IEEE Solid-State Circuits Magazine - Spring 2016 - 76

Introduction
It is very important to understand
exactly what the CMOS power amplifier (PA) circuitry is doing to have
assurance that it will reliably perform as designed through very high
volume production. This means,
among other things, that any information out in the design community
that is not quite true, or ambiguous,
must be identified and clarified.
Equally important, it is necessary

how they are used. This is not a trivial concern. Words matter because
this is the way we communicate and
how we keep historical records. It
is important to realize that all communication of information occurs
at the receiver. A transmitter on its
own is useless. However, if what the
transmitter sends is not fully comprehended by the receiver (whether
electronic or human), then the
desired or intended communication

Those of us who are writing or speaking need
to be sure that what we are sending out is
of a form that our intended receivers, listeners
or readers, will comprehend.
to firmly understand what the most
important technical foundations are
so that all design activities can be
cross-checked to not only validate
all interim results but, most critically, to catch any errors early so
that design and product development projects stay on track toward
successful and on-time results.
It is my practice to continuously
reach back to important first principles to not get lost in mathematics and simulations. This provides
a useful and vital check on whether
what the math and simulations are
saying is reasonable or not.
Most of this installment (Part 4)
in this series is about words and

does not occur. Those of us who are
writing or speaking need to be sure
that what we are sending out is of
a form that our intended receivers,
listeners or readers, will comprehend. From comments received at
the International Solid-State Circuits
Conference 2015 Forum where this
material was originally presented,
the topics presented in this article
are the ones most favorably appreciated by the audience.

Common Misunderstandings
Several misperceptions exist in the
signal processing and circuit design
communities, of which I am a part.
Having encountered and wrestled

Waveform Value

1.5
1
0.5
0
-0.5
-1

-1.5
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
Phase (Radians)
To -Infinity

FIGURE 1: The valid extent of signal phase is infinite in both directions.

S P R I N G 2 0 16

IEEE SOLID-STATE CIRCUITS MAGAZINE

To Infinity

with them, my purpose here is to
present them and show how these
misperceptions are properly handled. For uniformity, each of these
is listed as a misunderstanding in
the following discussion.

Misunderstanding #1:
Phase Is Unique Only
Within a Length-2 r Interval
When asking most engineers the
question "What is the unambiguous
extent of phase?" the answer back
is nearly always "an interval of 2r "
or "phase is modulo 2r ," a position
put forward in [2] and [3], which
otherwise are excellent books, and
appears to largely follow from the
1954 paper [4]. A simple view of
sinusoid functions shows that these
responses cannot be true. Phase,
the total argument of the sinusoid,
is valid across all real numbers.
This is illustrated in Figure 1.

Clarification
What is true is that our instantaneous
observation of phase through a sinusoid waveform or a pair of orthogonal sinusoidal waveforms (e.g., sine
and cosine) is periodic with period
2r. It is important, however, to not
transfer properties of our observations of the quantity being observed
onto being a property of that quantity, here being signal phase. Phase
has an infinite extent. What phase
does not inherently have is a clear
origin value: where does phase = 0?
This is indeed arbitrary and can be
selected for local convenience, as
stated in [5].
This infinite extent of phase provides important capabilities to communications. The recognized value
to radio navigation of the infinite
extent of signal phase has a long history [6], where the counting of signal
cycles to keep track of this infinite
extent (a memory process) is explicitly stated. This property, however,
is nearly always not included in
discussions of signal modulation.
There is more on why this happened
later in the discussion of Misunderstanding #4.

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