is a measure of the interaction between two coils and is defined as the ability of one coil to induce a voltage in the other coil. If the current in one coil produces a magnetic field that reinforces the magnetic field of the other coil, the mutual inductance is positive. Conversely, if the magnetic fields oppose each other, the mutual inductance is negative.

Does Mutual Inductance Depend on Current?

Yes, mutual inductance depends on the current flowing through the coils. According to Faraday’s law of electromagnetic induction, the induced voltage in a coil is directly proportional to the rate of change of magnetic flux through the coil. Therefore, the greater the current flowing through a coil, the stronger the magnetic field it produces, and the higher the mutual inductance between the coils.

How to Measure Mutual Inductance?

Mutual inductance can be measured using various techniques. One common method is to connect the two coils in series and apply an alternating current to one of the coils. By measuring the voltage induced in the other coil, the mutual inductance can be determined. Another method involves using a mutual inductance bridge circuit, which allows for more precise measurements. Additionally, mutual inductance can also be calculated indirectly by measuring the self-inductance of each coil and using the mutual inductance formula.

How to Calculate Mutual Inductance of a Transformer?

The mutual inductance of a transformer can be calculated using the formula:

M = (k * √(L1 * L2))

Where M is the mutual inductance, k is the coupling coefficient (a value between 0 and 1 that represents the degree of magnetic coupling between the coils), L1 is the self-inductance of one coil, and L2 is the self-inductance of the other coil. The mutual inductance is typically measured in henries (H).

Difference Between Mutual Induction and Mutual Inductance

Mutual induction and mutual inductance are related concepts but have distinct meanings. Mutual induction refers to the process by which a changing current in one coil induces a voltage in another coil. It is a fundamental principle of electromagnetic induction and is the basis for the operation of transformers and inductive coupling in electrical circuits.

On the other hand, mutual inductance is a quantitative measure of the interaction between two coils. It represents the ability of one coil to induce a voltage in the other coil and is determined by factors such as the number of turns, the orientation of the coils, and the current flowing through them. Mutual inductance is calculated using the mutual inductance formula and is expressed in henries (H).

In summary, mutual induction is the phenomenon, while mutual inductance is the measure of that phenomenon. Understanding the concepts of mutual induction and mutual inductance is essential in the study of inductors, transformers, and the physics of inductance in electrical engineering.

Conclusion

In conclusion, mutual inductance is a fundamental concept in the field of electromagnetism. It refers to the phenomenon where a changing current in one coil induces a voltage in another nearby coil. This mutual interaction between the coils is crucial in various applications, such as transformers and inductors.

Mutual inductance plays a vital role in the efficient transfer of energy between different circuits. It allows for the transformation of voltage levels, enabling the transmission of electrical power over long distances. Additionally, mutual inductance is utilized in devices like electric motors and generators, where the conversion of electrical energy to mechanical energy is required.

Understanding mutual inductance is essential for engineers and scientists working in the field of electronics and electrical engineering. It provides the foundation for designing and analyzing complex circuits and systems. By grasping the principles of mutual inductance, we can harness its power to create innovative technologies that shape our modern world.

Multiple Choice Questions

MCQ on Inductor

1. What is an inductor?
2. A. A device that stores electrical energy in a magnetic field
3. B. A device that converts electrical energy into mechanical energy
4. C. A device that generates electrical energy from light

5. D. A device that regulates the flow of current in a circuit

6. Which of the following is true about inductance?

7. A. It is the property of a circuit that opposes changes in current
8. B. It is the property of a circuit that allows easy flow of current
9. C. It is the property of a circuit that converts electrical energy into mechanical energy

10. D. It is the property of a circuit that regulates the voltage

11. What is the unit of inductance?

12. A. Ampere (A)
13. B. Ohm (Ω)
14. C. Henry (H)

15. D. Volt (V)

16. Which formula is used to calculate the inductance of a coil?

17. A. Ohm’s Law
18. B. Faraday’s Law
19. C. Henry‘s Law
20. D. Coulomb’s Law

MCQ on Mutual Inductance Transformer Related

1. What is mutual inductance?
2. A. The property of a circuit that opposes changes in current
3. B. The property of a circuit that allows easy flow of current
4. C. The property of a circuit that converts electrical energy into mechanical energy

5. D. The property of a circuit that relates the change in current in one coil to the change in current in another coil

6. What is a transformer?

7. A. A device that stores electrical energy in a magnetic field
8. B. A device that converts electrical energy into mechanical energy
9. C. A device that generates electrical energy from light

10. D. A device that transfers electrical energy between two or more coils through electromagnetic induction

11. How is mutual inductance calculated in a transformer?

12. A. By using Faraday’s Law
13. B. By using Ohm’s Law
14. C. By using Henry’s Law

15. D. By using Coulomb’s Law

16. What is inductive coupling?

17. A. The transfer of energy between two coils through mutual inductance
18. B. The transfer of energy between two coils through self-inductance
19. C. The transfer of energy between two coils through capacitive coupling
20. D. The transfer of energy between two coils through resistive coupling

Remember to choose the most appropriate answer for each question. Good luck!

Detailed Solutions to Problems and MCQs

Welcome to the detailed solutions section, where we will explore various problems and multiple-choice questions related to electromagnetic induction, Faraday’s law, and other concepts in the field of inductance. Let’s dive right in!

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In this section, we will focus on the concept of electromagnetic induction and its applications. Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor when it is exposed to a changing magnetic field. This phenomenon, discovered by Michael Faraday, forms the basis of many electrical devices and plays a crucial role in electrical engineering.

To understand the principles of electromagnetic induction, let’s start with a simple example. Imagine we have a coil of wire and a magnet. When we move the magnet towards the coil, the magnetic field passing through the coil changes. This change in magnetic field induces an emf in the coil, causing an electric current to flow. This is the basic principle behind generators and electric motors.

Now, let’s move on to some problems and multiple-choice questions to test our understanding of electromagnetic induction and related concepts. Here are a few examples:

1. Problem: Calculate the magnetic field strength inside a solenoid with 500 turns and a current of 2A flowing through it.
   Solution: We can use the formula for the magnetic field inside a solenoid, which is given by B = μ₀ * n * I, where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. Plugging in the values, we get B = (4π * 10^-7 T*m/A) * (500 turns/m) * (2A) = 0.004 T.

2. Multiple-Choice Question: Which of the following is an example of inductive coupling?
   a) Capacitor
   b) Transformer
   c) Resistor
   d) Diode
   Answer: b) Transformer

3. Problem: Calculate the self-inductance of a coil with an inductance of 5 H and a current changing at a rate of 2 A/s.
   Solution: We can use Faraday’s law of electromagnetic induction, which states that the emf induced in a coil is equal to the rate of change of magnetic flux through the coil. The formula for self-inductance is L = Φ/I, where L is the self-inductance, Φ is the magnetic flux, and I is the current. Rearranging the formula, we get Φ = L * I. Plugging in the values, we get Φ = (5 H) * (2 A/s) = 10 Wb.

These are just a few examples to give you an idea of the types of problems and multiple-choice questions you may encounter when studying electromagnetic induction and inductance. Remember to practice and understand the underlying concepts to excel in this field.

In conclusion, electromagnetic induction and the concepts of inductance play a crucial role in electrical circuits and the field of electrical engineering. Understanding the principles behind electromagnetic induction, Faraday’s law, and other related concepts is essential for designing and analyzing electrical systems. So keep exploring and learning more about the fascinating world of inductance and its applications!

Frequently Asked Questions

1. Can mutual inductance be negative?

No, mutual inductance cannot be negative. It is a measure of the amount of magnetic flux generated in one coil due to the change in current in another coil. It is always a positive value, as it is based on the absolute value of the magnetic field interaction between the two coils.

2. What is the mutual inductance formula?

The mutual inductance formula is M = N2Φ/I1, where M is the mutual inductance, N2 is the number of turns in the second coil, Φ is the magnetic flux through one loop of the second coil, and I1 is the current in the first coil.

3. What does mutual inductance mean?

Mutual inductance is a property that exists between two coils when the change in current in one coil induces a voltage in the other coil. It is a fundamental concept in electromagnetic induction and is measured in Henrys (H).

4. How to measure mutual inductance with an LCR meter?

To measure mutual inductance with an LCR meter, connect the two coils in series and measure the total inductance. Then, reverse the connections of one coil and measure the inductance again. The difference between these two measurements divided by 4 gives the mutual inductance.

5. How does mutual induction occur?

Mutual induction occurs when a change in current in one coil induces a voltage in a nearby coil. This happens due to the magnetic field produced by the current-carrying coil, which links with the turns of the nearby coil and induces a voltage in it according to Faraday’s law of electromagnetic induction.

6. What is the mutual inductance of a pair of coils?

The mutual inductance of a pair of coils is a measure of how much a change in current in one coil will induce a voltage in the other coil. It depends on factors like the number of turns in each coil, the area of the coils, the distance between the coils, and the medium in which the coils are located.

7. How to reduce mutual inductance?

Mutual inductance can be reduced by increasing the distance between the coils, decreasing the number of turns in the coils, or orienting the coils so that their magnetic fields do not interact significantly.

8. What is the mutual inductance in a transformer?

In a transformer, the mutual inductance is the property that allows the transfer of energy from the primary coil to the secondary coil. It is a measure of how effectively the magnetic field generated by the primary coil induces a voltage in the secondary coil.

9. What is the symbol for mutual inductance?

The symbol for mutual inductance is ‘M’. It is measured in Henrys (H).

10. How is the mutual inductance of a pair of coils affected when the distance between them changes?

The mutual inductance of a pair of coils decreases as the distance between them increases. This is because the magnetic field generated by one coil has less effect on the other coil when they are further apart.

A D Flip Flop stores a single bit of data; its output mirrors the input (D) when the clock (CLK) is high. Truth table: When CLK=1, if D=0, output Q=0, if D=1, Q=1; When CLK=0, Q remains unchanged. It’s edge-triggered, changing state only at clock edges, ensuring stable data storage and synchronization in digital circuits. Ideal for shift registers, data storage, and synchronizing asynchronous inputs.

A flip flop is the fundamental sequential circuit element, which has two stable states and can store one bit at a time. It can be designed using a combinational circuit with feedback and a clock. D Flip-Flop is one of that Flip Flop that can store data. It can be used to store data statically or dynamically depends on the design of the circuit. D Flip-Flop is used in many sequential circuits as register, counter, etc.

What is D flip flop ?

D flip-flop or Data flip flop is a type of flip Flop that has only one data input that is ‘D’ and one clock pulse input with two outputs Q and Q bar. This Flip Flop is also called a delay flip flop because when the input data is provided into the d flip-flop, the output follows the input data delay by one clock pulse.

Full Form of D flip flop

D stands for Delay or Data in D flip-Flop.

D flip flop Diagram

The given circuit represents the D flip-flop circuit diagram, where the whole circuit is designed with the help of the NAND gate. Here the output of one NAND gate is feed as one input to the other NAND gate, which forms a latch. Then, the latch is gated with two more NAND gates where D is one input and clock is the other input. 

The final output of the D flip-flop is Q and Qbar, where Qbar is always complementary to Q.

D Flip Flop Truth Table

What is D Flip Flop Truth Table ?

The truth table of the d flip flop shows every possible output of the d flip-flop with the all possible combination of the input to the d flip flop, where Clock and D is the input to the D flip-flop and Q and Qbar is the output of the D flip-flop.

CLOCK	D	Q	Qbar
0	0	NO CHANGE	NO CHANGE
0	1	NO CHANGE	NO CHANGE
1	0	0	1
1	1	1	0

D flip flop Excitation Table

The exaltation table or state table shows the minimum input with respect to the output that can define the circuit. Which mainly represents a sequential circuit with its present and next state of output with the preset input and clock pulse. This table is also known as a characteristic table for D flip-flop.

Din	CLK	Present state ‘Q’	Next state ‘Q’
X	0	0	0
X	0	1	1
0	1	0	0
0	1	1	0
1	1	0	1
1	1	1	1

D flip flop Boolean Expression

The boolean expression of the D flip-flop is Q(t+1)=D because the next value of Q is only dependent on the value of D, whereas there is a delay of one clock pulse from input D to output Q.

How D Flip Flop Works ?

Working of D flip flop

D Flipflop is a bi-stable memory element, which can store one bit at a time, either ‘1’ or ‘0’. When the D input is provided to the Flip Flop, the circuit check for the clock signal is the signal of the clock is high ( for level triggered d flip-flop) then with every clock pulse, the input D propagates to the output Q. 

For edge triggered flip-flop, the circuit check for the transition of clock pulse according to which the flip Flop propagates the input to the output; edge triggered can be positive edge triggered or negative triggered. Positive edge triggered D flip-flop changes its output according to input with every transition of the clock pulse from 0 to 1. As for the negative edge triggered D flip-flop changes its output according to input with every transition of the clock pulse from 1 to 0.

D flip flop Timing Diagram

As shown in the given figure, there is a clock pulse representation, with which D, which is the input to D flip-flop, and Q which is the output, is represented, where Qbar is the complement output of the output Q, here we see the timing diagram of a positive edge flip flop, that’s why here the output changes with every positive transition in the clock pulse according to the input.

D flip flop Block Diagram

The diagram shown below is the block representation of the d flip-flop, where D is the input, the clock is another input to the Flip Flop, where a preset and clear signal is used to set or reset the output Q of the D flip-flop. 

What is D flip flop Symbol ?

D flip flop Clear and Preset

The given figure is the block diagram of a D flip-flop having preset/set and rest / clear as additional input to the Flip Flop, where Preset/Set is used to set the output Q of the flip Flop set to 1. Rest/Clear is to set the output Q of the flip Flop to 0.

D flip flop with Set

D flip-flop can have set the input as a requirement, and it can change the output and set the output Q to 1. It can be synchronous or asynchronous, Synchronous when the output can change only with the clock pulse, asynchronous is when the output can be set to 1 at any point of time regardless of the clock pulse.

D flip flop with Reset

D flip-flop can sometimes reset / clear input only in addition to data input and clock input, resetting the output Q to zero of the d flipflop as a requirement. Reset/Clear be active low input or active high input depends on the Flip Flop design.

Asynchronous Set and Reset

D flip flop with Asynchronous Set and Reset

D flip-flop can have an asynchronous set/preset and reset/clear as input independent of the clock. That means the output of the Flip Flop can be set to 1 with preset or reset to 0 with the reset despite the clock pulse, which means the output can change with or without a clock, which can result in asynchronous output.

D flip flop with Asynchronous Reset

D flip-flops can have asynchronous reset, which can be independent of the clock. Regardless of the clock, the reset can change the output Q to zero, which can cause asynchronous output.

D flip flop with Synchronous Reset

D flip-flop with synchronous reset means the output can reset to zero with the reset input but only with the clock, which makes the reset input dependent on the clock pulse; without clock pulse reset will not be able to set the output Q to zero, which will give you a synchronous output always.

D Flip Flop with Enable

Other than set/preset or reset/clear D flip-flop can have enabled as one input when enable is high, the Flip Flop can operate with the data input and clock input, but when the enable is low then regardless of any other input, the flip Flop stays in a hold state.

D flip flop with Enable Truth Table

EnableDQn01NO CHANGE00NO CHANGE111100Table: D flip-flop truth table with enable input

 

D flip flop Truth Table with Preset and Clear

PR (ACTIVE LOW)	CLR(ACTIVE LOW)	CLK	D	Q	Qbar
0	1	X	X	1	0
1	0	X	X	0	1
0	0	X	X	NOT DEFINED	NOT DEFINED
1	1	1	1	1	0
1	1	1	0	0	1
1	1	1	X	NO CHANGE	NO CHNAGE

D flip flop Truth Table with Clock and Reset

CLK	RESET	D	Q
0	X	X	NO CHANGE
1	1	X	0
1	0	1	1
1	0	0	0

Asynchronous D flip flop

When D flip-flop generates output independent of the clock signal, then the output produced may be asynchronous. It is mainly caused by an asynchronous set/preset or clear/reset signal, which can set or reset the output of the flip Flop at any intent of time, which disrupt synchronicity in the D flip-flop.

State Diagram for D Flip Flop

The state diagram is the representation of a different stable state with the transition between the states with the cause of transition. Here every stable state output of the D flip-flop is represented with a circle. In contrast, the transition between the state is represented by the arrow between the circle, which is leveled with the cause of the transition.

When the state changes from 0 to 1, it is caused by the input D, which is high, and when the output state is 0, and at the time D=0 that produces no change in the output, the arrow with D=0 starts with state 0 and also returns to state 0.

ASM Chart for D flip flop

An algorithmic state machine chart contains three blocks: state block, condition block, and conditional output box. The rectangle box represents one state; the diamond box is the condition box true or false if the condition decides the branch to follow.

D flip flop schematic | D Flip Flop Schematic Circuit | D Type Flip Flop Schematic

The figure shows the schematic representation of the D flip-flop; the schematic diagram represents the procedure using abstract. 

Two diagrams show the working of the D flip-flop when the clock is high and another showing when the clock is low. When the clock is high, the input data passes through the circuit, but when the clock is low, the input can not pass through the circuit, which shows regardless of the change in input, there will be no change in output when the clock is low.

Dynamic D flip flop

Flip Flop is generally a static storing device, but a dynamic flip flop can dynamically store data. In the given schematic diagram of a dynamic flip flop, we can see a capacitor connected to each stage. When there is no clock pulse for a long time, the capacitor’s charge can be lost. However, because of the presence of the capacitor, the circuit will be able to store data dynamically.

Dynamic D flip-flop is designed for faster operation; the area covered by dynamic flip flop is less than that of a static flip flop.

D flip flop Metastability

Metastability refers to the state where output is not deterministic. It can cause oscillation, unclear transitions in the circuitry. For example, flip Flop faces the problem of metastability; it happens to a flip flop when the clock pulse and data change at the same instate of time, which causes the result to behave unpredictably.

To avoid metastability in flip Flop the operation of flip Flop should operate considering the setup time and hold time of the Flip Flop. Still, metastability cannot be eliminated completely, but it can be minimized.

Application of D flip flop

Important applications of D flipflop listed as follows :

• D flip-flop can be used to produce a controlled delay in the circuitry.
• Used to design frequency divider circuity.
• For creating counters.
• For developing registers.
• Used in pipelining.
• For synchronization.
• Can be used to avoid glitches.
• Used to fix clock frequency as for the requirement of the circuitry.
• Can be used for isolation.
• As Toggle switch.
• Can be used for Data transmission.
• Sequence generator.
• Can be used as a memory element.

Difference Between D and T flip flop

D FLIP-FLOP	T FLIP FLOP
The output of a d flip flop follows the input with a delay of one clock pulse.	The output of T flip flop toggles with a high input with every clock pulse.
It is known as delay flip flop	It is known as toggle flip flop
With low input the output also changes to low with clock pulse	With low input the output does not change at all, it stays in hold state.

Difference Between D flip flop and JK flip flop

D flip-flop	J K flip flop
The output of a d flip flop follows the input with a delay of one clock pulse.	The output of a J K flip flop sets to 1 with J and resets to 0 with R  when there is clock pulse.
It is known as delay flip flop.	It is also called universal flip flop.
It has less number of input combinations.	It has more number of input combinations.

Difference Between D latch and D flip flop

D latch	D flip-flop
D latch is a gated SR latch, which do not have clock input	D flip-flop is combination of D latch with clock input
Less complex circuit	Complex circuit
D latch is has enable signal which can enable or disable the latch operation	D flip-flop has clock signal which can hold or operated the flip flop when no set or reset input is available.
D latch can be active high input or active low input latch.	D flip-flop in which data input is always active high, where set or reset input can be active high or active low input.
D latch is always a level triggered circuit.	D flip-flop can be level triggered or edge triggered circuit.
Less number of transistor is required for design.	More number of transistor is required for design.
Asynchronous in nature.	Generally synchronous in nature.

Q: What is a flip-flop in digital electronics?

A: In digital electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information. They are fundamental building blocks in sequential logic, with the D-type flip flop being a commonly-used type.

Q: What is a d-type flip flop?

A: A D-type flip flop is a type of flip flop circuit that has a D (data) input and a clock input. The D flip-flop captures the value of the D-input at a definite portion of the clock cycle (such as the rising edge). This can be thought of as the flip flop “sampling” the D input and storing it.

Q: How do logic gates interact in a d-type flip flop?

A: A D-type flip flop can be implemented using a combination of logic gates such as AND and OR gates, as well as inverters. The particular arrangement of these gates determines the output of the flip-flop for each input condition.

Q: What distinguishes a d-type flip flop from an sr flip-flop?

A: One key difference is that an SR flip-flop requires two inputs, namely S (Set) and R (Reset), while a D-type flip flop takes both a data input and a clock input. Consequently, the behaviour and use cases of these flip flop types are different in digital electronics.

Q: Can you explain the working of a D flip-flop action on the rising edge of the clock?

A: The D flip-flop is sensitive to the clock edge, i.e., the transition from low to high (rising edge) or high to low (falling edge). When the clock signal goes from low to high on the rising edge, the value on the D input is transferred to the flip-flop’s output. At other times, the output remains what was last stored.

Q: How does a D flip flop compare to a JK flip-flop?

A: The JK flip-flop and the D type flip-flop are two types of flip-flops in digital electronics. The JK flip-flop, like the SR flip-flop, has two inputs but does not have the invalid state that the SR flip-flop has when both inputs are 1. The D flip-flop, on the other hand, eliminates this ambiguity by having only one input that determines what state the flip flop will change to, with the change in state being triggered by a clock edge.

Q: How does a D flip-flop function in shift registers?

A: In a shift register, multiple D flip-flops are chained together in a configuration known as a cascade. Each flip-flop passes its output as the input to the next flip-flop on each clock cycle, effectively shifting the binary data held by the register.

Q: What is a truth table in the context of a D flip-flop?

A: A truth table for a D flip-flop is a table that describes how the output of the flip-flop depends on its current output and current input. For a D-type flip-flop, the next state is exactly what the data input is at the time of a positive clock edge.

Q: What is the characteristic equation of a D flip- flop?

A: The characteristic equation of a D flip-flop is simple: The next output Q(next) equals the current input D (Q(next) = D). This is as per data input from the flip flop at the time of a positive clock edge.

Q: How does a delay flip-flop (D FF) work?

A: A delay flip-flop (D FF), sometimes known as a D-type flip-flop, behaves just like a wire delayed by one clock period. It takes an input signal and outputs that same signal, but delayed by one clock cycle. In essence, the D FF “remembers” the input value at the rising edge of the clock and delays it by one clock cycle.

Q: What is an SR flip-flop in digital electronics?

A: An SR flip-flop, one of the types of flip-flops in digital electronics, is a form of a sequential logic circuit often utilized for data storage. An SR flip-flop requires two inputs, specifically, the set (S) and reset (R) inputs. The output changes or retains its state when it faces different input conditions, making it a fundamental building block of digital electronics.

Q: How does a D-type flip flop work?

A: A D-type flip-flop operates with a data input and a clock input. At the rising edge of the clock input, the d-type flip flop transfers the input data to the output. Thus, it acts as a delay or edge-triggered device in digital electronics, transmitting the data input from the flip flop’s input to its output during clock pulses.

Q: What is a JK flip-flop?

A: A JK flip-flop is another type of flip flop circuit found in digital logic. It extends the functionality of the SR flip flop by addressing the input condition issue where both inputs are 1. With a JK flip-flop, this state triggers a toggle, causing the flip flop to change state at every clock edge.

Q: What are logic gates, and how do they relate to flip flops?

A: Logic gates are fundamental building blocks in digital electronics that process binary inputs to produce a binary output based on the type of gate. Flip flops, including D-type and SR flip-flops, are composed of interconnected logic gates. The combination of these logic gates determines how a flip flop behaves in terms of its characteristic equation.

Q: Can flip flops be used as shift registers in digital logic?

A: Yes, flip flops can be utilized to implement shift registers in digital logic. A shift register is a sequential device that utilizes flip-flops to store binary data. In a shift register, data is passed from the output of one flip flop to the inputs of the next flip-flop in a cascade configuration, in synchronization with clock pulses.

Q: What are the input signals in a flip flop?

A: The input signals in a flip flop vary depending on the type of flip flop circuit used. For an SR flip-flop, the two inputs are known as set and reset. For a D-type flip-flop, the two inputs are data and clock. An additional input, known as ‘enable’, may be used in certain types of flip-flops.

Q: What happens when a flip flop receives a rising edge input signal?

A: When a flip flop receives a rising edge input signal, i.e., a transition from a low voltage to a high voltage, a state change typically occurs. In a D-type flip flop, for instance, the state of the data input is captured at the moment of the rising edge of the clock and is transferred to the output.

Q: What role does an inverter play in the operation of a flip flop?

A: An inverter, another basic block of digital electronics, plays a crucial role in the functioning of a flip flop. It is used in a flip flop circuit to invert the output, specifically, a high output becomes low, and vice versa. In the SR flip-flop, for instance, an inverted output from one part of the circuit is often looped back as an input to another part, creating a form of feedback that enables the flip flop to maintain its state.

Q: What is meant by ‘since the output of a flip flop would always change’?

A: When we say ‘since the output of a flip flop would always change’, we’re referring to the inherent characteristic of a flip flop as a bistable device. This means that it has two stable states and can transition between these states based on its input. Thus, depending on the input conditions and type of flip flop circuit, the output of the flip flop can change or retain its prior state, making it a crucial component in digital electronics where data storage and transfer are required.

Q: What leads a flip flop to change state?

A: A flip flop changes state based on its input signal(s). For instance, an SR flip-flop changes state when either the Set or Reset input is activated, and a D-type flip flop changes state based on the data input at the moment of a clock edge, especially a rising edge. The change state feature of flip flops makes them pivotal in designing digital systems for various applications, from basic data storage units to complex microprocessors.

What is current and voltage division?

Voltage and current divider

Current and voltage division are real-life examples of Kirchhoff’s laws. The current division takes place in a parallel circuit, while voltage division occurs in a series circuit.

What are the current divider rule and voltage divider rule?

Current divider rule | Current divider law

What is a current divider?

The current-divider rule is a practical application of Kirchhoff’s current law. It states that,

In a circuit with a parallel combination of resistors, the current gets divided into all the branches having the same voltage across them. Thus a parallel circuit behaves as a current divider.

What is Voltage divider with current source ?

Voltage divider current

A voltage divider with a current source divides the supply voltage in the resistances. The voltagedrop across any resistor is the multiplication of the resistances with the value of current in the circuitry.

Current divider circuit example

Let us take a circuit with a DC voltage source of V volt and two resistors R₁ and R₂, connected in parallel. The total current in the circuit is i,  current through R₁ is i₁, and R₂ is i₂.

What is Current divider theory | Current divider rule definition | Current divider definition ?

Current divider theorem | Current divider principle

The current-divider rule says that the current in any branch of the parallel circuit is equal to the total current in the circuit multiplied by the ratio of the resistance of the opposite branch and the total circuit resistance.

Current divider rule derivation | Formula derivation

Current divider parallel

In the image1, we can see two parallelly connected resistances R₁ and R₂, are joined with a DC voltage V and currents thru them are i₁ and i₂, respectively.

The equivalent resistance of the circuit is

=11

What is Voltage and current divider formula ?

Current divider rule formula

According to the currentdivider rule,

Current in through any resistor = Total current of the network x resistance of other resistor/equivalent resistance of the circuit.

Voltage divider rule

According to the voltage divider rule,

The voltage drop across any resistor = Total current of the network x resistance of that resistor

Current divider equation | Derive current divider equation

For the above circuit, we can see that resistances R₁, R₂, R₃, and R_X are connected in parallel. A voltage source is added to this combination, and current I_T flows through the circuit. The equivalent resistance of R₁, R₂, and R₃ is denoted as R_T, and If the current across resistor R_X is I_X, we can say that,

What is Current divider rule for 2 resistors in parallelly connected ?

Parallel circuit current divider | Current divider formula for parallel circuit

Two resistors R₁ and R₂, are connected in parallel with a DC source V. If the currents i₁ and i₂ flow through them and the total current is I then,

What is the Current divider rule for 3 resistors in parallelly ?

Current divider rule for 3 resistors

Three resistors R₁, R₂, and R₃, are connected in parallel with a voltage source V. Total current in the circuit is I_T and branch currents are i₁, i₂, and i₃, respectively. Therefore,

Current in a voltage divider

As the voltage dividers are series circuits, the current through all the resistors or impedance elements is the same. With the help of the total current, the voltage divider rule is constructed. The voltage drop across any resistor equals the total current multiplied by the resistance of that resistor present in the circuitry.

Current divider applications | Current divider examples

• The main purpose of using a current division is to reduce complexity while solving for current in any circuit. It divides the current into small components.
• Current division is used to protect circuits from overheating. As it divides the total current into fractions, small current components generate, and large current flow is avoided. This allows less heat dissipation and saves the circuits from any damage.

High current voltage divider

A voltage divider that can deliver a high amount of current is difficult to be built with a traditional resistor network. A switching regulator or a buck converter type design can come in handy in this case. For the buck converter approach, its voltage reference can be replaced with a divider derived from the incoming supply.

Series voltage divider with parallel load current

If a load resistance is connected with the voltage divider in parallel, the overall equivalent resistance decreases. Therefore the current in the circuit increases, but the voltage at the divider output drops.

AC current divider

AC circuits function the same as DC. Just the impedances must be written with their phasor representations using the complex quantity j.

Current divider impedance

If we generalize the resistive network equation for elements other than resistance,

Where I_T is the total current, I_X is the current through a particular branch, Z_T is the equivalent impedance of the circuit, and ZX is the impedance of that branch.

To know about Inductors in Series and Parallel click here

How to use the current divider rule? How to apply the current divider rule? | How to divide current in a parallel circuit?

Current divider method

The current division is calculated in the following steps:

• First, find the equivalent resistance R_T of the other circuit elements, excluding the one for which current needs to be calculated (R_X)
• Compute the fraction of this R_T and R_T + R_X
• Multiplying this quantity with the total current would fetch the desired branch current I_X.

What is the difference between voltage divider and current divider ?

Voltage divider and current divider | Current divider vs voltage divider

Current Divider	Voltage Divider
It is constructed through parallel circuits.	It is constructed through series circuits.
The values of current through the resistors are measured.	The values of voltage drop through the resistors are measured.
The voltages in all the resistors are equal, the currents vary.	The currents in all the resistors are equal, the voltages vary.

Low current voltage divider

Voltage divider circuits with low or almost zero current can be used to design switches with an additional transistor.

Voltage divider current limit

There’s no specific limit for current in a voltage divider. However, observed values suggest that currents over 1 amp can be regarded as high for the voltage dividers.

Current divider problems with solutions

Current and voltage divider

Q. Two impedances, Z₁ = 2+j5 and Z₂ = 5+j2, are connected in a parallel circuit. Total current, I = 10 amp. Using the current division, find out the currents through individual impedances.

We know,

Therefore, I₁ = 10 x (5+j2)/ 2+j5+5+j2 = 5(7-j3)/7 amp

I₂ = I – I1 = 10 – 5(7-j3)/7 = 5(7+j3)/7 amp

Current and voltage divider examples | current and voltage divider problems

Q. Three resistors of 6 ohm, 12 ohm, and 18 ohm are connected in series with DC supply voltage 54V, then calculate the voltage drop across all the resistors.

The voltage divider rule says that voltage drop across any resistor in a series circuit = resistance of that resistor x the current.

Now, equivalent resistance of the circuit = 6 + 12 + 18 = 36 ohm

So, net current in the circuit = 54/36 = 1.5 A

Therefore, voltage drop across 6 ohm resistor = 1.5 x 6 = 9 Volt

voltage drop across 12 ohm resistor = 1.5 x 12 = 18 Volt

voltage drop across 18 ohm resistor = 1.5 x 18 = 27 Volt

Current divider rule example problems | Current divider sample problems

Q. 4 resistors with resistances 5 ohm, 10 ohm, 15 ohm, and 20 ohm are connected in parallel with a voltage source. The total current in the circuit is 5A, then compute the current thru the 10Ω resistor.

The equivalent resistance of the circuit = 5 x 10 x 15 x 20 / (50 + 75 + 100 + 150 + 200 + 300) = 17.14 Ohm

Therefore, current through the 10 ohm resistor = 5 x 17.14/10 = 8.57 A

Q. Two resistors of 10 ohm and 20 ohm are connected in parallel with a 200 V DC supply, then compute current thru the 20Ω resistor.

Net resistance in the circuit = 10 x 20/ 30 = 20/3 ohm

Total current in the circuit = 200/(20/3) = 30 A

So the current through 20 ohm resistor = (20/3)/20 x 30 = 10 A

Q. For the network with n resistances shown below, R₁ = R₂ = R₃ = ………= R_n = R. Find the current passing through R_n.

Equivalent resistance of the circuit,

We know the total current in the circuit is I

Therefore, current through R_n = (R/n)/R x I = I/n

Frequently Asked Questions | Short Notes | FAQs

Q. How can we calculate the current division?

Current division occurs in a parallel circuit. The supply current gets divided into branches connected in parallel. The voltage across all the branch resistors is equal to voltage supplied. With the help of Ohm’s law and Kirchhoff’s current law, the current division is calculated. The divided current in one branch is the multiplication of the total current and the ratio of the other branch’s resistance with the sum of all the resistance.

Q. In which condition is the current divider rule applicable?

The currentdivider rule is applicable for any circuit where resistance or other impedance parameters are connected in parallel.

Q. What is the advantage of applying the current-divider rule in a parallel circuitry ?

The basic reason for using the current-divider rule in parallel circuits is to make problem-solving easier. In a parallel circuit, the current gets divided into branches, So calculating current thru the branches becomes less time-consuming if the total current is known.

Q. Does the current division rule disobey Ohm’s law?

The Current-divider rule is based on Ohm’s law itself. The fundamental concept of Ohm’s law is used to calculate the divided currents.

Q. State the difference between a voltage divider and a current divider?

The main difference between a voltage divider and a current-divider is the operating circuit. The Voltage divider rule is applied in series circuits where as the current-divider rule is utilized in parallel circuit.

Q. When can we apply the voltage divider and the current divider rule?

In a series circuit, the voltage divider rule is used to calculate the voltage drop across the resistors. In a parallel circuit, the current-divider rule is used to calculate the branch currents.

Q. What are the voltage dividers?

The voltage dividers are linear circuits where the output voltage is obtained from the fraction of input voltage. The most common example of voltage is a potentiometer.

Q. How to use a rheostat so that it works as a potential divider and current limiter?

A rheostat can be used as a large variable resistor. It has three terminals, two at the ends and one movable contact. By adding voltage sources at the ending terminals, the voltage across the other terminal is obtained. This way the rheostat works as a potential divider, and the terminals work as current limiters.

Q. What are the advantages of a voltage divider?

A voltage divider helps in getting the voltage drop across components from the large supply voltage.

Q. How can we calculate the value of current passing through the resistor R₁ in the circuit?

The current through resistor R₁ is the total current multiplied by the other resistance divided by the sum of all resistance in the circuit.

Q.Why cannot we use the voltage divider method to get a constant current?

The supply voltage keeps fluctuating in a circuit. So we cannot get a constant current.

Q. Three parallel branches with resistances are connected across a DC voltage. What would be the ratio of the branch currents I₁, I₂, and I₃ if the branch resistance ratio is  R₁: R₂ : R₃ = 2 : 4 : 6?

Let us assume that R₁ = 2x ohm, R₂ = 4x ohm and R₃ = 6x ohm

Equivalent resistance of the circuit = 2x x 4x x 6x/ 8×2 + 24×2 + 12×2 = 12x/11 ohm

Therefore, I₁ = I x 12x/11/(2x) = 6I/11 A

I₂ = I x 12x/11/(4x) = 3I/11 A

I₃ = I x 12x/11/(6x) = 2I/11 A

So I₁ : I₂ : I₃ = 6:3:2

Q. Can we apply the voltage divider rule in an ac circuit?

Voltage divider rule is equally applicable for AC circuit calculations, but only if phasor representation is used involving the imaginary quantity ‘j’.

Q. How to obtain zero output voltage using a potential divider?

Zero output voltage can be achieved by keeping a potentiometer in series with a resistance. When this combination is subjected to supply voltage, an end terminal and the middle terminal of the potentiometer fetch output. When the slider terminal is at one end, the voltage is zero.

Q. In a series RC circuitry, the voltage across the capacitor and resistor are 60V & 80V, then What will be total voltage in the circuitry?

By simply applying voltage divider rule, the total voltage is the summation of the voltages across the resistors and the capacitors, So Total voltage = V_R+V_C=60+80=140V.

Q. Current flow is divided between the different branches in a __.

The answer would be parallel circuitry.

Q. Does a voltage divider affect current?

A voltage divider is nothing but a parallel circuit,will not affect the total current of the circuit. However, the branch current values differ according to the branch impedance.

Q. Is current divided in a parallel circuit?

By the rule of current division, we can say that the parallel circuits divide current flowing through them.

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Concept of mutual inductance | Mutual inductance definition

In two adjacent conductor coils, the variation in current in one coil will cause induced emf in the other coil, This phenomenon is called mutual induction. Mutual induction is not a single coil’s property as both/multiple the inductor/inductors are impacted by this property at same time. The primary coil is the coil in which variation of current takes place, and the 2nd coil in which emf is induced named secondary.

Unit of mutual inductance | SI unit of mutual inductance

The unit of mutual inductance is same as inductance, i.e. So SI unit of mutual inductance is Henry(H).

Dimension of mutual inductance

Dimension of mutual inductance = dimension of magnetic flux/dimension of current = [MLT^-2I^-2]

Mutual inductance equation

Mutual induction is the principle that current running through a conductor will generate a magnetic field, and a changing magnetic field will induce a current in another conductor.
From Faraday’s law and Lenz’s law, we can write,

E = -(dφ/dt)

E ∝ dφ/dt

We already know, ? ∝ i [ as B=μ₀ni and ?=nBA]

Therefore, E ∝ di/dt; E =-Mdi/dt [M is proportionality constant]

This M is called the mutual inductance.

M = -E/(di/dt)= emf induced in the secondary coil/rate of change of current in the primary coil

We can also write by comparing that,

-Mdi/dt = dφ/dt

Integrating both sides, we get, ? = Mi

Define Mutual Inductance of 1 Henry

This is the measurement in one coil having 1 m² area, produced 1 V by the variation of the inducing current of 1 Amp/sec in other coil in the existence of 1 T magnetic field.

Derive an expression for mutual inductance

Mutual inductance circuit analysis | Mutual inductance equivalent circuit

Let us consider, two inductor coils with self-inductance, L₁ and L₂, are kept in close contact with each other. Current i₁ flows through the first one, and i₂ flows through the second one. When i₁ changes with time, the magnetic field also varies and leads to a change in magnetic flux linked to the 2nd coil, the EMF is induced in the 2nd coil due to the change in current in the 1st coil and can be expressed as,

E₂₁ = -N₂(dφ₂₁/dt)

Therefore, N₂φ₂₁ ∝ i₁

Or, N₂φ₂₁ = M₂₁i₁

Or, M₂₁= N₂φ₂₁/i₁

This proportionality constant M₂₁ is called the mutual inductance

Similarly we can write, N₁φ₁₂ = M₁₂}i₂ or M₁₂ = N₁φ₁₂ /i₂

M₁₂ is called another mutual inductance

Mutual inductance of a coil
Define mutual inductance between a pair of coils

The mutual inductance of a pair of coils is the ratio of magnetic flux linked with one coil and current passing through another coil.

Where, μ₀=permeability of free space
N₁, N₂ are turns of the coil.
A is the cross-sectional area of the coil.
L is the length of the coil.

Mutual inductance formula | Mutual inductance of two solenoids

Mutual inductance between two coils,

M = μ₀N₁N₂A/L if there’s no core in between two coils

M = μ₀\\μ_rN₁N₂A/L if the soft iron core is placed between the coils

How to find the mutual inductance of two long co-axial solenoid ?

Derivation of mutual inductance of two long coaxial solenoids

Let us assume that two solenoids S₁ and S₂, are placed in close contact with each other. Due to the phenomenon of mutual induction, the current passing through 1st coil will induce EMF in the another coil. Now, we connect S₁ with a battery through a switch and S₂ with a galvanometer. The galvanometer detects the presence of current and its direction.

Due to the flow of current in S₁, magnetic flux is generated in S₂, and a change in magnetic flux causes the current in S₂. Due to this current, the galvanometer needle shows deflection. Therefore we can say current i of S₁ is proportional to ? in S₂.

? ∝ i

? = Mi

Here M is called mutual inductance.

Now, in the case of coaxial solenoids, one coil is placed inside another so that they share the same axis. Suppose S₁ and S₂ have turns N₁, N₂, and areas A₁, A₂ respectively.

Mutual inductance formula derivation

For inner coil S1:

When current i₁ flows through S₁, magnetic field, B₁ =μ₀N₁i₁

Magnetic flux linked with S₂, φ₂₁ = B₁A₁ = μ₀N₁i₁A₁

This is the flux for a single turn. [Though the area of S₂ is A₂, the flux will only generate in the area A₁]

Therefore for N₂ turns φ₂₁ = μ₀N₁i₁A₁ x N₂/L …..(1), where L is the length of the solenoids

We know,
? = Mi
?₂₁ = M₂₁i₁…….(2)

Equating (1) and (2), we get,

M₂₁i₁ = μ₀N₁i₁A₁N₂/L
M₂₁ = μ₀N₁A₁N₂/L

For outer coil S2:

When current i₂ flows through S₂, magnetic field, B₂ = μ₀N₁i₂

Magnetic flux linked with S₁ for N₁ turns, φ₁₂ = N₁/L x B₂A₁ = μ₀N₁N₂i₂A₁/L ….(3)

Similar to the inner coil we can write,
?₁₂ = M₁₂i₂……(4)

Equating (1) and (2), we get,

M₁₂i₂= μ₀N₁N₂i₂A₁/L
M₁₂ = μ₀N₁N₂A₁/L

From the above two findings, we can say that M₁₂=M₂₁ = M. This is the mutual inductance of the system.

Mutual inductance of a coil inside a solenoid | Mutual inductance between two loops

A coil with N₂ bindings is placed inside a long thin solenoid that contains N₁ number of bindings. Let us assume that the bindings of the coil and the solenoid are A₂ and A₁, respectively, and the length of the solenoid is L.

It is known that the magnetic field inside a solenoid due to current i₁ is,

B = μ₀N₁i₁/L

Magnetic flux that passes through the coil due to the solenoid,

?₂₁ = BA₂cos? [? is the angle between the magnetic field vector B and area vector A₂]

φ₂₁ = μ₀N₁i₁/L x A₂ cosθ

Mutual inductance, M = φ₂₁N₂/i₁= μ₀N₁N₂ A₂ cosθ/L

Mutual inductance in parallel

In this circuit 2-inductors having self-inductance L₁ and L₂, are adjoined in parallel, Let us assume the total current is i, the sum of i₁( current through L₁) and i₂(current through L₂) Mutual inductance between considered as M.

i= i₁ + i₂

di/dt = di₁/dt+ di₂/dt

Effective flux through L₁, ?₁ = L₁i₁ + Mi₂

Effective flux through L₂, ?₂ = L₂i₂ + Mi₁

Induced EMF in L₁,

Induced EMF in L2,

We know in case of parallel connection, E₁ = E₂

-L₁(di₁/dt) – Mdi₂/dt = E … (1)
-L₁(di₂/dt) – Mdi₁/dt = E … (2)

Solving the two equations, we get,

di₁/dt = E(M-L₂)/L₁L₂ – M²

di₂/dt = E(M-L)/L₁L₂ – M²

We know, E = -L_eff (di/dt)

Or, L_eff =-E/(di/dt) = L₁L₂ – M²/L₁-L₂-2M

To know more about the Inductors in series and parallel click here

Calculating mutual inductance between circular coils | Mutual inductance of two circular loops

Let us take two circular coils of radii r₁ and r₂ sharing the same axis. The number of turns in the coils are N₁ and N₂.
The total magnetic field in the primary coil due to current i,

B = μ₀N₁i_2r1

Magnetic flux produced in the secondary coil because of B,

We know mutual inductance,

Factors affecting mutual inductance | Mutual inductance M is dependent on what factors

• Material of the core- Air core or Solid core
• No of Turn (N) of the coils
• Length (L) of the coil.
• Cross-sectional area(A).
• Distance(d) between the coils.
• Alignment/Orientation of the coil.

Mutual inductance coupling | Coupling coefficient k

The fraction of the magnetic flux generated in one coil that is linked with another coil is known as the coefficient of coupling. It is denoted by k.
Coefficient of mutual inductance,

• If coils are not coupled, k = 0
• If coils are loosely coupled, k<½ If coils are tightly coupled, k>½
• If coils are perfectly coupled, k = 1

The formula for self-inductance and mutual inductance

Self-inductance L = N?/i = number of turns in the coil x magnetic flux linked with the coil/current flowing through the coil
Mutual inductance M = ?/i = magnetic flux linked with one coil/current passing through another coil

Mutual inductance between two parallel wires

Let us think that two parallel cylindrical wires carrying equal current, each of l length and radius a. Their centers are d distance apart.
The mutual inductance between them is determined with the help of Neumann’s formula.

M = 2l[ln(2d/a) -1 + d/l] (Approximately)

Where, l>>d

What is the difference between self and mutual inductance ?

Self-inductance	Mutual inductance
Self-inductance is the property of an individual coil.	Mutual inductance is shared by both the coils
It is the ratio of the total magnetic flux produced in the coil and the current.	It is the ratio of the total magnetic flux produced in one coil and the current passing through another coil.
If the own current increases, the induced current opposes that.	If the own current of one coil increases, the induced current in the other coil opposes that.

What are the application of self induction and mutual induction ?

Applications of self-inductance

The principle of self-induction is used in the following devices-

• Choke coils.
• Sensors.
• Relays
• DC to AC converter.
• Ac filter.
• Oscillator circuit.

Applications of mutual inductance

The principle of mutual induction is used in the following devices-

• Transformers.
• Metal detector.
• Generators.
• Radio receiver.
• Pacemaker.
• Electric motors.

Mutual inductance circuits | Mutual inductance circuit example

T-circuit:

Three inductors are connected like a T-shape as shown in the figure. The circuit is analyzed with the two-port network concept.

Π-circuit:

Contrarily, two coupled inductors can be created using a π equivalent circuit with optional ideal transformers at each port. The circuit can look complicated initially, but it can further be generalized into circuits that have more than two coupled inductors.

What is the Difference between mutual induction and mutual inductance ?

Mutual induction vs Mutual inductance

Mutual inductance is the property shared by two inductive coils in which varying current in one coil induces EMF in the another one, If mutual induction is the cause, mutual inductance can be said to be its effect.

Mutual inductance dot convention

The relative polarity of the mutually coupled inductors decides whether the induced EMF is additive or subtractive. This relative polarity is expressed with dot convention. It is denoted by a dot sign at the ends of the coil. At any instance, if the current enters a coil through the dotted end, mutually induced EMF on the other coil will have a positive polarity at the dotted end of that coil.

Energy stored in mutually coupled inductors

Let us assume that two mutually coupled inductors have self-inductance values L1 and L2. Currents i1 and i2 travel in them. Initially, the current in both the coils is zero. So the energy is also zero. The value of i1 rises from 0 to I1, while i2 is zero. So the power in inductor one,

So, the energy stored,

Now, if we keep i1 = I1 and increase i2 from zero to I2, the mutually induced EMF in inductor one is M12 di2/dt, while the mutually induced EMF in inductor two is zero since i1 does not change.
So, the power of inductor two due to mutual induction,

Energy stored,

The total energy stored in the inductors when both i1 and i2 have reached constant values is,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

If we reverse the current increments, that is, increase i2 from zero to I2 first and later increase i1 from zero to I1, the total energy stored in the inductors is,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

Since, M₁₂ = M₂₁, we can conclude that the total energy of mutually coupled inductors is,

w = w₁ + w₂ = 1/2L₁I₁² + 1₂L₂I₂² + MI₁I₂

This formula is correct only when both the currents enter dotted terminals. If one current enters the dotted terminal and the other leave, the energy stored will be,

w = w₁ + w₂ = 1/2L₁I₁² + 1/2L₂I₂² – MI₁I₂

Mutual inductance devices

Mutual inductance transformer model

An AC voltage can be increased or reduced according to the requirements of any electrical circuit by using a static device. It is called a transformer. It is a four-terminal device that consists of two or more mutually coupled coils.
Transformers follow the principle of mutual induction. They transfer electric energy from one circuit to another when the circuits are not electrically connected.

Linear transformer:

If the coils in the transformer are wound on magnetically linear material, then it is called a linear transformer. Magnetically linear materials have constant permeability.

In a linear transformer, magnetic flux is proportional to the current passing through the windings. The coil that is directly joined to a voltage source is known as the primary coil and the coil adjoined to load impedance is entitled as secondary. If R₁ is connected in the circuit with the voltage source and R₂ is connected in the circuit with the load.

Applying Kirchhoff’s voltage law in two meshes, we can write,

V = (R₁ + jΩL₁)I₁ – jΩMI₂……(1)

-jΩ MI₁ + (R₂ + jΩL₂ + Z_L)I₂ = 0.…..(2)

Input impedance in the primary coil,

Z_in = V/I₁ = R₁+ jΩL₁ + Ω₂M₂/R₂+jΩL₂ + Z_L

The first term (R₁+jωL₁) is called the primary impedance and the other second term is called the reflected impedance Z_R.

Z_R = Ω²M₂/R₂+jΩ L₂ + Z_L

Ideal transformer

A transformer that doesn’t have any type of loss is called an ideal transformer.

Characteristics:

• An ideal transformer has zero primary and secondary winding resistance.
• Permeability of the core is considered as infinite.
• No leakage flux is there in an ideal case.
• Hysteresis does not take place.
• The value of eddy current loss is zero.
• The ideal transformer is said to be 100% efficient.

Mutual inductance of transformer formula-

There’s zero power loss in an ideal transformer. So, the input power = output power

W₁i₁cosφ = W₂i₂cosφ or W₁i₁ = W₂i₂

Therefore, i₁/i₂ = W₂/W₁

Since voltage is directly proportional to the no. of turns in the coil.,
we can write,

V₂/V₁ = W₂/W₁= N₂/N₁ = i₁/i₂

If V₂>V₁, then the transformer is called a step-up transformer.
If V₂<V₁, then the transformer is called a step-down transformer.

Applications of transformer:

• A transformer can electrically isolate two circuits
• The most important application of a transformer is to step up ( increase) or step down (decrease) the voltage. It can raise or lower the value of current and voltage so that if any of the quantities increase or decrease, power remains the same.
• It can also increase or decrease the impedance, capacitance, or inductance values in a circuit. In other words, the transformer can perform impedance matching.
• Transformer will prevent carrying direct current from one circuit to other.
• It is used in mobile chargers to avoid damages caused by high voltage.
• It is used to generate a neutral in three-phase power supply.

Heaviside Mutual Inductance Bridge | Mutual Inductance measurement bridge

We use mutual inductance in various circuits to determine the values of self-inductance, frequency, capacitance, etc. Heaviside bridge is a component where we can measure mutual inductance with the help of a known self-inductance. A modified version of this bridge can be used in performing the reverse application i.e. measuring self-inductance with the help of known mutual inductance.

Operation

Let us take a combination of elements in the form of the bridge circuit shown in the figure. The coil S₁ with mutual inductance M is not the part of the bridge but it is mutually coupled with the coil S₂ in the bridge which has self-inductance L₁. Current passing through S₁ produces flux that is linked with S₂. As per the dot convention, we can say, current i passes through S₁ and further gets divided into i₁ and i₂. The current i₁ passes through S₂.

Under balanced condition,
i₃=i₁; i₄=i₂ ; i=i₁+i₂

As no current passes through the galvanometer, the potential of B is equal to the potential of D.

Therefore we can say, E₁=E₂

Or, (i₁+i₂)jΩM + i₁(R₁+jΩ L₁) = i₂(R₂+jΩ L₂)

i₁R₁+jΩ (L₁i₁+ M(i₁+i₂))= i₂R₂ + jΩ L₂i₂ …..(1)

i₁[R₁+jΩ (L₁+M) = i₂[R₂+jΩ (L₂-M)] ……(2)

Similarly, E₃=E₄

i₃R₃=i₄R₄

Or, i₁R₃=i₂R₄…….(3)

Dividing (1) by (3) we get,

R₁+jΩ (L₁+M)/R₃ = R₂ + jΩ (L₂-M)/R₄

Taking the real parts of both sides, we can write,

R₁/R₃=R₂/R₄

Taking the imaginary parts of both sides, we can write,

L₁+M/R₃=L₂-M/R₄

So, M=R₃L₂-R₄L₁/R₃+R₄

We can conclude from the above equation that the value of L₁ must be known. Now if R₃=R₄,

R₁=R₂ and M = L₂-L_1/2

Or, L₂= L₁+2M

This way we can find out the value of unknown inductance L₂

The bridge that measures the unknown mutual inductance in terms of two known self-inductance L₁ and L₂, is called the mutual inductance measurement bridge or Campbell bridge.

The field-armature mutual inductance of the synchronous motor

In an AC rotating synchronous motor, steady-state speed is proportional to the frequency of the current passing through its armature. Therefore, a magnetic field is produced. The current rotates at the same speed as that of the rotating synchronous speed of the field current on the rotor. Due to this phenomenon, a mutual induction develops between the armature and the field wingdings. It is known as field-armature mutual inductance.

In this article, we will study detail about notch-filters.

Notch Filter Definition

Before discussing in detail about notch-filter, let us find out the definition of it. A notch-filter can be defined as a band stop that has a very narrow frequency bandwidth. Great depth, high-quality factor, and sharpness in band-reject characterize a notch-filter. There are several kinds of notch-filters which we will discuss later.

Checkout these two articles for more details –

Notch Filter Equation

Some of the important equations of notch-filter are given below.

• The HF cut-off of the LPF: f_L = 1 / ( 2 * R_LP * C_LP * π)
• The LF cut-off of the HPF: f_H = 1 / ( 2 * R_HP * C_HP * π)
• The quality factor of the notch filter:  Q = fr / Band Width

How does a notch filter work ?

Working of notch filter

A notch-filter has the same working principle as of band-reject filter. It allows all other frequency components of the signal and blocks the specified narrow bandwidth. For a passive design, the resistive, capacitive and inductive reactance play the part of controlling the frequency.

Notch filter graph | Notch filter phase response

The following is the notch-filter graph.

Notch Filter Q

Q of a notch-filter is a very important parameter. Q or Quality Factor of a Notch-filter is given by the following equation: Centre Frequency/Bandwidth. Q is the measurement of the selectivity of the filter.

The center frequency is the Notch Frequency, and it is the center frequency of the passband.

Notch filter applications | Use of notch filter

There are several applications of different kinds of notch-filters. Let us discuss some of them.

• Communication Systems: Notch-Filters is one of the important pieces of equipment for a communication system. There is a high probability that the message signals get interfered with by harmonic noises in long-term communication. Notch-filters eliminate the noise.
• Audio Engineering: One of the basic components of audio engineering is a notch-filter. Eliminating noise, spikes are some of the tasks performed by a notch-filter.
• Medical Engineering: Notch-filters have been used in Medical Engineering. Reading of EEG is impossible without a notch-filter.
• Digital Signal Processing: Notch-filters have applications in Digital Signal Processing. A notch-filter is important when there is a need for mixing up signal or condition of elimination of certain frequency component.
• Digital Image Processing: Notch-filters help to eliminate noises from digital images.
• Optical Applications: Notch-filters have applications in optical applications. Blocking off a certain wavelength of light is done by specific optical notch-filters.

Notch filter EEG

EEG or Electroencephalogram is a very important process in medical sciences. Several filters are used to display the output data produced by the machine. Without the filters, it is quite impossible to read the values.

There are three kinds of filters used in an EEG reading. They are – high pass filter, low pass filter, and notch-filter. High pass filter filters out high-frequency components, whereas low pass filters do the same for common frequency components. The notch-filters filter out a certain given range of frequency.

Especially the supplied frequency of the AC interferes with the EEG readings. Notch-filter removes such interference. For North America, the supply frequency is 60 Hz, so a 60 Hz notch-filter is used. In India and other countries where the supply frequency is 50 Hz, a 50 Hz notch-filter is used.

Optimum notch filter in image processing

There is certain kind of periodic noises in digital images. The noises are repetitive and unwanted. They create certain patterns and affect the picture badly. One of the solutions to the problem is an optimum notch-filter.

At first, the noise frequency is determined, then the notch-filter produces the repetitive noise, and the output with lesser noise is produced.

Notch filter transfer function

The following expression gives the transfer function of a notch-filter –

Here, wz refers to the Zero-Circular Frequency, whereas wp refers to the pole-circular frequency. Finally, q means the Quality Factor of the notch-filter.

How to use a notch filter ?

When there is a need to reject a certain narrow band of frequency, a notch-filter is used. A notch-filter is placed after any source from which the signal needs to be eliminated. In most cases, the filter is set as the very last component of any circuit.

Difference between notch filter and band stop filter

A notch-filter is one type of bandstop filter. The only difference between a band stop filter and a notch-filter is that a notch-filter has a narrower bandwidth than a normal bandstop filter.

Bandpass vs Notch filter

There are some differences between the bandpass filter and the notch-filter. Let us elaborate on them.

Points of Discussion	Bandpass Filter	Notch-Filter
Principle	Allowing certain band	Rejecting certain band
Bandwidth	Comparatively wider band is passed.	A comparatively narrower band is rejected.

Anti notch filter

Notch-filters reject the very narrow bandwidth of signals and allow other components of that signal. The same but opposite task is performed by bandpass filters. The bandpass filters allow passing a certain band of frequency and block different parts of the movement.

Notch filter characteristics

Some of the attributes of a notch-filter –

• Narrow bandwidth
• High Q value
• Great depth

Notch filter high q

Twin T notch-filters can provide a very good amount of depth, almost infinite. If an LM102 voltage follower is added to the network, the Q of the circuit gets a skyrocketing growth from 0.3 to 50. That is how a high Q is achieved.

Gain of notch filter

The gain of a notch-filter can be calculated using the following equation.

Notch filter coefficients

Notch-filter coefficients are referred to as the coefficients of the transfer functions.

Here, wz refers to the Zero-Circular Frequency, whereas wp refers to the pole-circular frequency. Finally, q means the Quality Factor of the notch-filter.

Transfer function of notch filter in s domain

The following expression gives the transfer function of a notch-filter –

Different types of Notch-Filters

Active notch filter

An active notch-filter is a combinational circuit of two separate circuits. For example, connecting a low pass filter and a high pass filter in a parallel connection and adding an op-amp for amplifying purposes will work as an active notch-filter.

Inverse notch filter

Inverse notch-filter is a special type of Notch-filter that has an infinite impulse response. Inverse notch-filters are very useful in medical image processing where there is a need to eliminate narrowband signals. Inverse notch-filters do the job efficiently.

Cavity notch filter

Notch-filters are a special type of Cavity filter. Cavity filters allow a certain narrow band of frequency. So, we can say that the working is the same as notch-filters. That is why often cavity filters and-notch-filters are termed cavity notch-filters.

Adjustable notch filter | Adaptive notch filter

Adjustable notch-filters are also tunable notch-filters. One can adjust the frequency as per the need. Some of the Adjustable notch-filters are very important in audio engineering.

Adjustable q notch filter

Adjustable q notch-filters can change the Q value of the notch-filter. Therefore, the Q is a very important parameter of the filter.

The adjustable Q value is needed for the audio engineering department.

Bandpass notch filter | Notch band pass filter

Notch-filters are a special type of bandpass filter. Bandpass filters allow a certain band of frequency to pass. In bandpass filters, theoretically, any range of rounds can be given by the required design. But, in bandpass filters, the band’s scope is typically narrower than the usual ones.

Notch filter VST

VST is a filter envelope plugin. An envelope provides several edges to a filter. VST notch-filters offer many advantages like mixing up audios very finely, etc.

FM Notch filter

FM notch-filters or Frequency Modulation notch-filters are some of the important instruments for Software-Defined Radios. Even these filters made the Software-defined Radios popular. It also helps in radio communications.

Tunable fm notch filter

Tunable FM notch-filters are special kind of notch-filters which can adjust the center frequency as per the need of the applications. No need to say again that the FM filters need the tunable filters because several frequency bands need to be blocked from a signal in FM.

RF Notch filter

RF or Radio-Frequency Notch-filters are used to reject only one frequency from a given band of frequency. Generally, RF notch-filters have a Q. Basic RF filters are designed from low-pass filters to achieve high efficiency. However, converting them into a notch-filter is a tough process and needs a high level of caution and efficiency. 

Tunable notch filter RF

Just like other tunable notch-filters, the tunable rf notch filter can adjust the frequency band as per the need.

60 Hz Notch filter EEG

EEG or Electro-Encephalograph Machines has an inbuilt 60 Hz notch-filter. The high pass filters and low pass filters are fixed at their highest and lowest calibrations.

What is a 60 Hz filter? Click Here!

60hz Notch filter IC

There is a readymade filter IC available to minimize the circuit. It includes one low pass and one high pass filter, and one op-amp for summing up the outputs of both the filters. The most popular 60hz notch-filter IC from Texas Instruments is UAF42.

Circuit of 60 Hz filter… Click Here!

50 Hz notch filter

A 50 Hz notch-filter can reject a 50 Hz signal by keeping the power of the movement almost intact. A 50 Hz notch-filter is needed when the 50 Hz band is necessary to be accurately rejected.

50 Hz notch filter circuit

A 50 hz circuit can be designed using the same frequency of a 60 hz notch-filter as given previously. Some typical values for creating a 50 Hz filter are given below. C= 47 nano-farad, Resistance R1, R2 = 10 kilo-ohm, R3, R4 = 68 kilo-ohm.

switched capacitor notch filter

A switched capacitor notch-filter is another advanced topology. This topology provides high precision, high Q value. This topology has several applications.

HF notch filter

HF Notch-Filter stands for High-Frequency Notch-Filters. Notch-filters of 50-60 Hz cannot give a good depth value or a high Q. High-frequency notch-filters (which rejects or allows a high-frequency component) are more realistic, provides a desired bandwidth and depth.

1khz notch filter

A one kilo-hertz notch-filter has a basic principle, the same as the previously discussed 50 hz or 60 hz filters. The only difference is that a one khz notch-filter is more realistic and can be designed for real-time applications. The 50-60 Hz filters are capable of giving 40 to 50 dB depth. But as an engineer, one must focus on the depth and the Q value. So, the one khz filter comes into action.

Notch filter in frequency domain

Notch-filters deal with frequency. The main principle of a notch-filter is to block a certain narrow band of frequency. So we can say the notch-filter works in the frequency domain only.

2 meter notch filter

A 2 meter notch-filter is a solution to a very general communication problem called – intermodulation. But the filter suffers a high loss during operation.

Audio notch filter

A notch-filter is an important instrument for audio engineering. Generally, some unwanted frequency components get mixed up in the original audio. To remove or eliminate such frequency, an audio notch-filter is used.

Notch filter equalizer

A notch-filter can be used as an equalizer in audio engineering. It can help to find out several unwanted spikes or noise, and also, it can remove those noise and spikes. That is how it helps to make the audio clear.

Periodic noise reduction using a notch filter

There is certain kind of periodic noises in digital images. The noises are repetitive and unwanted. They create certain patterns and affect the picture badly. One of the solutions to the problem is an optimum notch-filter.

At first, the noise frequency is determined, then the notch-filter produces the repetitive noise, and the output with lesser noise is produced.

Acoustic notch filter

As mentioned earlier, Notch-filters are important for audio engineering. After the audio is being recorded, different audio or acoustic audio is needed to mix up. There is a probability that any spike gets introduced in the mix-up. An acoustic notch-filter can remove such noise and spikes.

Variable notch filter

Variable notch-filters are essential for audio engineering. These kinds of notch-filters can change the intended frequency in a certain range.

In audio engineering, several unintended frequencies may present; to remove them, we need notch-filters. Instead of using one filter to omit a single frequency is not a great solution. Variable notch-filters serve our purpose here.

T Notch filter

T notch filter is a basic notch-filter with a ‘T’ network of RCR components. It is a special design technique.

Double T Notch filter | Double notch filter

Double T notch-filter or Twin T filter is an updated version of the T network. As the name suggests, here, two T networks are connected to form a notch-filter. One network consists of RCR components. Another is of CRC components.

Crossover notch filter

Crossover notch-filters can be described as series of notch-filters connected. These filters are designed so, to eliminate the driver resonance from the filter networks.

Series notch filter

Series notch-filters are used for the elimination of the driver resonance. Series notch-filters are designed using Capacitor, Resistance, and an Inductor. All the components are connected in a series connection, and the driver is connected in parallel with them.

Parallel notch filter

Parallel notch-filters are specially designed to eliminate significant unwanted peaks from the driver’s response. This filter is similar because all the basic elements are connected in parallel, unlike the series notch-filter.

High Q notch filter

High Q notch-filters are popular for providing great depth in rejection. Generally, Twin T notch-filters are used to get a high q value and get more depth—the Q value changes from normal 0.3 to 50 for a Twin T filter.

Sallen key notch filter

Sallen Key is a topology for designing higher-order filter circuits. Using this topology, notch-filters can also be created. The topology is also termed as Voltage Controlled Voltage Source. R.P. Sallen and E.P. Key first started it in the year 1955. Therefore, the topology is named after them.

Butterworth notch filter

Butterworth filters provide the flattest possible frequency response. So now, if a notch-filter is designed to provide a flat response, then the notch-filter will be called a Butterworth notch-filter.

AM Notch filter

AM Notch-Filter or Amplitude Modulation Notch-filter is designed to help the measurement of emission of a broadcasting station using a spectrum analyzer. AM Notch-filter is very useful for AM radio communication stations when there are nearby other towers. This is because it can allow only AM band EAS reception while the other strong fields are present.

Dynamic notch filter

The dynamic filter is a set of algorithms. First, the algorithm finds the noise frequencies. Then, active notch-filters are used to eliminate such spikes of noise.

Microstrip notch filter

As we can see, there are several filters available in the market for different uses. But Microstrip notch-filters are especially useful for wireless communication systems.

Analog notch filter

A notch-filter can be classified into the main domain; one is Analog another – Digital. We have previously discussed Digital Notch-filter, like – IIR, FIR, etc. Analog notch-filters are RLC notch-filters, RC notch-filters, T notch-filters, Twin T notch-filters, etc.

RC Notch filter

RC notch-filters are analog notch-filters that are designed with resistors and capacitors. In this kind of filter, manually, we can supply values of r and c.

IC Notch filter

LC notch-filters are analog notch-filters that are designed with an inductor and capacitor. In this kind of filter, manually, we can supply values of L and c.

Arduino Notch filter

Several digital filters can be designed using Arduino. Writing appropriate codes will help an engineer to realize even Notch-Filter digitally. The digital filter codes are available on GitHub. Try to modify them to make a notch-filter.

Coax stub Notch filter

Coax stub notch-filter is a type of notch-filter build within coaxial cables to remove noise and attenuation. ‘T’ coaxial connector will be very useful for designing such a filter. The addition of a second stub will be very helpful to improve the situation. Radio, Television centers use this filter.

FM broadcast notch filter

Almost in every major city, there is a high possibility that one can receive the radio frequency from the FM radio stations. The FM broadcast notch-filter will provide a 30db attenuation for the FM signals in the range of 88 to 108 MHz.

GPS Notch filter

GPS notch-filters help to catch the satellite signals. However, the basic rule is that the GPS module will receive a comparatively weaker signal from the satellite. This is because the nearby located towers may interfere with the incoming signal.

The GPS notch-filter will help here to attenuate the signal by – 30 dB. In addition, it will allow the GPS module to receive a fairer band from the satellite.

Bainter Notch filter

Bainter notch-filter is nothing but a basic notch-filter. A notch-filter consisting of one low pass filter, one high pass filter, and one adder to get the output frequency response can be termed a Bainter Notch-filter.

Wideband notch filter

If a band-reject filter has a wideband frequency as the operational band, then the filter is technically a wideband filter. If the band-reject filter has a narrow band of frequency, the filter is known as the Notch-filter. So, a Notch-filter cannot be a wideband notch-filter. It is technically impossible.

Eagle notch filter

A QAM notch-filter is based upon the phase cancellation concept. Eagle Comtronics Inc designs this narrow network. That is why QAM notch-filters are popular as Eagle Notch-Filter.

Crystal notch filter

Notch-Filters can be designed using crystals also. A crystal has a very high-Quality factor. A crystal notch-filter is useful for creating a notch-filter that has a very narrow band.

Peak notch filter

It is a digital notch-filter. The filter can resist each channel of an input signal for a certain center frequency and a bandwidth of 3 dB.

Narrow notch filter | Narrow band Notch filter

Notch-filters reject a very sharp band of frequency, saying a very narrow band of frequency. That is why notch-filters are often termed narrow notch-filters.

TV channel Notch filter | TV Notch filter | Cable Notch filter

The TV notch-filters help to solve the modulation problem that could occur in the transmission line. The tv notch-filter can make room for the modulated channel once it is installed in the queue. The filter also prevents reverse broadcasting to the coaxial cable. The increasing bandwidth now increased the demand for cable television notch-filters.

MNE Notch filter

MNE is popular software which provides us platform to build several electronics instrument. For example, we can design certain notch-filters in the MNE platform by writing some specific code.

Opposite of Notch filter

Notch-filters reject the very narrow bandwidth of signals and allow other components of that signal. The same but opposite task is performed by bandpass filters. The bandpass filters allow passing a certain band of frequency and block different parts of the signal.

Automatic Notch filter

An automatic notch-filter is something that can change the center frequency as well as the Q value as per the need. Several mechanical systems use these kinds of filters.

Gaussian Notch filter

A gaussian notch-filter is a digital filter. This filter is used to remove noise from various digital images. The specialty of the filter made it popular and is used in multiple applications as well as in various investigating agencies.

Notch filter parameters

There are some parameters to measure the accuracy of the notch-filter. One of the important among them is the Q factor or Q (Details given above). Another is the depth of the output. Finally, the bandwidth is also one of the parameters.

Notch filter impulse response

The following image shows a notch-filter impulse response.

Second order Notch filter transfer function

The following expression shows the second order notch-filter’s transfer function.