Datasheet
87
x ln
Z =
(5.98 x h)
(th + 0.8W)
Hr + 1.41)
D
d
d
S
W
h
COAX CABLE
PARALLEL
WIRE
TRACK OVER
GROUND
LMH6559
SNOSA57C –APRIL 2003–REVISED MARCH 2013
www.ti.com
In these three options it is seen that there is more than one preferred method to reach an (end) point on a
transmission line. Until a certain point the designer can make his own choice but the designer should keep in
mind never to break the rules about high frequency transport of signals. An explanation follows in the text below.
TRANSMISSION LINES
Introduction to transmission lines. The following is an overview of transmission line theory. Transmission lines
can be used to send signals from DC to very high frequencies. At all points across the transmission line, Ohm's
law must apply. For very high frequencies, parasitic behavior of the PCB or cables comes into play. The type of
cable used must match the application. For example an audio cable looks like a coax cable but is unusable for
radar frequencies at 10GHz. In this case one have to use special coax cables with lower attenuation and
radiation characteristics.
Normally a pcb trace is used to connect components on a pcb board together. An important considerations is the
amount of current carried by these pcb traces. Wider pcb traces are required for higher current densities and for
applications where very low series resistance is needed. When routed over a ground plane, pcb traces have a
defined Characteristic Impedance. In many design situations characteristic impedance is not utilized. In the case
of high frequency transmission, however it is necessary to match the load impedance to the line characteristic
impedance (more on this later). Each trace is associated with a certain amount of series resistance and series
inductance plus each trace exhibits parallel capacitance to the ground plane. The combination of these
parameters defines the line's characteristic impedance. The formula with which we calculate this impedance is as
follows:
Z
0
= √(L/C)
In this formula L and C are the value/unit length, and R is assumed to be zero. C and L are unknown in many
cases so we have to follow other steps to calculate the Z
0
. The characteristic impedance is a function of the
geometry of the cross section of the line. In (Figure 39) we see three cross sections of commonly used
transmission lines.
Figure 39.
Z
0
can be calculated by knowing some of the physical dimensions of the pcb line, such as pcb thickness, width of
the trace and ε
r
, relative dielectric constant. The formula given in transmission line theory for calculating Z
0
is as
follows:
where
• ε
r
= relative dielectric constant
• h= pcb height
• W= trace width
• th= thickness of the copper (1)
If we ignore the thickness of the copper in comparison to the width of the trace then we have the following
equation:
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