This
thesis deals with the modeling of spiral inductors and transformers. A lumped
element representation is used to model the spiral behavior. The spiral is
broken down into individual turns and represented by RLC components. A series
inductance and resistance represent each turn, and capacitances associated with
the turn and the different loss mechanisms are modeled.
Finite Element analysis is used to
find the magnetic field within the spiral and then to calculate the inductance.
The same analysis is used to calculate the different coupling coefficients
between the inductors. Resistance is calculated based on the sheet resistance
of the metal layer and the width and length of the turn. Parallel plate
capacitance formulas are used to determine the different capacitances.
Two new
approaches are used in this thesis for modeling substrate eddy currents and
current crowding. These losses are modeled using inductance and resistance
loops. Because of the current flowing in the loops and the magnetic coupling to
the main turn inductors, these losses add to the other losses already modeled.
The current flowing through the eddy and current crowding loops are determined
by calculating the flux generated by each turn and finding the percentage that
is coupled to the other turns.
Single and
multi-layered inductors along with stacked, interwound and stacked-interwound
transformers are modeled. These models were validated against measured values
from inductors and transformers under different processes. Inductors were
validated in a six-layer copper bulk CMOS process and in an silicon-on-sapphire
(SOS) process. An interwound-stacked transformer model was validated in a
silicon-on-insulator (SOI) process. The validations indicate that the quality
factor (Q) and inductance (I) are within 10% of measured value whereas the self
resonant frequency (SRF) varied 10 – 20 % depending on the absence or presence
of ground shield.