IEEE Solid-State Circuits Magazine - Winter 2014 - 15

frequency capability of active electronic devices has progressed from
the low megahertz range to the high
gigahertz range over the past fifty
years, the science and art of radio
receiver design has undergone enormous advances. These developments
have opened up many opportunities
along the way for innovation and
research in receiver architecture
and circuitry. In my research and
design work in RF circuits prior to
1990, I often had cause to use inductors in various roles. These inductors had been realized in the form
of wirewound discrete inductors,
shorted transmission line stubs,
and in my work with HP, thin-film
spiral inductors printed on insulating substrates in hybrid circuits. In
the early days of silicon ICs in the
1960s, attempts had been made to
fabricate usable spiral inductors on
standard silicon substrates, but the
relatively low frequencies of interest demanded inductance values
near a microhenry, which proved to
be unattainable with usable Q. The
metal line widths of the day were
also too large to allow fabrication of
generally useful inductors. However
gigahertz frequency range applications for Si RF ICs (predominantly
for cellphones) were rapidly appearing by 1990 and I was finding many
situations where small inductors in
the nanohenry range could give significant leverage in RF circuit performance. I decided to revisit the
question of inductors on silicon, and
some rough calculations convinced
me that with the fabrication line
widths available at the time, useful inductors could potentially be
made on chip. I enlisted my graduate student Nhat Nguyen to work on
the project and he laid out some test
structures. Signetics fabricated the
devices for us in a standard Si fab
process. Since I was consulting with
Signetics one day a week at the time,
I took the measurements myself one
night in their Sunnyvale test facility.
I remember quite well the moment
when the S11 impedance plot of the
on-chip test inductor appeared on

the network analyzer and showed
a classical inductor trace in the
low gigahertz range with a useable Q factor. That was an exciting
moment. When I got back to Berkeley I wrote something like "now we
have access to inductors as useful
Si RF IC design elements" across
the S11 chart and distributed it to
my students and colleagues [19].
Paul Gray immediately saw the significance of the discovery. He had
been one of the pioneers of CMOS
analog baseband IC design and soon
began a research program to exploit

My first serious brush with oscillators occurred in my early teaching career when I had to make the
subject accessible to undergraduate
engineering students. I found that
the standard texts of the day were
quite inadequate and superficial in
their treatment of the subject, and I
was determined to do better. Working from my background in amplifier design, I decided that a good
approach would be to begin by analyzing a 3-pole (RC dominated) negative feedback amplifier with which
most students were comfortable.

In addition to the enormous value of the resulting
technical stimulation and research leads, such
consulting helped augment the rather meager
salary of an Assistant Professor.
the potential of combining on-chip
inductors with CMOS to realize RF
circuits for gigahertz range ICs. He
had great success in this work in the
following years. The use of on-chip
inductors was rapidly embraced by
the RF IC design community and
inductors on silicon are now used
routinely in many kinds of HF Si
ICs. The technology has progressed
enormously to allow fabrication of
inductive elements of many flavors
including transformers and baluns
and operating frequencies up to 100
GHz and beyond. Two of my PhD.
graduates, Professors Asad Abidi of
UCLA and Ali Niknejad of UCB have
been major contributors to the field.

Oscillators
Oscillators rival amplifiers as my
favorite class of electronic circuits.
In fact, the two groups of circuits
are rather closely related, as many
amplifier designers will attest. Oscillators are all around us in our environment, being present in structures
ranging from our economic system to
oscillating garden water sprays, and
are present in almost all radios. They
are fascinating, complex circuits with
many traps for the unwary.

Using this example I would show
how the poles of its linear transfer function entered the right-half
plane at a critical value of the loopgain magnitude, with a resulting
transient response that contained
an exponentially growing sinusoid.
I found over the years that essentially all the students "got it" with
this approach and were fascinated
to watch the oscillation grow (from
essentially nothing) on their SPICE
simulation time-domain plots. Of
course, the steady-state condition
is the most important characteristic of an oscillator, so I would show
how the presence of nonlinearity
eventually limited the growth of the
waveform and allowed us to calculate the final steady-state amplitude. I illustrated this phenomenon
using the more common LC tank
oscillator. After several years of
teaching, fielding students' (penetrating) questions and performing
numerous simulations, I developed
a pretty good grasp of the topic.
My first experience of pathology in oscillators occurred in the
seventies when I was asked to provide consulting assistance to a large
microcomputer manufacturer who

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Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Winter 2014