Electromagnetic Interference Coupling Methods

7/31/2019 Electromagnetic Interference Coupling Methods

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Electromagnetic Interference Coupling MethodsPreviously, we described what causes electromagnetic interference, abbreviated as EMI. Now we will

look at ways that this phenomenon makes its way from its source to a victim circuit / component.

There are four basic ways that an electromagnetic noise can be coupled to (or received by) anothercircuit. Think of it this way how can you get from New York to Oregon? You can travel by land in a

car or on a bike (if youre up for that,) you can catch a flight and soar across the country, or you could

even take a boat out onto the ocean if you have the time, money, and patience. Electromagnetic

waves can propagate from one point to another in the same vein; that is, through multiple paths. Here

are the four ways EMI waves couple from a noise source to another component or circuit known as the

victim:

1) Conductive Coupling This is the easiest form of coupling to understand because it is straight

forward. If a device creates a high frequency pulse, such as a power supply switching on or off, the

current pulse caused by the switch will be seen on the lines. Conductive coupling is when there is adirect, hard-wired connection between the source and victim, whether the connection is a 4/0 AWG

cable or an Ethernet cable. During product compliance testing, it is typical to test for conducted

emissions first with the reason being that if the noise is removed from the incoming/outgoing cables

and noise loop areas are reduced, then radiated emissions will thereby be reduced to manageable, if

not passing, results.

2) Inductive Coupling This is no different than what youve read about in college. When two

conductive loops are within proximity of one another, inductive coupling will take place through the

wonder of magnetic fields! Current flowing in one conductor will create a magnetic field (left hand rule

or right hand rule, dependent upon which hand you use to operate a fork or scratch your head) thatthen induces current flow on a nearby conductor. This coupling mechanism is intensified or attenuated

by adjusting the loop area of the noise source conductor.

Capacitive coupling: the speed dating of the electrical world.

3) Capacitive Coupling When a conductor has alternating current flowing within it, a potential

difference will exist between it and any nearby conductors. This creates an electric field, or capacitive

coupling. The victim transmission line, cable, or trace will see this potential difference and current flow

will occur. Much like inductive coupling, proximity is key to how well a noise source can couple through


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this method. Often it is advised to keep cables/traces separated by a rule-of-thumb distance of three

times the diameter of the cable/trace. Likewise, proper shielding affectively eliminates electric fields.

4) Radiation The other aspect of EMC testing is measuring radiated emissions from a product. In

radiation coupling, the distance between the source and victim are great enough that straight-up

electric or magnetic fields will not be a cause for concern. However, with electromagnetic waves,

metallic objects will begin to act as antennas, a.k.a. objects that transmit and receive with bold

indiscretion for your feelings.

A lesser advertised way of coupling noise but one that still exists is common impedance coupling.

When two lines from separate circuits combine into one the most evident example being a common

ground path - both the natural impedance of the line and any additional impedance from common

components is seen by both circuits. Current flowing through the common component caused by one

circuit will create a voltage change in the other circuit. Think of how voltage across an inductor is

calculated: the dreaded V=L(di/dt). Whenever current flows through a wire, especially if it happens

quickly, or there is a lot of it, a voltage is induced which can affect the voltage across the load in the

victim circuit or cause the reference potential to change in the victim circuit. These problems can be

severe and are referred to as crosstalk and ground bounce. In either case, they are forms of

interference and only get worse with higher frequencies.

As you can see, electromagnetic interference can be coupled from one circuit to another in just about

every way physically possible. Whereas with 60 Hz signals where opening breakers and contacts can

quickly move one towards the source of an issue, in the world of EMI space, proximity, and everything

conductive are at play. This is another reason why I still have a job. The thrill of working with EMI is

that it brings out the most visceral, barbaric desires for hunting within oneself. To see amplified noise

levels, to sniff out and find the source, and to alter the system configuration to a point of non-

interference is integral to satisfying the Cro-Magnon thirst within me.

Complex NumbersA complex number is made up of both real and imaginary components. It can be represented by an

expression of the form (a+bi), where a and b are real numbers and i is imaginary. When defining i

we say that i = . Then we can think ofi2 as -1. In general, ifc is any positive number, we

would write:

.

If we have a complex numberz, where z=a+bi then a would bethe real component (denoted: Re z) and b would represent the

imaginary component ofz (denoted Im z). Thus the real

component ofz=4+3i is 4 and the imaginary component would be


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3. From this, it is obvious that two complex numbers (a+bi) and (c+di) are equal if and only ifa=cand b=d, that is, the real and imaginary components are equal.

The complex number(a+bi) can also be represented by the ordered pair(a,b) and plotted on a

special plane called the complex plane or the Argand Plane. On the Argand Plane the horizontalaxis is called the real axis and the vertical axis is called the imaginary axis. This is shown in

Figure 1 on the right:

Properties of the Complex SetThe set of complex numbers is denoted . Just like any other number set there are rules ofoperation.

The sum and difference of complex numbers is defined by adding or subtracting their real

components ie:

The communitive and distributive properties hold for the product of complex numbers ie:

When dividing two complex numbers you are basically rationalizing the denominator of a rational

expression. If we have a complex number defined as z =a+bi then the conjuate would be .

See the following example:

Example:


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ConjugatesThe geometric inperpretation of a complex conjugate is the reflection along the real axis. This canbe seen in the figure below where z = a+bi is a complex number. Listed below are also several

properties of conjugates.

Properties:


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Absolue Value/ModulusThe distance from the origin to any complex number is the absolute value ormodulus. Looking at

the figure below we can see that Pythagoras' Theorem gives us a formula to calculate the absolutevalue of a complex numberz = a+bi

And from this we get:

This explains why rationalizing the denominator using conjugates works in general for complexquotients.

There are also some properties of absolute values dealing with complex numbers. These are:


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Polar FormAlong with being able to be represented as a point (a,b) on a graph, a complex numberz = a+bi

can also be represented in polar form as written below:

Note: The Arg(z) is the angle , and that this angle is only unique between which iscalled the primary angle. Adding

Example:Using the principle argument, write the following complex number in its polar

coordinates.

Multiplication and division can be given geometric interpretations and new insight when looking at

polar forms:

Let and be complex numbers.


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We can see from this that in order to multiply two complex numbers we must multiply the length

or absolute values together and add the arguments.

In the case of division, it is similarly shown that:

by using the subtration rule of sine and cosine, as apose to multipling the lengths we divide and as

apose to adding the arguments, we subtract.

Example:

DeMoivre's TheoremDeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar

form.


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Looking at from the eariler formula we can find (z)(z) easily:

Which brings us to DeMoivre's Theorem:

If and n are positive integers then

Basically, in order to find the nth power of a complex number we take the nth power of theabsolute value or length and multiply the argument by n.

Example:

Working backwards we can also use DeMoivre's Theorem to find the nth root. Letand n be a positive integer.Then z has n distinct nth roots given by:

where k = 0, 1, 2, ... , n-1

To show this we let and where .


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Example:

Euler's FomulaFrom Calculus, we know the functions ex, sin x and cos x have power series expansions or Taylor

series.

When looking at complex numbers it is interesting to see that the power series for ez allows z to becomplex and obeys the usual rules for exponents. In particular it holds true that:

e

z1

+z2

= e

z1

z2

letting z = iy where i is imaginary and y is a real number


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From the fact that:

This gives us the result ofEuler's Formula

eiy

= cos y + isin y

Then we can also define z as:

Example:

It is also important to mention that if and

From tringonometry we can then say:

Electromagnetic Interference Coupling Methods

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