IEEE Solid-State Circuits Magazine - Winter 2016 - 35

domain of MOS ICs beyond the realm
of voice telephony. On this front,
Carleton University doctoral student
David Ribner took on the task of
extending the operating frequency
of switched-capacitor filters to well
beyond the voice frequency range.
In parallel, I started investigating the
use of MOS transistors as the precision conversion element rather than
the hitherto popular MOS capacitor.
The motivation to consider the use
of the MOS transistor came from process technology and speed considerations. To build linear MOS capacitors,
an additional polysilicon layer was
needed that added to the fabrication cost and could reduce the process yield. Visionaries like Prof. Miles
Copeland and Bob Hadaway of Northern Telecom were looking far into the
future where systems-on-a-chip would
have a large digital section performing much of the signal processing and
occupying most of the chip area and a
small-area analog portion that would
interface with the real world of analog signals. It is desirable to realize
all analog functions in a purely "digital" process technology that does not
have a second polysilicon layer. Data
converters could then use MOS current sources instead of MOS capacitors as the fundamental conversion
element. In addition to simplifying the
manufacturing process, current-mode
converters would offer a much higher
conversion speed. This was a daring
move by Prof. Copeland and Hadaway,

since most researchers working in the
area of analog MOS design were still
engaged in improving charge redistribution data converters and switchedcapacitor filters. This is a hallmark of
Prof. Copeland's career: the effortless
ability to successfully transition from
one area to another.
To enable this change of design
philosophy, the conception of my
Ph.D. thesis at Carleton was rooted
in a thorough understanding of the
matching behavior of the transistors, which is essential to realize
high accuracy and high product
yield. Unknown to us, research in

square root of the channel area, there
are a number of important differences. Shyu et al. [5] looked at the
mismatch of a current source as a
whole. Such an approach will have
limited value, as the current mismatch is a strong function of the
operating point. The results obtained
for one operating point could not be
used at another bias condition. In
[6], starting from the simple squarelaw model, the threshold voltage
and conductance constant are identified as the only two statistically
significant parameters contributing
to mismatch. With this approach,

This is a hallmark of Prof. Copeland's career:
the effortless ability to successfully transition
from one area to another.
this area had already begun in Prof.
Gabor Temes' team at the University
of California, Los Angeles. They were
the first to publish limited results
regarding the mismatch in N-channel
MOS (NMOS) current sources operating in the active or saturation region
[5]. Around the time of this publication, I had completed all of my theoretical work and also collected vast
amount of experimental data for
both NMOS and P-channel MOS transistors. It took two more years to see
the results of that work in print [6].
While both [5] and [6] show that
matching accuracy improves as the

it is possible to estimate the overall mismatch in a current source at
any operating point. Another important difference is that the depletion
charge in the channel was treated as
having no variability in [5]. In contrast, we showed that it is also a random variable and also hypothesized
that it follows a Poisson distribution.
In fact, this is a major cause of mismatch in the threshold voltage. This
component puts a fundamental limit
on the degree of matching that can be
realized, even in the absence of any
layout or manufacturing equipmentrelated anomalies.

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Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Winter 2016