IEEE Solid-States Circuits Magazine - Fall 2023 - 13

SHOP TALK: WHAT YOU DIDN'T
LEARN IN SCHOOL
Chris Mangelsdorf
I
Phase Data:
You're not going to throw that away, are you?
I hate to throw things out. Clinically,
this is known as " hoarding
disorder. " Sure, all of the piles of old
newspapers in my house are starting
to become a nuisance, but this
affliction does have a benefit when
it comes to distortion analysis. It
turns out that the discarded phase
information in FFTs-which you
may never have even looked at-can
be your best friend when tracking
down harmonics. (See Figure 1.)
Half of the total information content
in a Fourier transform is in the
form of phase data, and yet everybody
ignores it. Classical spectrum
analyzers don't even measure it.
People adventurous enough to take a
peek at the phase info are punished
with a plot like Figure 2(b), and that's
usually enough to scare them off.
You may or may not be concerned
with the phase response of
the fundamental
in your circuit,
but nobody cares about the phase
of the distortion products. We
just want them gone. However, for
tracking down the source of those
spurious components, phase can be
a lifesaver.
In general, plotting harmonic
phase versus frequency yields a
much smoother, more intelligible
plot than amplitude information,
which makes it perfect for diagnostics.
And phase tends to integrate
the effect of resonant parasitics, so
that problem spots can be identiDigital
Object Identifier 10.1109/MSSC.2023.3315669
Date of current version: 14 November 2023
fied with a minimum number of frequency
samples.
In what follows, two unorthodox
techniques for looking at phase
and distortion are discussed. Neither
will likely be your first line of
defense, but it's good to have them
both in your arsenal for when you
hit the wall. The first topic is simply
how to correctly read the phase
of distortion components. The second
topic deals with the strongest
application of that analysis: evenorder
distortion.
These two techniques apply to
all analog circuits, as long as you
can digitally analyze the output
spectrum. So, an ADC front end or
any analog block followed by an
ADC or accessible by a digitizing
scope would fall into this category.
Phun With Phase
Phase is a strange beast. If you pick a
point on the phase plot of Figure 2(b)
and read the number, it will do you
no good at all! Bupkis. It's a random
number. If you average it over multiple
FFTs, it will converge to 0 (or π if
your output is 0 to 2π). Always. That's
because it is a uniformly distributed
random number between -π and
+π. ... How can that be a " lifesaver " ?
You see, the FFT defines phase
as the angular value of each Fourier
component at the very start of the
digitized time record. (It turns out
that cosine waves are the baseline,
FIGURE 1: Harmonics, and their evolution versus frequency have quite a story to tell. To
appreciate their clues, however, you must capture the phase data and interpret it correctly.
(This example analyzes a differential signal by examining the distortion of each side
independently. The net differential distortion is the vector difference of the blue and black
curves at any given frequency.)
IEEE SOLID-STATE CIRCUITS MAGAZINE
FALL 2023
13

https://orcid.org/0000-0002-1214-3346

IEEE Solid-States Circuits Magazine - Fall 2023

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