IEEE Solid-States Circuits Magazine - Fall 2023 - 18

harmonic, H2. This is NOT guaranteed
to work. Putting a single-ended signal
into a differential system means
that half of the signal swing is going
to appear as common mode to the
circuit, and many architectures cannot
handle that. Fortunately, some
switched capacitor circuits don't mind
at all. You may be able to tell by looking
at the schematic. It's also easy
to test: if a single-ended test yields
wildly different bandwidth and distortion
than a differential measurement,
go no further. The circuit can't handle
the common-mode. (Remember that a
single-ended input should only exercise
half of the signal range. A singleended
signal that generates a full-scale
output will take the circuit outside of
its designed operating range...by a
factor of 2!)
Figure 6 shows the second harmonics
of single-ended sweeps on the two
halves of a differential signal path.
Their vector difference is also plotted.
You can see a resonance on one side
and how the phase delay of one signal
contributes to the large increase
in the net amplitude of the differential
distortion at high frequency.
The next step (not shown) is to
compare the vector difference of the
single-ended measurements, the blue
trace in Figure 6, against the normal
differential data to see if the second
harmonic behaves the same way over
the frequencies of interest. If it doesn't
look roughly the same, you know that
the single-ended measurements have
not captured all of the relevant phenomena,
or that perhaps the common
mode associated with the measurements
has screwed things up. Even
if you don't get a good fit, the singleended
data may point you in the right
direction. The resonance indicated by
note A in Figure 6, for example, may
be an important clue.
If you do get good correlation
between differential and singleended
harmonic data, you're on the
right track, but you're not done yet.
You still don't know what to fix. There's
no way to tell if it is the source of the
harmonics (labeled " Nonlinearity " in
Figure 5) or the subsequent parasitics
in the signal paths (labeled " Filtering " )
that are causing the offending imbalance
in the differential circuit.
Nonlinearity Filtering
AC: 0 dBfs at f0
+
+
_
Measure H2 at 2f0
Nonlinearity
(a)
Filtering
The Source Versus the Path
To estimate the frequency response
that the distortion will see, the " filtering, "
repeat the single-ended tests
with a small signal at the harmonic
frequency, as illustrated in Figure 5(c).
(A small test signal does not exercise
the nonlinearity, effectively taking it
out of the measurement.) You must
also include a phase-locked tone at the
fundamental frequency (also tiny) to
have some way to measure the relative
phase. After capturing these small-signal,
single-ended transfer functions,
you will know two things:
1) If the measured small-signal
transfer functions match well side
to side, then the imbalance you're
looking for is not in the path. You'll
need to look elsewhere.
AC: -6 dBfs at f0
Nonlinearity Filtering
+
+
_
Measure H2 at 2f0
2) You can use the inverse small-signal
transfer functions to " undo "
the filtering effect of the paths
and see exactly how much spurious
tone is actually being created
or coupled in from outside.
Like everything else about this
Nonlinearity
(b)
Filtering
AC: tiny at 2f0
Nonlinearity Filtering
+
+
_
Measure at 2f0
exercise, interpretation of the results
can be difficult, but generally, it lets
you look at the relative impact of the
basic distortion mechanism and the
filtering of the signal path independently
versus frequency.
You may have already figured out
Nonlinearity Filtering
(c)
FIGURE 5: Cartoon version of the single-ended test plan. (a) Normal differential distortion
measurement. (b) Single-ended distortion measurement. (c) Small-signal single-ended
measurement at second harmonic frequency. Include a phase-locked pilot tone at f0
phase reference. (f0
for
is a frequency of interest, usually swept. H2 is the second harmonic.)
18
FALL 2023
IEEE SOLID-STATE CIRCUITS MAGAZINE
that the previous plan is not foolproof.
What if the filtering mismatch
is in front of the offending nonlinearity,
for example? And when you
consider all of the possible alternatives
and coupling sources, the result
is a massive dilemma that does not fit
into a pretty debugging flowchart.
Don't panic. The foregoing method

IEEE Solid-States Circuits Magazine - Fall 2023

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