IEEE Solid-States Circuits Magazine - Fall 2023 - 17

The real payload comes when
you plot the relative angles of the
harmonics versus frequency. How
distortion evolves as the fundamental
picks up speed can give
you valuable clues as to the source
or the propagation of the harmonics.
And there are some circumstances
where the phase domain is
easier to interpret than the amplitude
domain.
Figure 4 is one such example.
Here, the simulated response of
a collection of different circuit
nodes following the input signal are
assembled into a polar scatterplot.
The groupings indicate the fundamental
input frequencies that were
used to generate the distortion. If
you look closely, the radial magnitude,
(or amplitude) data don't convey
much information, making it
hard to draw any conclusion. The
phase of the groupings, however,
shows a dramatic shift between
5 GHz and 6 GHz input, clearly indicating
a resonance.
Depending on your situation,
it
may be difficult to tease a diagnosis
from a polar plot, but one thing
is certain: your colleagues will be
impressed! Any yahoo can make a
Cartesian graph. Using polar coordinates
to visualize your analysis
sets you apart as a person of deep
insight with powerful intellectual
tools at your fingertips. A promotion
is almost guaranteed.
Aside from the showmanship
potential of phase analysis, there is
one problem area where it is absolutely
indispensable: even-order distortion.
Application Example:
Even-Order Distortion
In the modern world of differential
and pseudodifferential signaling,
even harmonics are not supposed to
be a problem. At least that's what the
brochure says. If the two halves of a
differential signal pass through the
same nonlinearity, any even-order
distortion components that appear
are identical side to side, and thus
cancel out differentially. They show
up as a tiny common mode, but it is
generally too small to be a concern.
While this may be true in some
alternate universe, the world we live
in is not so simple. For even harmonics
to cancel out, the signals,
circuitry, and parasitics must all be
perfectly matched side to side. Simulators
happily maintain the illusion
of a perfectly balanced differential
world, but in reality, everything is
mismatched to some degree.
Thus, the key to diagnosing an
even-order distortion problem is to
find the imbalance that is causing
it. And that is why we're here: signal
paths must be balanced, not just
in amplitude but in phase as well.
So, being able to analyze harmonic
phase, as in the previous sections, is
an important skill. You're welcome.
The diagnosis job is to determine
if the imbalance is in
■ the creation of even-order components.
Is the offending nonlinearity
itself mismatched side to side?
■ the propagation of the harmonics.
Parasitics can easily dominate
transistor effects in modern processes.
Are the two halves of your
differential signal path really balanced
parasitically? Do they even
have the same bandwidth?
■ the coupling of the harmonic. Distortion
can come from adjacent
circuits operating at the same frequency.
Or it can come from the
block itself but find its way into the
signal path via the power supply.
(Some circuits generate enormous
second harmonic currents in their
supplies; see [1].) Or the fundamental
can couple back in and mix with
the fundamental in the signal.
The number of suspects is daunting.
How're you going to sort this out?
How will you know where to look?
Half a Differential Signal
If you were really good in a previous
technical life, you may be able
to measure each path in your differential
signal separately. Figure 5(b)
shows what this connection would
look like when testing for the second
FIGURE 4: Phase data when analyzed properly can be amazing. This is a plot of a specific
distortion component simulated at several input frequencies: 4, 5, 6, and 7 GHz. Each color
data point represents a different node in the circuit. The thing to notice here is that the
magnitude does not reveal much, but the phase has a lot to say. (Radial axis is voltage
magnitude.)
IEEE SOLID-STATE CIRCUITS MAGAZINE
FALL 2023
17

IEEE Solid-States Circuits Magazine - Fall 2023

Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2023