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Fundamentals of wireless power transmission

Saturday, 20 January 2018

Goal:

At the end of this article you would be able to grasp the working phenomenon of wireless power transmission and would be able to apply it in building your own wireless power transmission project.

Introduction:

In my previous post, I talked about how I made money with my design skills just when I was still in school. Well this could be called a sequel to that. One of the project I handled back in the days was the development of a wireless charger. A wireless charger uses the technology of wireless power transmission to transmit power from a charging pod to a receiver which is normally built in the phone that is being charged.

How it works (Analogy):

Wireless power transmission works in a similar way to an AC transformer in which an insulated copper wire is wounded around a core of a transformer. Most times the core is designed in form of an E-shape, I-shape, rectangular, circular etc. for more about transformer core design click here. Regular electronic transformers are in form of the E-shape. A transformer comes with two winding; a secondary winding and a primary winding.
Fundamentals of wireless power transmission

In a conventional step down transformer the secondary is connected to the AC mains while the primary winding is connected to the device being powered e.g. radio set or television. A transformer works by obeying the principle of electromagnetic coupling in which two coils placed close together induces an emf (electro-motive force) when current is varied in one coil, this is also known as mutual inductance.

Mutual inductance:

Mutual induction can be defined as the current flowing in one coil that induces a voltage in an adjacent coil. In addition, irrespective of the type of core used either solid (iron) or gas (air) mutual inductance always takes place as far as the two coils are placed close together. Mutual inductance is one of the principle that aid in wireless power transmission. For more information on mutual inductance click here.
mutual inductance

The inductance of an air core coil that causes the coil to undergo self-induction can be derived using the formula below;
mutual inductance formula
Where;
L = inductance of the coil.
d = the diameter of coil in inches.
n = number of turns.
l = length of coil in inches.

The formula above can be used to calculate the inductance of a coil but in cases where another coil is brought close the other coil, mutual inductance would take place, this is because the two coils tends to couple. Therefore transmission is based on inductive coupling of the two coil. To know the extent of coupling between the two coils means calculating the coupling coefficient which is a function of mutual inductance which can be given as;
mutual inductance formula
Where;
M = Mutual inductance.
L1 = Inductance of L1
L2 = Inductance of L2

Since the formula above can be used to solve for the mutual inductance of two coils in close proximity it is assumed that there was a complete mutual inductance. In other words the voltage in L1 is equal to the voltage in L2 at time t = 0. But in a real life scenario there would be loss due to several factors like distance between the two coils, angle of inclination etc. In that case M ≠ √ (L1 ˟ L2). Therefore we assume a value K which will multiply to equate the equation properly to give;
mutual inductance formula

Where;
K = Coupling Coefficient or Factor of Coupling.

Coupling Factor or Coupling Coefficient

The coupling Factor K ranges from 0 to 1, when it is equal to 0 it means no mutual inductance. Thus there would be no transmission from L1 to L2, this depict a situation where the coil are kept far apart. When K approaches 1 it means there is mutual inductance to some extent, this could mean the two coils are in range of transmission and reception. Several factors can also affect inductive coupling. Factors like type of coil, number of turns, coil design, core etc.

The equation above can be further expatiated to give the following;
inductive coupling formula


Where;
V2 = voltage on receiving coil.
V1 = Voltage on transmitting coil.
N2 = Number of turns on receiving coil.
N1 = Number of turns on transmitting coil

For information on how the above equation was derived click here.
In conclusion wireless power transmission has been in existence since the time of Nickolas Tesla, this article just concentrates on power transmission through inductive coupling of coils in a close proximity. Since the invention of wireless power transmission in 1904 by Nickolas Tesla there have been invention of newer ways to transfer power wireless e.g. microwave, resonance inductive coupling, light-waves etc. In my next post I will go through the stages of wireless power transfer through inductive coupling.

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