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Keffective

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Click here to go to our page on filling factor

Here we will explain the term "Keff" which is short for "K_effective".

Dk

Let's start by discussing Keff's cousin, Dk. "Dk" is often used as the "dielectric constant", a material property. Why not "DC" you ask? Unless you are not an electrical engineer, you'd realize that DC was already taken as "direct current!" The dielectric constant Dk, also known as epsilon relative (ER) is a material property, a measure of the material's property of slowing electromagnetic waves down.  Dk is usually nearly constant with frequency, which is why it is called the dielectric constant. Sometimes Dk is anisotropic, meaning that it has different values depending on the direction of the electric field. Given that a particular two-conductor transmission line provides perfect transverse electromagnetic (TEM) propagation and is fully encased in a uniform material (such as coax or stripline), the propagation velocity would be c/SQRT(Dk). Dk is also the parameter used in capacitance calculations: Dk is proportional to capacitance value for a given capacitor plate area and plate separation. Note that you can replace "Dk" with "ER" in the previous four sentences and they will still read correctly!

Keff (or K_effective)

In this context, "K" refers to the effective dielectric constant, which might also be called Epsilon_effective (Ee).  K effective takes into account the geometry of a transmission line, which makes it less than Dk of the substrate in many cases.  By substrate, we mean the sheet of dielectric material that supports microstrip transmission lines, for example. For microstrip, part of the wave is in air (Dk=1), and part is in the substrate material (Dk>1). Once a "filling factor" is calculated for what percentage of electric field is in the material, then Keff is equal to ERxFF+1x(1-FF). The second term comes from the percentage that is in air (ER=1). Most calculations for microstrip ignore filling factor and directly provide Keff and Z0.  As an example, a GaAs substrate has Dk=12.9, while a fifty ohm microstrip line on GaAs might have Keff=7 (the exact value will depend on the strip metal's thickness).

In all transmission lines, the propagation velocity is c/SQRT(Keff).  This includes the enclosed-TEM case, where Dk=Keff.

Note that there are many geometries that have three or more dielectrics. Keff is best calculated using one of the popular EM tools in cases such as microstrip that is processed on multiple sheets of disparate materials, or CPW that is over-molded or coated.  Check out our page on multi-dielectric coax where we show a closed-form solution for Keff.

Velocity factor

Many cable manufacturers provide data on "velocity factor".  This is merely the ratio of propagation velocity in the cable to that of air, and is equal to 1/SQRT(Keff). For PTFE-filled cables it is approximately 70% (1/SQRT(2.2)).

Here's a page that explains filling factor.

Here's a page on how to extract Dk from transmission line measurements. 

 

 

 

Author : Unknown Editor

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