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United States Patent Application 
20180131381

Kind Code

A1

Knierim; Daniel G.

May 10, 2018

TEST AND MEASUREMENT INSTRUMENT INCLUDING ASYNCHRONOUS TIMEINTERLEAVED
DIGITIZER USING HARMONIC MIXING AND A LINEAR TIMEPERIODIC FILTER
Abstract
A test and measurement instrument, including a splitter configured to
split an input signal having a particular bandwidth into a plurality of
split signals, each split signal including substantially the entire
bandwidth of the input signal, a plurality of harmonic mixers, each
harmonic mixer configured to mix an associated split signal of the
plurality of split signals with an associated harmonic signal to generate
an associated mixed signal, a plurality of digitizers, each digitizer
configured to digitize a mixed signal of an associated harmonic mixer of
the plurality of harmonic mixers, and a linear timeperiodic filter
configured to receive the digitized mixed signal from each of the
digitizers and output a timeinterleaved signal. A firstorder harmonic
of at least one harmonic signal associated with the harmonic mixers is
different from a sample rate of at least one of the digitizers.
Inventors: 
Knierim; Daniel G.; (Beaverton, OR)

Applicant:  Name  City  State  Country  Type  Tektronix, Inc.  Beaverton  OR  US
  
Assignee: 
Tektronix, Inc.
Beaverton
OR

Family ID:

1000003002149

Appl. No.:

15/818702

Filed:

November 20, 2017 
Related U.S. Patent Documents
       
 Application Number  Filing Date  Patent Number 

 15347600  Nov 9, 2016  9859908 
 15818702   

Current U.S. Class: 
1/1 
Current CPC Class: 
H03M 1/1215 20130101; G01R 19/2506 20130101; H03M 1/121 20130101; G01R 13/0236 20130101; G01R 13/0272 20130101 
International Class: 
H03M 1/12 20060101 H03M001/12; G01R 19/25 20060101 G01R019/25; G01R 13/02 20060101 G01R013/02 
Claims
1. A method, comprising: measuring a plurality of T impulse responses of
a linear timeperiodic filter; storing the measured plurality of impulse
responses in a memory as an array h of size T, in which the array entry
h[t] equals the response of the filter at a time t, and in which
h[0]=h[T].
2. The method of claim 1, further comprising convolving the array h with
an input signal to produce an output signal, in which the input signal
results from digitization of a harmonically mixed signal, the
digitization using a sample rate that is not a multiple or submultiple
of a harmonic signal used to produce the harmonically mixed signal.
Description
CROSSREFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent application Ser.
No. 15/347,600, filed Nov. 9, 2016, which is a continuation of U.S.
patent application Ser. No. 14/851,937, filed Sep. 11, 2015, issued as
U.S. Pat. No. 9,525,427, each of which are hereby incorporated by
reference into this application in their entirety.
TECHNICAL FIELD
[0002] This invention relates to test and measurement instruments and,
more particularly, to test and measurement instruments including one or
more asynchronous timeinterleaved digitizers, which use harmonic mixing
for reducing noise.
BACKGROUND
[0003] Useable bandwidths of test and measurement instruments, such as
digital oscilloscopes, can be limited by an analog to digital converter
(ADC) used to digitize input signals. The useable bandwidth of an ADC can
be limited to the lesser of the analog bandwidth or one half of a maximum
sample rate of the ADC. Various techniques have been developed to
digitize higher bandwidth signals with existing ADCs.
[0004] For example, synchronous timeinterleaving can be used to achieve
an effective higher sample rate. Multiple ADCs can sample an input signal
offset in time within a single sample period. The digitized outputs can
be combined together for an effectively multiplied sample rate. However,
if the analog bandwidth of the ADCs becomes the limiting factor, a high
bandwidth front end, such as a multiway interleaved track and hold
amplifier is needed to achieve a higher bandwidth.
[0005] Conventional track and hold amplifierbased timeinterleaved
systems cause the track and hold amplifier to be clocked at a sample rate
similar to or slower than the ADC channel bandwidth so that the ADC will
have sufficient time to settle to the held value. The ADC is
synchronously clocked to the track and hold amplifier to digitally
capture each held value. Such a limitation on the track and hold
amplifier in turn limits the ADC sample rate. Moreover, to satisfy the
Nyquist sampling theorem, the ADC sample rate is lowered to less than
twice the bandwidth of the ADC channel. As a result, many
timeinterleaved ADC channels are needed to achieve the desired
performance.
[0006] As the number of ADC channels increases, the overall cost and
complexity of the system also increases. For instance, the front end chip
must now drive more ADC channels, including additional ADC circuitry,
clocking circuitry, or the like, to get the overall net sample rate up to
a suitable value. The size and complexity of the chip also results in
longer communication paths, and therefore, an increase in parasitic
capacitance, electromagnetic noise, design difficulties, and so forth.
[0007] In another technique, subbands of an input signal can be
downconverted to a frequency range that can be passed through a lower
sample rate ADC. In other words, the wide input bandwidth can be split
into multiple lowerbandwidth ADC channels. After digitization, the
subbands can be digitally upconverted to the respective original
frequency ranges and combined into a representation of the input signal.
One significant disadvantage of this technique is the inherent noise
penalty when digitizing an arbitrary input signal whose frequency content
may be routed to only one ADC channel. The recombined output will contain
signal energy from only one ADC, but noise energy from all ADCs, thereby
degrading the SignaltoNoise Ratio (SNR).
[0008] Accordingly, a need remains for improved devices and methods for
digitizing any frequency input signal by all ADC channels in an
asynchronous timeinterleaved architecture, thereby avoiding the noise
penalty.
[0009] U.S. Pat. No. 8,742,749, titled TEST AND MEASUREMENT INSTRUMENT
INCLUDING ASYNCHRONOUS TIMEINTERLEAVED DIGITIZER USING HARMONIC MIXING,
issued Jun. 3, 2014, incorporated by reference herein in its entirety,
discusses an asynchronous timeinterleaved system with a reconstruction
algorithm to reconstruct the signal after the signal has been split and
processed.
SUMMARY
[0010] Embodiments of the disclosed technology are directed to a test and
measurement instrument, including a splitter configured to split an input
signal having a particular bandwidth into a plurality of split signals,
each split signal including substantially the entire bandwidth of the
input signal; a plurality of harmonic mixers, each harmonic mixer
configured to mix an associated split signal of the plurality of split
signals with an associated harmonic signal to generate an associated
mixed signal; a plurality of digitizers, each digitizer configured to
digitize a mixed signal of an associated harmonic mixer of the plurality
of harmonic mixers; and a linear timeperiodic filter configured to
receive the digitized mixed signal from each of the digitizers and output
a timeinterleaved signal. A firstorder harmonic of at least one
harmonic signal associated with the harmonic mixers is different from an
effective sample rate of at least one of the digitizers.
[0011] Embodiments of the disclosed technology are also directed to a
method including splitting an input signal having a particular bandwidth
into a plurality of split signals, each split signal including
substantially the entire bandwidth of the input signal; mixing each split
signal with an associated harmonic signal to generate an associated mixed
signal; digitizing each mixed signal; receiving the digitized mixed
signal from each of the digitizers at a linear timeperiodic filter; and
outputting a timeinterleaved signal from the linear timeperiodic
filter. A firstorder harmonic of at least one harmonic signal associated
with the harmonic mixers is different from a sample rate of at least one
of the digitizers
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a block diagram of an ADC system for a test and
measurement instrument using harmonic mixing.
[0013] FIG. 2 is a block diagram of an ADC system for a test and
measurement instrument using harmonic mixing according to some
embodiments of the disclosed technology.
DETAILED DESCRIPTION
[0014] FIG. 1 is a block diagram of an ADC system for a test and
measurement instrument using harmonic mixing. In this embodiment, the
instrument includes a splitter 10 configured to split an input signal 12
having a particular frequency spectrum into multiple split signals 14 and
16, each split signal including substantially the entire spectrum of the
input signal 12. A splitter 10 can be any variety of circuitry that can
split the input signal 12 into multiple signals. For example, the
splitter 10 can be a resistive divider. Thus, substantially all frequency
components of the input signal 12 can be present in each split signal 14
and 16. However, depending on the number of paths, harmonic signals used,
or the like, the frequency responses for various split signals of a
splitter 10 can be different.
[0015] The split signals 14 and 16 are inputs to harmonic mixers 18 and
24, respectively. Harmonic mixer 18 is configured to mix the split signal
14 with a harmonic signal 20 to generate a mixed signal 22. Similarly,
harmonic mixer 24 is configured to mix the split signal 16 with a
harmonic signal 26 to generate a mixed signal 28.
[0016] As used herein, a harmonic mixer is a device configured to mix a
signal with multiple harmonics. Although multiplication and/or mixing has
been described in connection with harmonic mixing, a device that has the
effect of multiplying a signal with multiple harmonics can be used as a
harmonic mixer.
[0017] A digitizer 30 is configured to digitize mixed signal 22.
Similarly, a digitizer 32 is configured to digitize mixed signal 28. The
digitizers 30 and 32 can be any variety of digitizer. Although not
illustrated, each digitizer 30 and 32 can have a preamplifier, filter,
attenuator, and other analog circuitry as needed. Thus, the mixed signal
22 input to the digitizer 30, for example, can be amplified, attenuated,
or otherwise filtered before digitization.
[0018] The digitizers 30 and 32 are configured to operate at an effective
sample rate. The effective sample rate is a rate that allows the
digitizers 30 and 32 to adequately digitize the signals 22 and 28, and
may be chosen, for example, to optimize the signaltonoise ratio within
the frequency band of interest within signals 22 and 28. In some
embodiments, the digitizer 30 can include a single analog to digital
converter (ADC). However, in other embodiments, the digitizer 30 can
include multiple interleaved ADCs operating at lower sample rates to
achieve a higher effective sample rate.
[0019] A firstorder harmonic of at least one of the harmonic signals 20
and 26 is different from an effective sample rate of at least one of the
digitizers 30 and 32. In some embodiments, the firstorder harmonic of a
harmonic signal need not be an integer multiple or submultiple of the
effective sample rate of the at least one of the digitizers. In other
words, in some embodiments, the firstorder harmonic of a harmonic signal
associated with the harmonic mixers is not an integer multiple or
submultiple of the effective sample rate of the at least one of the
digitizers.
[0020] It should be understood that all bands of the input signal 12 go
through all paths. In other words, when more than one channel is combined
for processing a single input signal 12, each channel or path receives
substantially the entire bandwidth of the input signal 12. As the input
signal 12 is transmitted through all of the digitizers, the signal to
noise ratio is significantly improved.
[0021] A filter 36 can be configured to filter the digitized mixed signal
34 from digitizer 30. Similarly, a filter 42 can be configured to filter
the mixed signal 40 from digitizer 32. Filters 36 and 42 may be, for
example, equalization and interpolation filters. Harmonic mixers 46 and
52 are configured to mix the filtered mixed signals 38 and 44 with
harmonic signals 48 and 54, respectively. In some embodiments, the
harmonic signals 48 and 54 can be substantially similar in frequency and
phase to the corresponding harmonic signals 20 and 26. While the harmonic
signals 20 and 26 are analog signals, and the harmonic signals 48 and 54
are digital signals, the scaling factors for these harmonic signals can
be the same or similar to each other. The output signals 50 and 56 are
referred to as remixed signals 50 and 56. A combiner 58 is configured to
combine the remixed signals 50 and 56 into a reconstructed input signal
60. In some embodiments, the combiner 58 can implement more than mere
addition of signals. For example, averaging, filtering, scaling, or the
like can be implemented in the combiner 58. That is, the combiner 58 may
include a lowpass filter (LPF) 62 or the LPF 62 may be placed outside
the combiner, as shown in FIG. 1.
[0022] The filters 36 and 42, the harmonic mixers 46 and 52, harmonic
signals 48 and 54, the combiner 58, and other associated elements can be
implemented digitally. For example, a digital signal processor (DSP),
microprocessor, programmable logic device, general purpose processor, or
other processing system with appropriate peripheral devices as desired
can be used to implement the functionality of the processing of the
digitized signals. Any variation between complete integration to fully
discrete components can be used to implement the functionality.
[0023] For example, some filtering can occur prior to digitization. The
mixed signals 22 and 28 could be filtered with a low pass filter having a
cutoff frequency near one half of the effective sample rate of the
digitizers 30 and 32. The filtering of filters 36 and 42 can add to such
inherent and/or induced filtering.
[0024] In some embodiments, the net filtering of the mixed signals 22 and
28 can result in a frequency response that is substantially complementary
about one half of a frequency of the firstorder harmonic of the harmonic
signals 20 and 26. That is, the frequency response at a given offset
higher than frequency F.sub.1/2 and the frequency response at a given
offset lower than frequency F.sub.1/2 can add to one. Although one has
been used as an example, other values can be used as desired, such as for
scaling of signals. Furthermore, the above example is described as an
ideal case. That is, the implemented filtering can have different
response to account for nonideal components, calibration, or the like.
[0025] In the event of interleaving errors due to analog mismatch,
hardware adjustments can be made for mixing clock amplitude and phase.
The adjustments can then be calibrated to minimize interleave mismatch
spurs. Alternatively, or in addition to the above approach, hardware
mismatches can be characterized, and a linear, timevarying correction
filter 64 may be used to cancel the interleave spurs.
[0026] Moreover, although the digital filtering, mixing, and combining
have been described as discrete operations, such operations can be
combined, incorporated into other functions, or the like. In addition, as
the above discussion assumed ideal components, additional compensation,
can be introduced into such processing as appropriate to correct for
nonideal components. Furthermore, when processing the digitized signals,
changing frequency ranges, mixing, and the like can result in a higher
sample rate to represent such changes. The digitized signals can be
upsampled, interpolated, or the like as appropriate.
[0027] A memory 66 may be provided between digitizer 30 and filter 36 in
the upper ADC channel and a memory 68 between digitizer 32 and filter 42
in the lower ADC channel. An acquisition can be performed and the
digitized mixed signal 34 or the digitized mixed signal 40 can be stored
in memories 66 and 68, respectively, before being sent to filters 36 and
42, respectively.
[0028] As discussed above, the reconstruction applies
equalization/interpolation filters 36 and 42 to the ADC data streams,
mixes them with a digital version of the harmonic mixing function via
harmonic mixers 46 and 52, averages the results via combiner 58, lowpass
filters 62 the averaged results to remove upper mixing products, and then
applies a linear, timevarying correction filter 64. All of these steps
are linear operators, i.e. for any scalars a and b and input signals x(t)
and y(t),
F{ax(t)+by(t)}=aF{x(t)}+bF{y(t)} (1)
[0029] Since digital signal processors are used, time is represented in
discrete time intervals, represented by an integer value "t," where each
increment oft represents one sample point of time. The sample interval
between adjacent points in time, for example, may be 5 ps. However, any
other sample interval may be used.
[0030] The equalization/interpolation filters 36 and 42 and lowpass
filter 62 are timeinvariant as well as linear, i.e.,
F{x(tt.sub.0)}=F{x(t)}tt.sub.0 (2)
The variable to is any arbitrary integer time delay. These filters will
be referred to herein as linear timeinvariant (LTI) filters. An LTI
filter can be fully and uniquely represented by its impulse response, and
a cascade of LTI filter components is also an LTI filter, with an impulse
response equal to the convolution of the components' impulse responses.
[0031] The mixing functions 48 and 54 and linear, timevarying correction
filter 64 vary over time. However, if the mixing frequency is
harmonically related to the underlying ADC interleaving rate, both steps
will be timeperiodic, i.e.,
F{x(tkT)}=F{x(t)}tkT (3)
[0032] The variable k is any integer and T is the least common period of
the mixing function and the interleave rate. These are referred to as
linear, timeperiodic filters ("LTP"). For example, the mixing function
may be 75 GHz, the interleave rate is 12.5 GS/s, and T=16, which at 5 ps
per sample point represents 80 ps. The mixing function is being viewed as
a filter with a single coefficient, one point duration impulse response,
which varies periodically over time (completing six cycles in 16 samples
in this example).
[0033] LTI filters may be a subclass of LTP filter by letting to =kT.
Thus, the reconstruction may be represented as a cascade of LTP filters.
[0034] An LTP filter can be fully and uniquely represented by an array of
T impulse responses, where T is the integer period of the LTP filter.
Array entry 0 equals the response of the filter to an impulse at time
t=0, array entry 1 equals the response of the filter to an impulse at
time t=1 advanced by one sample, array entry 2 equals the response of the
filter to an impulse at time t=2 advanced by two samples, etc. Note that
if an array entry is defined at T, it would be the response of the filter
to an impulse at the time t=T advanced by T samples, but by the
periodicity property that is identical to the response of an impulse at
t=0, which is already stored in array entry 0. Hence, the array of T
impulse responses defines the response to an impulse at any time, and by
linearity, the response to any signal (represented as a linear
combination of impulses at different times) can be determined. An LTI
filter, as a subclass of LTP filters of period T, would be represented by
having all T entries identical.
[0035] An LTP filter response of duration N samples can be stored as a
twodimensional T by N array, indexed by the input impulse location
(modulo T) and the output sample. For simplicity of notation, let bold
font represent modulo T, i.e.,
i=i(modulo T) (4)
[0036] Then, the output y(t) of an LTP filter "f" can be expressed in
terms of its input x(t) akin to a convolution:
y(t)=x(t)*f=.SIGMA..sub.ix(i)f(i,ti) (5)
[0037] Likewise, the output y(t) of a cascade of two LTP filters "f" and
"g" can be expressed in terms of its input x(t):
y(t)=[x(t)*f]*g=.SIGMA..sub.j[.SIGMA..sub.ix(i)f(i,ji)]g(j,tj)=.SIGMA.
.sub.ix(i)[.SIGMA..sub.jf(i,ji)g(j,tj)]=.SIGMA..sub.ix(i){f*g}(i,t (6)
[0038] Where {f*g}(i,m) is defined as:
{f*g}(i,m)=.SIGMA..sub.kf(i,k)g(i+k,mk) (7)
[0039] Thus, the "periodic convolution" of LTP filters f and g can be
precalculated, the result can be stored as LTP filter f*g, and the input
x can be convolved with this new filter to calculate the output y. In a
similar fashion, the "periodic convolution" of any number of LTP filters
(such as all the steps of the reconstruction algorithm) may be
precalculated and just one LTP filter may be applied to the data at
runtime.
[0040] The "periodic convolution" of LTP filters follows the associative
rule, as does the convolution of LTI filters, as shown in equation (8):
(f*g)*h=f*(g*h) (8)
[0041] However, the communicative rule does not apply to LPT filters as it
does to LTI filters. That is, equation (9) applies to LTI filters, but
not necessarily to LTP filters:
f*g=g*f (9)
[0042] The first step of reconstruction applies an equalization and
interpolation filter 36 or 42 to each ADC channel's data stream. The
output rate of the equalization and interpolation filters 36 and 42 is
generally N times the input rate (where N is the number of interleaved
digitizers), and this is often viewed as a twostep process: inserting
N1 zero samples between the ADC samples to achieve N times the data
rate, then applying a lowpass LTI filter at the higher rate to remove
the aliased energy created by the alternating samples and zeroes. When
representing this losspass filter as an LTP filter, though, N1 of N
entries in the array of T impulse responses can be set to zero, so rather
than inserting zero samples to increase the rate, any arbitrary samples
may be inserted since they will subsequently get multiplied by a zero
impulse response. For example, the ADC samples from the other N1 ADC
channel(s) may be inserted.
[0043] This approach can be used for all equalization and interpolation
filters 36 and 42, choosing the nonzero rows in each array to correspond
with the associated digitizer's samples. This allows the same interleaved
data stream, containing interleaved samples from all ADC channels, to be
fed into all equalization and interpolation filters 36 and 42, and by
linearity, the N resultant LTP filters representing the N paths may be
added to obtain a single LTP filter to output a reconstructed data
stream. The whole reconstruction process then may become applying a
single LTP filter to the ADC data, taken as an interleaved stream.
[0044] As when convolving LTI filters, the duration of the response of
several convolved LTP filters will generally be the sum of the durations
of the component filters, minus the number of filters convolved, plus
one. However, the filter coefficients near either end are likely to be
very small, both because there are fewer nonzero terms to add together
in the summation and because those terms that do get added are the
product of coefficients from near the end of the component filter
responses, which tend to be small, making their product "small squared"
or very small. Thus, the duration of the final convolved LTP filter may
be practically limited to something less than the theoretical
combinations discussed above, saving even more execution time. In some
embodiments, applying a smooth windowing function may be useful to avoid
an abrupt truncation of the response.
[0045] This allows the entire reconstruction algorithm to be reduced to an
application of a single LTP filter to the interleaved ADC data stream,
thus reducing processing time and allowing faster update rates at long
record lengths. That is, an LTP system may be defined as a cascade of LTP
filters and be characterized as a single LTP filter by use of periodic
convolution. Alternatively, any algorithm that is known to be linear and
timeperiodic, i.e., is an LTP system, may be characterized as a single
LTP filter by application of the algorithm to T input records, where each
input record is an impulse at location t, where 0.ltoreq.t<T. This
technique directly measures the impulse responses which, after advancing
by t samples, are stored in the impulse response array of the single LTP
filter. This direct determination of the system impulse response array
can be applied to any LTP system, even if implemented inside a
"blackbox" wherein the operation of the algorithm cannot be directly
observed. For example, this approach of directly determining the impulse
response can be used with a system in a "blackbox" whether that system
internally operates as a cascade of LTP components or uses some other
processing technique, e.g., frequency domain analysis.
[0046] Precalculation of the LTP system impulse response array will take
time, whether done using periodic convolutions of the components or
applying the blackbox measurement approach. The execution time savings,
then, comes from assuming that the duration of the record(s) to be
reconstructed by one LTP filter are long compared to the duration of the
LTP system response. This assumption is often valid, as the record
lengths may go into the millions of samples, whereas the system response
duration is in the hundreds of samples.
[0047] However, if a user requests shorter records and triggers them far
enough apart to require recalculating the LTP filter to account for
hardware drift, it may be faster to apply each LTP component to the data
record in cascade. On the other hand, processing throughput may not be an
issue in this case with short records and slow triggers.
[0048] After reconstruction, a band width enhancement (BWE) filter 70 may
be applied using a much longer duration LTI filter using frequency domain
techniques. If this filter is much longer in duration than any of the LTP
filters, it may be kept separate. Treating the BWE filter 70 as part of
the LTP cascade, though mathematically accurate, would require
calculating T (16 in the examples above) longduration responses which
would complicate and potentially slow the frequencydomain filtering
technique in use. The periodic convolution technique applies best when
incorporating LTI filter durations less than or comparable to the longest
inherently time varying filter duration.
[0049] FIG. 2 illustrates the filters 36 and 42, harmonic mixers 46 and
52, combiner 58, lowpass filter 62, and lineartime varying filter 64 as
a single convolved LTP filter 72. That is, the output from the digitizer
30 and digitizer 32 may be inputted directly into the LTP filter 72,
rather than through each of the components shown in FIG. 1. The LTP
filter 72 outputs reconstructed interleaved signal.
[0050] Although FIG. 2 illustrates the filters 36 and 42, harmonic mixers
46 and 52, combiner 58, lowpass filter 62, and lineartime varying
filter 64 as being convolved into a single LTP filter 72, multiple LTP
filters may be used instead of a single LTP filter. Alternatively, LTP
filter 72 may include two or more of filters 36 and 42, harmonic mixers
46 and 52, combiner 58, lowpass filter 62, and lineartime varying
filter 64, while the filters not convolved remain.
[0051] Another embodiment includes computer readable code embodied on a
computer readable medium that when executed, causes the computer to
perform any of the abovedescribed operations. As used here, a computer
is any device that can execute code. Microprocessors, programmable logic
devices, multiprocessor systems, digital signal processors, personal
computers, or the like are all examples of such a computer. In some
embodiments, the computer readable medium can be a tangible computer
readable medium that is configured to store the computer readable code in
a nontransitory manner.
[0052] Although particular embodiments have been described, it will be
appreciated that the principles of the invention are not limited to those
embodiments. Variations and modifications may be made without departing
from the principles of the invention as set forth in the following
claims. For example, it is anticipated that a reordering of the digital
filtering, mixing, and/or combining may allow for more efficient
execution of the digital processing while still providing for
reconstruction of a digital representation of the input signal.
* * * * *