Radio Frequency Integrated Circuit Design - Webs

The Use and Design of Passive Circuit Elements in IC Technologies
imaginary part of Z in and dividing by 2�f. The Q is computed as in (5.13)
and the results are shown in Figure 5.17.
This example shows a Q of almost 20, but in reality, due to higher substrate
losses and line resistance leading up to the inductor, the Q will be somewhat
lower than shown here, although in most respects this example has shown very
realistic results.
5.15 Characterization of an Inductor
Once some inductors have been built and measured, S-parameter data will then
be available for these structures. It is then necessary to take these numbers and
convert them, for example, into inductance, Q, and self-resonance frequency.
The definitions of Q have already been given in (5.13) and �L is equal
to the imaginary part of the impedance. These definitions seem like simple
ones, but the impedance still needs to be defined. Traditionally, we have assumed
that one port of the inductor is grounded. In such a case, we can define the
impedance seen from port 1 to ground.
Starting with the Z-parameter matrix (which can be easily derived from
S-parameter data):
115
�V 1
V2� =� Z 11 Z 12
Z 21 Z 22��I1 (5.14)
I2�
Since the second port is grounded, V2 = 0. Thus, two equations result:
Figure 5.17 Inductor plot of L and Q versus frequency.