Radio Frequency Integrated Circuit Design - Webs

136 Radio Frequency Integrated Circuit Design
Figure 5.38 An IC in a package (delidded).
where L is expressed as nanohenry per millimeter. For typical bond wires, this
results in about 1 nH/mm.
For two round wires separated by d and a distance h above a ground
plane, the mutual inductance is estimated by
2h
M ≈ 0.1 ln�1 +� d � 2
�
(5.42)
where M is expressed as nanohenry per millimeter. As an example, for a pair
of bond wires separated by 150 �m (a typical spacing of bond pads on a chip),
1 mm from the ground plane, their mutual inductance would be 0.52 nH/mm,
which is a huge number. If the height is dropped to 150 �m above the ground
plane, then the mutual inductance of 0.16 nH/mm is still quite significant.
Note that parallel bond wires are sometimes used deliberately in an attempt to
reduce the inductance. For two inductors in parallel, each of value L s , one
expects the effective inductance to be L s /2. However, with a mutual inductance
of M, the effective inductance is (L s + M )/2. Thus, with the example above,
two bond wires in parallel would be expected to have 0.5 nH/mm. However,
because of the mutual inductance of 0.5 nH/mm, the result is 0.75 nH/mm.
Some solutions are to place the bond wires perpendicular to each other or to
place ground wires between the active bond wires (obviously of little use if we
were trying to reduce the inductance of the ground connection). Another
interesting solution is to couple differential signals where the current is flowing
in opposite directions. This could apply to a differential circuit or to power
and ground. In such a case, the effective inductance is (L s − M )/2, which, in
the above example, results in 0.25 nH/mm.