Page 318 - Analog and Digital Filter Design

31
Transmission Lines and Printed Circuit Boards as Filters

20 =- 59.96[ Ln (80) - 30.185 (E)']
-
JER nu,

This can be approximated by the simplified equation that was used for the wire
impedance, where the width of the track is taken as the wire diameter:

The problem with these equations is that the impedance is known. These have
to be transformed into equations to find the Dhv ratio. The distance betwcen
earth planes, D will be defined at the design stage, so you only need to find the
track width, N,.
For a wide track (:I' > 0.60):

zo 4G 1
~- -
94.18 (w,/D) + 0.44
94.18
iv
_-___- 0.44
D - ZOG
For a narrow track (w < 0.60):
E (3
Zo=-ln -

If this approximate equation is used to find a value for Dlw, and then this is
substituted into the full equation, an idea of the error can be found and assessed.
For example, let the dielectric constant have a value of 4.7 (fiberglass resin
board, type FR4) and D = 1.6m. This could be produced from two boards
8.8 m thick, one double-sided and the other single-sided.

For a narrow track:
D
_-_ e 6o
-
)I? 8