As mentioned in the previous section, resolving interference problems may be accomplished at three levels of the interference model: (a) by acting on the source - reducing the emission level and spectrum, (b) by acting on the victim - increasing its immunity to electromagnetic disturbance, and (c) by acting on the transmission path - making it less efficient.

The technique to be applied on the transmission path depends largely on the coupling phenomena, for example, for conductive interference problems the application of filtering might serve best, whereas for radiated interference, shielding techniques might be preferable. Shielding is directly related to the electromagnetic radiation and thus an introduction of shielding theory begins by covering basic electromagnetic theory - as it is relates to shielding principles.

Plane Electromagnetic Waves Theory

In simple terms, a plane wave is a form of wave having a one-dimensional spatial dependence.  A uniform plane wave is a particular solution of Maxwell’s equation with E (and H) assuming the same direction, same magnitude, and same phase in infinite planes perpendicular to the direction of propagation. In reality, a uniform plane wave does not exist in practice, due to the non-availability of an wave source infinite in extent. However, if we are far away enough from a source, the wavefront (surface of constant phase) becomes almost spherical; and a very small portion of the surface of a giant sphere is nearly a plane.

Starting from Maxwell’s equation in differential form, given below:

we find that for sinusoidal waves, the important propagation equations are:

If we assume that the one-dimensional spatial dependence of the plane wave in question, is in the z direction (i.e. the component of the wave will not change in the x-y plane) then the following equation set is obtained:

When a plane wave impinges of a shield, the electrons and other charged particles in the shield respond to the electric and magnetic fields according to Lorentz’s force law:

The charges in the shield move in response to the applied field, the movement of these charges results in the generation of an electric and magnetic field (referred to as scattered or  induced field) which changes the total field inside the shield, impacting the motion of charges. In summary, a good shield is one in which the sum of the fields inside the shield (incident and induced fields) is much less than the initial incident field; in order words a good shield generates a counter field in response to an incident field.

The above equation sets are very similar to the Transmission Line Equations.  These basic equations are the starting point from developing expressions for key shielding parameters.  When a plane wave is incident to a shield, reflection from, absorption into, and transmission through the shield occurs.  The degree of reflection is determined by the impedance of the incident wave and the intrinsic impedance of the shield material. The degree of absorption is a function of the thickness of the shield and frequency dependent skin depth in the shield, whereas the degree of transmission is determined by the reflections from both sides of the shield and absorption through the shield.

The ability of the shield to generate this counter field is a function of the electrical properties of the material.  For perfect conductors, the induced current is entirely along the shield’s surface, however in real applications the current and field penetrate a nonzero distance into the shield.

Electrical Properties of a Shield

1. 1. Propagation constant: The propagation constant is a complex value where the real part represents the attenuation during the propagation of the wave in the conducting material and the imaginary part represents the propagation part.
   
                              

   

   
   For conductors, where 

   

   
   

I

In this case, when a wave propagates through an insulating material, there will be no  attenuation during transmission.

2. 2.Wave Impedance: The wave impedance is the equivalent of the  characteristic impedance for transmission lines.  it is the ratio between the appropriate components of the electric and magnetic field, and is given by the equation below: