current return path, refer to
Figure 5.5
.
Figure 5.5a
represents a system of three inductive
signal pins coupled to an inductive ground return pin. Note that all of the current flowing
through the three signal inductors must return through the ground inductor. The effect of the
ground return pin can be represented as shown in
Figure 5.5b
, assuming that the inductors
are modified to include the inductive effects of the return path pin. This makes it easier to
see the effect that an inductive pin in the ground return path has on the signal. The response
of the system is shown in the following set of equations, which represent the response of
Figure 5.5a
:
(5.9)
is the voltage given by the simplified model. The result of
(5.9)
can easily be extended to
a group of n conductors with a single current return path:
(5.10)
where the voltage
in
Figure 5.5b
is given by
(5.11)
Note that the effective inductance is simply the signal pin inductance, plus the ground return
pin inductance, minus the mutual inductance.
Figure 5.5: Incorporating return inductance into the signal conductor: (a) three inductive
signal pins coupled to an inductive ground return pin; (b) effect of the ground return pin.
It should also be noted that the equations above are valid only for a coupled array of pins.
The total return path inductance will increase with distance from the corresponding signal pin
and should be modeled separately assuming that the path is significantly long or the total
return path inductance is much greater than L
gg
. The total current return inductance is the
sum of the pin inductance and the inductance of the path to and from the return pin. The
larger the total loop area in which the current flows, the larger the inductance. For example,
the total loop inductance of loop A in
Figure 5.4
has the largest total inductance, and loop C
is the smallest.