# What is Coupled Inductor : Working & Its Applications

An inductor is a two-terminal electrical component, used to store energy within a magnetic field once electric current supplies through it. It is also known as a choke, coil, or reactor. Generally, an inductor includes an insulated wire which is wounded into a coil. A pair of inductors is known as coupled inductors, which is used to transmit energy from one winding to another using the common core. So, this article discusses an overview of a coupled inductor and its differences from a transformer.

## What is Coupled Inductor?

Coupled inductor definition is when the connection of two coils or inductors can be done through electromagnetic induction. Whenever an AC flows throughout the primary coil, the coil will set up a magnetic field that is connected to the secondary coil & induces a voltage within the coil. The phenomenon of inducing voltage from one inductor to another is known as mutual inductance.

Coupled inductors are mainly used as essential parts for transformers, electronic circuits & power distribution systems. A pair of coupled inductors can be characterized by three parameters like two self inductances like L1, L2 & mutual inductance like L12=M. The coupled inductor symbol is shown below.

### Coupled Inductor Equations

The circuits which include coupled inductors are more complex as compared to other circuits because the coil’s voltage can be simply expressed in terms of their currents.

In the above-coupled inductor circuit, two coils like L1 & L2 are very close to each other. Because of the ‘i1’ current flowing throughout the primary coil ‘L1’, magnetic flux can be induced, and after that, it will be transferred to the secondary coil L2.

When ‘V1’ voltage is applied to the primary coil ‘L1’, then ‘i1’ current will start flowing throughout the coil L1. So the current change rate will generate a flux to supply throughout the magnetic core & generate a voltage within the secondary coil ‘L2’.

In primary coil ‘L1,’ the rate of change of current also changes the flux which further controls the induced voltage within secondary coil ‘L2’. So, the induced voltage within the primary coil ‘L1’ can be calculated by using the following formula.

V1 = M {di2(t)/dt}

From the above ‘V1’ equation, the mutual inductance ‘M’ is mainly responsible for the voltage which is induced mutually in two independent circuits. So, this mutual inductance (M) is the coefficient proportionality.

Similarly, for the first ‘L2’ coil, the mutually induced voltage because of mutual inductance for the ‘L2’ coil can be expressed as

V2 = M {di1(t)/dt}

Similar to the inductance, mutual inductance (M) can also be measured in Henry. So, the highest mutual inductance value can be expressed as √L1L2. When the inductance induces voltage through the rate of change of current, mutual inductance (M) also induces a voltage which is known as mutual voltage M(di/dt). So, this mutual voltage is either positive (+ve) or negative (-ve) mainly depending on the construction of the inductor & the flow of current direction.

#### DOT Convention

The polarity of the mutually induced voltage can be determined by an essential tool like Dot Convention. In dot conversion, the ‘dot’ mark symbol looks like a circular shape, which is used mainly at the two coils end within mutually coupled circuits. So this dot symbol provides the data regarding the winding construction in the region of its magnetic core.

In the above dot convention circuit, the inductors L1 & L2 are mutually coupled. The V1 & V2 voltages are developed across the two L1 & L2 inductors which are the outcome of current flowing into the two inductors on the dotted terminals.

By assuming the two inductors mutual inductance is M, the voltage which is induced can be calculated by using the below formula,

For the primary inductor ‘L1’, the induced voltage ‘V1’ is;

V1 = L1(di1/dt) ± M(di2/dt)

For the secondary inductor ‘L2’, the induced voltage ‘V2’ is;

V2 = L2(di2/dt) ± M(di1/dt)

Thus, the above circuit contains two types of induced voltage like the voltage induced because of self-inductance & the voltage induced mutually because of the mutual inductance.

The voltage induced based on the self-inductance can be calculated with the formula like V = L(di/dt) which is positive (+ve), however, the voltage induced mutually can be negative (-ve) or positive(+ve) based on the construction of winding & the current flow. Here, the dot is an essential parameter used to determine mutually induced voltage polarity.

### Coupled-Inductor Analysis and Design

The design and analysis of coupled inductors can be done by using the following flyback converter circuit. This circuit can be built with basic electronic components like a coupled inductor (flyback transformer), a diode, the capacitor, etc.

The flyback converter circuit is a power supply topology that uses a coupled inductor to store energy once current supplies throughout & the energy will be released once the power supply is detached. These converters are related to the booster converters in design & performance except the transformer’s primary winding can be replaced with an inductor whereas the secondary winding provides the o/p. Both the windings in the flyback arrangement are utilized as two separate inductors.

#### Coupled Inductor Working & Operation

The flyback inverter circuit is shown below. A flyback transformer in the circuit is a coupled inductor including a gapped core. Throughout every cycle, once the input voltage is provided to the primary winding of the transformer, energy can be stored within the core gap. After that, the energy is transferred to the secondary winding for providing energy to the load. These transformers are mainly used in flyback converters to provide transformation of voltage & circuit isolation.

The principle of a flyback converter is, when the flow of current throughout an inductor is disabled, then the energy stored within the magnetic field can be released by reversing the terminal voltage suddenly.

The flyback diode in the circuit is connected across an inductor for eliminating flyback, which means when voltage surge was seen across the load once its current supply is interrupted or reduced suddenly.  This diode is also known with different names like commutating diode, snubber diode, suppressor diode, freewheeling diode,  catch diode, or clamp diode.

Generally, a switching device used in a flyback converter circuit is a MOSFET transistor which is switched ON & OFF by a PWM signal. The polarity of the transformer is generally upturned such that once the transistor is switched on, the flow of current will be there in the primary winding, but, the second diode is reverse biased so, there is no flow of current in this winding.

The energy will be stored within the transformer until the transistor is turned OFF. So, the energy which is stored will generate a current, so that the diode can be forward-biased which rectifies it to generate a DC output.

Flyback converters are used in TV sets that use a small amount of power, chargers of cell phones, computers, high-voltage supplies in CRT, Lasers, copiers, Xenon flashlights, etc.

### Coupled Inductor Vs Transformer

The difference between coupled inductor and transformer is discussed below.

 Coupled Inductor Transformer The coupled inductor is mainly used for transmitting energy from the primary winding to the secondary through a core. A transformer is mainly used for power transmitting from the primary winding to the secondary. Coupled inductor utilizes a gapped magnetic core for changing the voltage between two coils & transmits power at time intervals which are controlled. The transformer utilizes a non-gap magnetic core for changing the voltage in between two coils & transmits the power in real-time. The coupled inductor includes an air gap. The transformer doesn’t include an air gap. In a coupled inductor, the entering power is not equal to the existing power. In a transformer, the entering power is equal to the existing power from the transformer. The storage of energy in the core can be possible in the coupled inductor. The storage of energy in the core does not possible in the transformer. It is used in DC to DC converter like flyback converter to decrease the voltage from 24V DC to 5V DC. It is used in AC to AC conversion like decreasing the voltage of AC wall outlet from 120VAC – 24VAC.

The advantages of a coupled inductor include the following.

• Current ripple can be reduced significantly
• Conversion of voltage.
• Circuit impedance can be changed.
• Galvanic isolation
• Switching power supplies comprise multiphase converters, SEPIC converters, galvanically isolated converters & special converter circuits that decrease the hard switching negative characteristics.

The disadvantages of coupled inductors include the following.

• Slightly higher losses
• Non-ideal operations within the flyback converter
• The coupled inductor’s current specifications will change based on their windings which are connected within series or parallel.

### Applications

The applications of coupled inductors include the following.

• Coupled inductors are used in electrical applications
• Used in power conversion-based circuits like SEPIC, flyback, ZETA, Fly-Buck, Cuk & multi-phase topologies.
• The properties of these inductors will allow to increase or decrease current & voltage.
• These are used to transfer impedance throughout a circuit
• These can be used to isolate two circuits electrically from each other.
• The windings of the coupled inductor can be connected in different configurations for different purposes.
• The windings of these inductors can be connected separately to circuits to use like common mode chokes & isolation transformers.

Thus, this is all about an overview of the coupled inductor. A coupled inductor is used in dc to dc converters for transferring one winding energy to another throughout the common core. These are existing in different sizes, current ratings, inductance values & shielded magnetically for low EMI (electromagnetic interference). The coupled inductor windings may have equivalent like 1:1 or un-equivalent turns ratios like 1:N. Here is a question for you, what is the function of an inductor?