2.11 Transmission lines – Design and Practical Realisation
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Figure 2.11-11 Effective dielectric constant as a function of W/h for different dielectric constants
Figure 2.11-13 and Figure 2.11-14, which are based on equation (2.11-6), show how the
characteristic impedance of the line varies with and respectively.
The narrower the width of the line , the smaller the cross section offered to the current to flow
through and hence the higher the impedance.
To understand the effect of the height of the substrate we need to recall how voltage is
actually worked out (section 1.2).
Figure 2.11-12 Integration path and electric field for voltage calculation
Consider Figure 2.11-12. Using equation (1.2-1) and assuming a uniform Electric field underneath the
signal line, we obtain
∫
This shows that increasing the height of the substrate increases the voltage thereby increasing the
impedance. Of course this is a rather simplistic explanation and only accounts for the field away
from the edges of the signal line which is similar to that of a parallel plate capacitor. Nevertheless it
gives an intuitive understanding of how the characteristic impedance of the line is related to
substrate height h. In real life however this relationship is not as linear as equation (2.11-8) would
indicate. This is because, at the edge of the line, fringing effects occur and the field lines are partially
contained in air and partially in the dielectric (Figure 2.11-11). This is reflected in Figure 2.11-14
which shows that the characteristic impedance of the line and height of the substrate are related in
a non-linear fashion.
(2.11-8)
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