Radio Frequency Integrated Circuit Design - Webs

The Use and Design of Passive Circuit Elements in IC Technologies
Figure 5.27 Basic model of transformer.
vias to decrease the effective series resistance. This will increase the Q, but at
the expense of increased capacitance to the substrate and a resultant decrease
in self-resonant frequency. This technique is of benefit for small inductors for
which the substrate loss is not dominant and that are at low enough frequency,
safely away from the self-resonant frequency.
The second method is to connect two or more layers in series. This results
in increased inductance for the same area or allows the same inductance to be
realized in a smaller area. A drawing of a two-level inductor is shown in Figure
5.29. Note that the fluxes through the two windings will reinforce one another
and the total inductance of the structure will be L top + L bottom + 2M in this
case. If perfect coupling is assumed and the inductors are of equal size, then
this gives 4L. In general, this is a factor of n 2 more inductance, where n is the
number of levels. Thus, this is a way to get larger inductance without using as
much chip area.
To determine the capacitance associated with the inductor, we consider
the top and bottom spirals as two plates of a capacitor with total distributed
capacitance C 1 [17]. In addition, we consider the bottom spiral and the substrate
to form a distributed capacitance C 2. Now the total equivalent capacitance of
the structure can be approximated. First, note that if a voltage V1 is applied
across the terminals of the inductor, the voltage across C 1 will go from V 1 at
the terminals down to zero at the via. Similarly, the voltage across C 2 will go
from zero at the terminal (assuming this point is grounded) to V 1/2 at the via.
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