IEEE Solid-State Circuits Magazine - Summer 2015 - 85

an accident, and is an artifact of Ohm's
law. Best amplifier linearity directly
corresponds to the highest power dissipation. From (2) we also know that
this minimizes amplifier energy efficiency. Such is physics. It is not what
we want, but Ohm's law doesn't care.
This is what is. And this is the fundamental reason for the energy efficiency
versus amplifier circuit linearity tradeoff. This tradeoff is a direct artifact
of Ohm's law. We cannot simply design
cleverly around it. Not without consequences, anyway.
As the drain voltage of the transistor varies in Figure 4, the current
through it follows the load line. Two
important characteristics are provided by the curves in Figure 4. First,
the value of VGS necessary to get a
particular load current is determined
by the intersecting transistor characteristic curve. Amplifier linearity
is determined by how uniform these
intersections are along the load line
for uniform spacing of the VGS values. In Figure 4, these intersections
are much closer together at low currents than at higher current, which
corresponds to 1) higher gain at
higher currents and 2) the fact that
this transistor is not a very good linear amplifier at any currents.
The second important characteristic
is the set of intersections between the
load line and the constant power contours for transistor power dissipation.
When there is no load current, there
is no dissipation in either the transistor or the load. Progressing backwards
up along the load line, as load current
increases, the transistor power dissipation increases until half way along the
load line. As the load current increases
further, the power dissipation in the
transistor decreases as the voltage
across the transistor decreases. Evaluation of amplifier behavior stops at the
open circle, the knee voltage along this
particular load line. Much more about
this knee voltage will be presented in
Part 6 of this series.
This transistor power dissipation
peak is explicitly shown in Figure 5.
Large VDS corresponds to small voltage drop across the load and thus

small load power dissipation. Bias for
transistor linear operation, Class A, is
at half of the current flowing at the
knee voltage condition. This is marked
on the transistor dissipation curve in
Figure 5 and is very near to the peak
power dissipation. Again, linear circuit operation maximizes power dissipation and, from (2), also minimizes
energy efficiency. Ohm's law is evaluated separately for the load resistor,
giving the dashed curve in Figure 5.
Since power dissipation in the load
is good, the wide separation between
load and transistor power dissipations
at low values of VDS is an attractive
condition. Exploring this condition is
the topic of Part 5 of this series.
One common approach to reducing transistor power dissipation is to
bias the amplifier transistor away from
the linearity optimum of Class A and
closer to transistor cutoff at Class B.
These intermediate bias points are
still described in the literature as linear amplifiers. It is very important
to realize that any shift in bias away
from Class A incurs nonlinear operation at the transistor. With Class AB
bias, the transistor necessarily spends
an increasing amount of time in cutoff
operation. Cutoff is very much a nonlinear mode of transistor operation.
We "fool" ourselves into thinking that
Class AB and Class B amplifiers are linear. They are not, certainly when looking at a single transistor's operation.
We get away with this thinking
because the output networks of non-
Class A amplifiers all contain bandpass resonators [3]. These resonators
filter out the harmonics that occur at
the transistor from operation in cutoff, and when we only look at the output with a spectrum analyzer we are
lulled into thinking that the amplifier transistor is operating linearly.
It is not. And the Fourier transform
must still be satisfied, so the output
signal is not getting larger. More, the
amplifier gain is varying because of
these transitions between controlled
current source and cutoff operation. Nothing of value-here being
the reduction in transistor power
dissipation-comes for free!

Another side effect of needing
this resonant output for non-Class A
amplifiers is the bandwidth restriction that comes from the resonance.
Making an amplifier with multiple
octaves of bandwidth is possible with
Class A bias. It is not possible with
any other bias scheme, unless some
circuit reconfiguration is used for
different frequencies.
The most important point to remember here is that circuit (meaning transistor) nonlinear operation is essential for
any improvement in efficiency above
the minimum exhibited by Class A.
The entire design practice of improving
amplifier efficiency is really an activity
in finding out how much and what type
of transistor nonlinearity is best used
for a particular design, and how to best
tolerate that nonlinearity. This fact was
realized more than a century ago. We
in the amplifier design community are
still working these trade-offs!

references

[1] W. Lepkowski, S. J. Wilk, J. Kam, and T.
J. Thornton, "40V MESFETs fabricated on
32nm SOI CMOS," in Proc. IEEE Custom
Integrated Circuits Conf. (CICC), San Jose,
California, 2013.
[2] H. Meyr, M. Moenclaey, and S. A. Fechtel,
Digital Communication Receivers. New
York: Wiley, 1998.
[3] E. McCune, "Physical relationships along
the power amplifier continuum," in Proc.
Workshop WSD at the Int. Microwave
Symp., Baltimore, MD, June 5-10, 2011.

About the Author
Earl McCune received his B.S. from the
University of California, Berkeley, his
M.S. from Stanford University, and his
Ph.D. from the University of California,
Davis. His experience in RF circuits,
signals, and systems spans more than
40 years. He cofounded two Silicon
Valley startups: one doing direct digital synthesis beginning in 1986, which
merged with Proxim in 1991; and the
second, Tropian, doing switch-based RF
transmitters beginning in 1996, which
was acquired by Panasonic ten years
later. He has 74 issued patents in the
United States. He has authored two
books, Practical Digital Wireless Signals
and Dynamic Power Supply Transmitters. He has been an IEEE MTT Distinguished Microwave Lecturer since 2013.

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Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2015