U.S. patent application number 14/220860 was filed with the patent office on 2015-03-19 for asynchronous time-interleaved digital to analog converter using harmonic mixing.
The applicant listed for this patent is Tektronix, Inc.. Invention is credited to JOHN E. CARLSON, JOAN MERCADE.
Application Number | 20150077169 14/220860 |
Document ID | / |
Family ID | 50478180 |
Filed Date | 2015-03-19 |
United States Patent
Application |
20150077169 |
Kind Code |
A2 |
CARLSON; JOHN E. ; et
al. |
March 19, 2015 |
ASYNCHRONOUS TIME-INTERLEAVED DIGITAL TO ANALOG CONVERTER USING
HARMONIC MIXING
Abstract
Waveforms generators include a splitter that splits a digital
input signal into a number of split signals each having a split
signal frequency bandwidth that is substantially similar to a
digital input signal frequency bandwidth. The split signals are
mixed with associated digital, harmonic signals to generate a
number of digital, mixed signals, which are then converted to
analog signals at an effective sample rate that is different from a
first order harmonic signal of at least one of the digital,
harmonic mixers. A number of analog, harmonic mixers mix the
associated analog signals with associated analog, harmonic signals
to generate mixed, analog signals. The mixed, analog signals are
combined into an output signal having an output signal bandwidth
that is greater than a bandwidth of at least one of the number of
DACs.
Inventors: |
CARLSON; JOHN E.;
(Beaverton, OR) ; MERCADE; JOAN; (BARCELONA,
ES) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Tektronix, Inc. |
Beaverton |
OR |
US |
|
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20140285251 A1 |
September 25, 2014 |
|
|
Family ID: |
50478180 |
Appl. No.: |
14/220860 |
Filed: |
March 20, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61803970 |
Mar 21, 2013 |
|
|
|
Current U.S.
Class: |
327/361 |
Current CPC
Class: |
H03M 1/08 20130101; H03M
1/662 20130101; H03D 7/1408 20130101 |
Class at
Publication: |
327/361 |
International
Class: |
H03D 7/14 20060101
H03D007/14 |
Claims
1. A waveform generator, comprising: a splitter structured to
receive a digital input signal having an input signal frequency
bandwidth and structured to split the digital input signal into a
plurality of split signals, each of the split signals having a
split signal frequency bandwidth that is substantially similar to
the input signal frequency bandwidth; a plurality of digital,
harmonic mixers structured to digitally mix an associated one of
the split signals with an associated digital harmonic signal to
generate a plurality of digital mixed signals; a plurality of
digital to analog converters, each of the plurality of digital to
analog converters structured to convert an associated digital mixed
signal of the plurality of digital mixed signals to an analog
signal, each of the digital to analog converters having an
effective sample rate that is different from a first order harmonic
signal of at least one of the associated digital, harmonic mixers;
a plurality of analog, harmonic mixers structured to mix an
associated one of the analog signals with an analog harmonic signal
to generate a plurality of mixed, analog signals; and a combiner
structured to combine the plurality of mixed, analog signals into
an output signal having an output signal bandwidth that is greater
than a bandwidth of at least one of the plurality of digital to
analog converters.
2. The waveform generator of claim 1, wherein the first-order
harmonic signal of the at least one of the associated digital,
harmonic mixers is not an integer multiple or sub-multiple of the
effective sample rate of the at least one digital to analog
converters.
3. The waveform generator of claim 1, wherein the first-order
harmonic of the at least one harmonic signal associated with the
digital, harmonic mixers is between the effective sample rate of
the at least one of the digital to analog converters and one half
the effective sample rate of the at least one of the digital to
analog converters.
4. The waveform generator of claim 1, wherein the plurality of
digital mixed signals includes at least two sub-bands of the
digital, input signal within a bandwidth of a single-sub-band.
5. The waveform generator of claim 4, wherein the single sub-band
is a baseband sub-band.
6. The waveform generator of claim 4, wherein each digital mixed
signal includes each sub-band of the digital input signal within
the bandwidth of the single sub-band.
7. The waveform generator of claim 1, further comprising a
plurality of symmetric, digital filters that are structured to
symmetrically filter the plurality of digital, mixed signals before
the digital, mixed signals are converted to analog signals.
8. The waveform generator of claim 1, wherein the analog, harmonic
mixers have a first order harmonic that is different from the
effective sample rate of the digital to analog converters.
9. The waveform generator of claim 3, wherein the first order
harmonic of the digital, harmonic mixer is substantially similar to
the first order harmonic of the analog, harmonic mixer.
10. A method of generating a waveform, comprising: splitting a
digital input signal having an input signal frequency bandwidth
into a plurality of split signals, each of the split signals having
a split signal frequency bandwidth that is substantially similar to
the input signal frequency bandwidth; digitally mixing each of the
split signals with an associated digital harmonic signal at an
effective sample rate to generate a plurality of digital mixed
signals; converting the plurality of digital mixed signals to a
plurality of analog signals at an effective sample rate that is
different from a first order harmonic signal of at least one of the
associated digital, harmonic mixing; mixing each of the analog
signals with an associated analog harmonic signal to generate a
plurality of mixed, analog signals; and combining the plurality of
mixed, analog signals into an output signal having an output signal
bandwidth that is greater than a bandwidth of at least one of the
plurality of digital to analog converters.
11. The method of claim 9, wherein the first-order harmonic signal
is not an integer multiple or sub-multiple of an effective
conversion sample rate at which the plurality of digital, mixed
signals are converted to the plurality of analog signals.
12. The method of claim 9, wherein the first-order harmonic signal
is between an effective conversion sample rate at which the
plurality of digital, mixed signals are converted to the plurality
of analog signals and one half the effective conversion sample
rate.
13. The method of claim 9, wherein the plurality of digital, mixed
signals includes at least two sub-bands of the digital, input
signal within a bandwidth of a single sub-band.
14. The method of claim 12, wherein the single sub-band is a
baseband sub-band.
15. The method of claim 12, wherein each digital, mixed signal
includes each sub-band of the digital input signal within the
bandwidth of the single sub-band.
16. The method of claim 12, wherein the first order harmonic of the
digital, harmonic signal is substantially similar to the first
order harmonic of the analog, harmonic signal.
17. The method of claim 12, further comprising symmetrically
filtering the digital mixed signals before the digital mixed
signals are converted to analog signals.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 61/803,970, filed Mar. 21, 2013, which is
incorporated herein in its entirety.
FIELD OF THE INVENTION
[0002] This disclosure relates to waveform generators and methods
of generating waveforms. More specifically, this disclosure relates
to high speed arbitrary waveform or function generators using
harmonic mixing.
BACKGROUND
[0003] Usable bandwidths of waveform generators, such as Arbitrary
Waveform Generators (AWGs) or Arbitrary Function Generators (AFGs),
can be limited by a digital to analog converter (DAC) that is used
to generate the signal from a digital waveform sequence. The usable
bandwidth of a DAC is limited by the lesser of the analog bandwidth
or one half the maximum sample rate of the DAC. Conventional
techniques for generating higher bandwidth output signals with
existing DAC limitations can be complex and expensive systems.
[0004] For example, synchronous time interleaving can be used to
achieve an effective higher DAC sample rate. Multiple DACs generate
waveforms from a split input sequence that is offset in time within
a single DAC sample period. The analog signals are combined for a
sample rate that is effectively multiplied. However, in the
examples in which the analog bandwidth of the DACs becomes the
limiting factor, a high bandwidth active combiner, such as an
analog multiplexer or sample and hold multiplexer, is needed to
achieve the higher bandwidth.
[0005] Conventional multiplexed time interleaved systems cause the
multiplexer to be clocked at a sample rate similar to the DAC
channel bandwidth so that the DAC has sufficient time to transition
and settle during the multiplexer clock interval. The DACs are
synchronously clocked to the multiplexer, in these conventional
systems, so that each DAC sample is gated and then selected by the
multiplexer. Such a limitation of the DAC bandwidth limits the DAC
sample rate and, in turn, limits the multiplexer clock rate. As a
result, these conventional systems need many DAC channels to
achieve the desired performance.
[0006] As the number of DAC channels increases, the overall cost
and complexity of the system correspondingly increases. For
instance, each DAC requires a separate memory and digital input
path, as well as clocking and a method of synchronizing all DAC
channels, which requires a physically large and complex
multiplexing chip. The increased size and complexity of the
multiplexing chip also results in longer communication paths, and
therefore, an increase in parasitic capacitance, inductance,
electromagnetic noise, and design difficulties, among other
challenges.
[0007] In another technique, sub-bands of an input signal are
digitally downconverted to a frequency range that can be passed
through a lower sample rate DAC. The large input signal bandwidth
is split into multiple low bandwidth DAC channels. After being
converted to analog signals at the low bandwidth of the DACs, the
sub-bands are digitally upconverted to the respective original
frequency ranges and combined into a representation of the digital
input signal. However, when converting an arbitrary input signal
having a frequency content that is routed through a single DAC
channel, the recombined output contains inherent noise because it
has signal energy from only one DAC channel and a noise energy from
all DAC channels, which degrades the overall signal-to-noise (SNR)
ratio of the system.
[0008] Accordingly, the art would benefit from waveform generating
devices and methods having an improved SNR.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is a block diagram of an example waveform generator
that uses harmonic mixing, according to embodiments of the
invention.
[0010] FIG. 2 is a block diagram of another example waveform
generator that uses harmonic mixing, according to embodiments.
[0011] FIGS. 3A, 3B, 4A, 4B, 5A, 5B, and 6 are example spectral
components of various signals generated by the example waveform
generator shown in FIG. 1.
[0012] FIGS. 7A, 7B, 8, 9, and 10 are circuit diagrams of example
harmonic mixers of the disclosed waveform generators.
DETAILED DESCRIPTION
[0013] This disclosure describes embodiments of a DAC system for
waveform generators that increases the sample rate and usable
bandwidth of the analog output signal by using harmonic mixing.
[0014] FIG. 1 is a block diagram of an example waveform generator
100 that uses harmonic mixing and, various filters, some of which
may be optional in various examples. The waveform generator 100
includes a splitter 102 that is structured to receive a digital
input signal 104. The splitter 102 is structured to split the
digital input signal 104 into a plurality of split signals 106. The
digital input signal 104 can be any suitable waveform data
sequence.
[0015] Each of the split signals 106 has a split signal frequency
bandwidth that is substantially similar to the input signal
frequency bandwidth. The splitter 102 can be any variety of
circuitry that can split the digital input signal 104 into multiple
signals. For example, the split signals 106 can include any desired
digital input stream having a given sample rate and includes
recorded, stored, and/or generated data sequences.
[0016] The split signals 106 are input to digital, harmonic mixers
108 that are structured to digitally mix its associated split
signal 106 with an associated digital, harmonic signal to generate
a digital, mixed signal 110. Each of the digital, harmonic mixers
produces a digital, mixed signal. The digital harmonic signal can
include a local oscillator (LO) 112 that applies the harmonic
signals to the split signals, as shown in FIG. 1. The digital LO
can be a numerically-controlled oscillator, in some example
systems.
[0017] The digital, harmonic mixers 108 are any device that is
configured to mix a signal with multiple harmonics. Although
multiplication and/or mixing has been described in connection with
harmonic mixing, as will be described in greater detail below, any
device that has the effect of multiplying a signal with multiple
harmonics can be used as a harmonic mixer.
[0018] In some examples, the multiple harmonics can include a
zero-order harmonic, or a DC component. For example, the harmonic
signal can be a signal represented by equation (1):
harmonic signal=1+2*cos(2.pi.*F.sub.1*t) (1)
[0019] In equation (1), F.sub.1 represents the first-order harmonic
and t represents time. Thus, a signal having the form of equation
(1) has harmonics at DC and at frequency F.sub.1. An inverted phase
signal harmonic can be a signal represented by equation (2):
inverted harmonic signal=1-2*cos(2.pi.*F.sub.1*t) (2)
[0020] Similar to the harmonic signal represented by equation (1),
the inverted harmonic signal has harmonics at DC and frequency
F.sub.1. However, the first-order harmonic at frequency F.sub.1 is
out of phase by 180 degrees relative to the similar first-order
harmonic in the harmonic signal represented by equation (1).
[0021] Referring again to FIG. 1, the mixed, digital signals 110
are input to filters 114. The mixed, digital signals 110 can have a
sample rate that is greater than the maximum effective sample rate
of the DACs 122 and can include a frequency bandwidth that is
greater than one half the effective sample rate of the DACs 122.
The filter 114 can limit the bandwidth of the mixed, digital
signals to prevent aliasing signal distortion.
[0022] The filter can include a symmetric Low Pass Filter (LPF)
that generates a net filtering of the mixed signals that has a
frequency response that is substantially complementary to about one
half of a frequency of the first-order harmonic of the harmonic
signals. The frequency response at a given offset higher than
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. Further, the above example is described as an
ideal case. The implemented filtering can have a different response
to account for non-ideal components, calibration, and the like.
[0023] The symmetric filter is shown in the digital domain 116 of
the waveform generator shown in FIG. 1, but can, additionally or
alternatively, be included in the analog domain 118 in other
examples. The filtered, mixed digital signals 120 are input to
associated Digital to Analog Converters 122 (DACs). The sample rate
of the filtered, mixed digital signals 120 is downsampled to match
the sample rate of the DACs, which can be combined with the filters
114, in some examples. The downsampling can occur by decimating the
output sequence of the filtered, mixed digital signals 120, such as
by keeping a fewer number of samples of the output sequence.
[0024] Any of the above-described splitting, filtering, mixing,
and/or downsampling can be implemented by any suitable digital
circuitry including, but not limited to, a digital signal processor
(DSP), a microprocessor, a programmable logic device, general
purpose processor, or other processing system with appropriate
peripheral devices, as desired, including complete integration to
fully discrete components.
[0025] Each of the DACs 122 are structured to convert the filtered,
mixed, digital signals 120 into analog signals 124. The DACs 122
are any variety of circuitry that is configured to convert a
digital signal to an analog signal. Each DAC 122 can include an
amplifier, filter, attenuator, and other digital or analog
circuitry, as needed, to amplify, filter, attenuate or otherwise
process the signal before or after the digital signal is converted
to an analog signal.
[0026] The DACs 122 are configured to operate at an effective
sample rate. In the example waveform generator shown in FIG. 1,
DACs 122 are shown as a single DAC, but in other examples each DAC
may include multiple, interleaved DACs operating at a lower sample
rate to achieve a higher effective sample rate.
[0027] The effective sample rate of the DAC 122 (or the multiple,
interleaved DACs) is different from a first order harmonic signal
of at least one of the associated digital harmonic mixers 108. A
first-order harmonic of at least one of the digital, harmonic
signals is different from an effective sample rate of at least one
of the DACs 122. For example, the first-order harmonic F.sub.1 of
the harmonic signal could be 20 GHz and a sample rate of the DAC
122 could be 25 GS/s. Thus, the first-order harmonic F.sub.1 is
different from the effective sample rate of the DAC 122.
[0028] In some examples, the first-order harmonic of a digital,
harmonic signal need not be an integer multiple or sub-multiple of
the effective sample rate of the DACs 122. The first-order harmonic
of a harmonic signal that is associated with the digital, harmonic
mixers 108 is not an integer multiple or sub-multiple of the
effective sample rate of the DACs 122.
[0029] In some examples, the first-order harmonic of a harmonic
signal can be between the effective sample rate of the DAC 122 and
one half of the effective sample rate of the DAC 122. Such a
frequency of the first-order harmonic allows for higher frequency
components above and/or below the first-order harmonic to be
downconverted in frequency to be below one half of the sample rate
of the DAC 122. Thus, such frequency components can be effectively
converted to an analog signal 124 by DACs 122.
[0030] Each of the bands of the split input signal goes through all
paths. When more than one channel is combined for processing a
single input signal, each channel or path receives substantially
the entire bandwidth of the digital input signal. As the digital
input signal is transmitted through all of the DACs, the SNR is
improved.
[0031] The analog signals 124 are input to optional filters, such
as the reconstruction filters 126 shown in the example waveform
generator 100 of FIG. 1. The reconstruction filters 126 are
structured to filter the analog signals 124 from the DACs 122 and
substantially eliminate the DAC image frequency components in
signals 124. The reconstruction filters could be part of the DACs
and/or the mixers, in some alternative examples.
[0032] The filtered analog signals 128 are input to a number of
associated harmonic, analog mixers 130. There is one mixer 130 for
each of the split signal channels. The harmonic, analog mixers 130
are structured to mix an associated one of the filtered, analog
signals 128 with an analog, harmonic signal to generate a number of
mixed, analog signals 134. In some examples, the analog, harmonic
signals are substantially similar in frequency and phase to the
corresponding digital, harmonic signals. The harmonic, analog
mixers' harmonic signal can include a local oscillator (LO) 132
that applies the harmonic signals to the filtered analog signal
128. The LO 132 of the analog, harmonic signal can be synchronized
with the LO 112 of the digital harmonic signal, as described in
greater detail below.
[0033] The scaling factors for the digital, harmonic signals and
the analog, harmonic signals can be the same or similar to each
other even though they are respectively digital and analog signals.
The output signals from the analog, harmonic mixers are referred to
as remixed signals 134.
[0034] The remixed signals 134 are input to a single combiner 136
that is structured to combine the number of remixed (or mixed),
analog signals 134 into an output signal 138 having an output
signal bandwidth that is greater than a bandwidth of at least one
of the number of digital to analog converters. The analog, output
signal 138 from the combiner 136 is a reconstruction of the digital
input signal 104 that is applied to the splitter 102.
[0035] Some form of synchronization of the harmonic signals 112,
132 is used. For example, the harmonics of the analog harmonic
signals can be locked to a clock related to the DAC. A frequency of
the digital and analog mixers can be a harmonic of a lower-speed
clock that is present in the DAC channels in the analog form, but
is also correlated to the digital data stream. In other examples,
the digital harmonic signal or related signal is also converted by
a DAC and is available in the analog domain to synchronize with the
analog, LO signal. In still another example, out-of-band tones can
be added to one or more of the mixed, digital signals. Using a
first-order harmonic of 20 GHz, 11.25 GHz, or 9/16 of 20 GHz, can
be added to the mixed, digital signal. Since the added tones can be
set to be outside of the bandwidth that is established by the
optional digital filter(s), approximately 9 GHz depending on the
transition band, the tones can have a substantially negligible
effect on the reconstructed signal that is output from the
combiner. The tones, however, can be less than a Nyquist frequency,
i.e., less than 12.5 GHz for a 25 GS/s sample rate, which means
that the tones can be acquired by using the analog, mixed signal
before it is filtered. Regardless of the synchronization technique
used, a phase and frequency relationship between the digital,
harmonic signals and the analog, harmonic signals is
maintained.
[0036] FIG. 2 is an example of a waveform generator 200 having an
input signal 202 that is split by a splitter 204 into two DAC
channels 206, 208. The example shown in FIG. 2 includes specific,
example values for various components and for the signal frequency,
sample rates, etc. The digital input signal 202 is an arbitrary
waveform sequence having a sample rate of 50 GS/s. The digital
input signal 202 is band-limited to 18 GHz to prevent mixing
components from the various harmonic signals from extending past
adjacent harmonic frequencies. The sequence is replicated and each
path is interpolated to 2.times. the sample rate of the digital
input signal or 100 GS/s by the splitter 204.
[0037] The replicated signal is then digitally mixed by digital
mixers 210, 211 with the zero'th and first harmonics of a 20.3125
GHz clock 212, 213, using an inverted (180 degree phase-shifted)
clock between the two paths 206, 208. The mixed, digital signals
214 are then symmetrically low pass filtered 216 and decimated to a
sample rate of 25 GS/s, which is the sample rate at the input of
each associated DAC 218. The digital harmonic mixing and the
filtering step can be combined with a decimating filter, if
desired. The DAC outputs are again filtered with a reconstruction
filter 220 to remove the image signal produced by the DAC itself
and to have a net response from the analog mixer output that is
symmetric in amplitude around a frequency of 10.15625 GHz (i.e.,
half the harmonic signal bandwidth).
[0038] The filtered, analog signals 222 are then mixed by an analog
mixer 224 in the analog domain with the same zero'th and first
harmonics of the 20.3125 GHz digital clock 212, again using an
inverted (180 degree phase-shifted) clock between the two paths.
The two paths are summed at the combiner and filtered to remove
content above 20.3125 GHz. In the example arbitrary waveform
generator 200 shown in FIG. 2, the LOs 212, 213 of the digital,
harmonic mixers 210, 211 and the LO 226 of the analog, harmonic
mixers 224 can use the 13.sup.th harmonic of a divided sample
clock. (25 GHz/16=1.5625 GHz, 13*1.5625=20.3125 GHz).
[0039] FIGS. 3A-6 are examples of spectral components of various
signals in the waveform generator system shown in FIG. 2. FIG. 3A
shows spectrum 300 as a spectrum of the digital input signal and
hence, the split signal of FIG. 2. Using the above example of the
harmonic signal defined in equation (1), a DC component of the
harmonic mixer passes the split signal, as represented by spectrum
300. However, the spectrum 300 in the input signal is also mixed
with the first-order harmonic at frequency F.sub.1. The resulting
spectrum 302 is the product of such mixing. Thus, the digital mixed
signal includes components of spectrum 300 and spectrum 302. Here,
and in other figures, the spectral components are illustrated as
separate and overlapping, however, the actual spectrum would be the
combination of the spectra 300 and 302.
[0040] Referring to FIG. 3B, spectrum 310 similarly represents
components of the inverted digital mixed signal due to the mixing
of the digital input signal with the DC harmonic of the inverted LO
signal of the digital harmonic mixer. The spectrum 312 similarly
represents the mixed product of the inverted LO and the spectrum
310. As described above, the first-order harmonic of the inverted
LO signal of the digital harmonic mixer is phase shifted by 180
degrees from the first-order harmonic of LO signal 212. The 180
degree phase shift in the inverted digital harmonic signal induces
a 180 degree phase shift in the spectrum 312. The 180 degree phase
difference is illustrated as a dashed line in FIG. 3B.
[0041] FIGS. 4A and 4B represent the spectrums of the filtered
digital mixed signals. Filtering can occur, in this example, in the
digital and/or analog domain of the disclosed waveform generator
systems and methods. For example, the digital mixed signals could
be filtered with a digital symmetric LPF having a cutoff frequency
near one half of the effective sample rate of the DACs. In some
examples, the filtering can be a function of inherent filtering of
the corresponding DACs, the digital filters, or the like.
[0042] In some examples, the net filtering of the digital mixed
signals can result in a frequency response that is substantially
complementary to about one half of a frequency of the first-order
harmonic of the LO signals of the digital mixers. The frequency
response at a given offset that is 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 is used in this example,
other values can be used, as desired, such as for scaling of
signals. Further, the above example is described as an ideal case
and additional filtering can be used to account for non-ideal
components, calibration, etc. In an example system, a decimation
filter, symmetric filter, and calibration filter are also used to
compensate for non-ideal responses in the analog domain.
[0043] In a particular example of the frequency response, using the
20.3125 GHz F.sub.1 described above, frequency F.sub.1/2 is
10.15625 GHz. From DC to 9.12625 GHz, the frequency response is
one. From 9.15265-11.15625 GHz, the frequency response linearly
changes from one to zero, passing through 1/2 at 10.15625 GHz. The
resulting spectral components are shown in FIGS. 4A and 4B. FIG. 4A
shows the filtered, mixed analog signal that includes a lower
frequency portion of the spectrum 200, illustrated by 400, and a
lower frequency portion of spectrum 302, illustrated by spectrum
402. Due to the digital mixing, spectrum 402 includes frequency
components of a higher sub-band of spectrum 300, albeit reversed in
frequency. Similarly, the spectral components 410 and 412 of FIG.
4B correspond to the lower frequency components of spectra 310 and
312 of FIG. 3A. The 180 degree phase relationship of spectrum 312
is preserved in spectrum 412.
[0044] Accordingly, through the harmonic mixing, two sub-bands of
the digital input signal are converted to analog signals even
though the span of the sub-bands would have exceeded a Nyquist
bandwidth associated with the DACs. Each mixed signal, whether
analog, digital, filtered, or the like, includes components of each
sub-band of the digital input signal, such as a low frequency
sub-band and a high frequency sub-band of the spectrum 300 shown in
FIGS. 4A and 4B.
[0045] For example, the sub-bands of the digital input signal are
frequency shifted to be within a bandwidth of a baseband sub-band.
In some examples, each sub-band of the digital input signal is
frequency shifted to be within the bandwidth of the single
sub-band. However, depending on the number of sub-bands, and the
harmonic signals, each sub-band may not be present in each mixed
signal.
[0046] FIGS. 5A and 5B represent the spectra of the remixed signals
that are input to the combiner. As described above, the analog,
harmonic signal and the digital, harmonic signal can have
substantially similar frequency and phase. Accordingly, the spectra
of FIG. 4A are mixed with a DC component and a first-order analog
harmonic signal. Spectra 500 and 502 represent the spectra from
mixing the spectra 400 and 402 of FIG. 4A with the DC component.
Spectrum 504 represents the result of mixing the spectrum 400 with
the first-order harmonic. Spectra 506 and 508 represent the mixing
of spectrum 402 of FIG. 4A with the first-order harmonic.
[0047] Similarly, FIG. 5B represents the spectra of the remixed
signal for the inverted harmonic signal. Spectra 510 and 512
represent the mixing of the DC component with the spectra of FIG.
4B. Spectrum 514 represents the mixing of the first-order harmonic
of the inverted analog, harmonic signal with the spectrum 410 of
FIG. 4B. In particular, as the first-order harmonic of the
inverted, analog harmonic signal has a relative 180 degree phase
shift, the resulting spectrum 514 also has a 180 degree phase
shift, represented by the dashed line.
[0048] Spectrum 412 of FIG. 4B is also mixed with the first-order
harmonic of the inverted, analog harmonic signal; however, the
spectrum 412 already had a 180 degree induced phase shift. Thus,
the additional 180 degree phase shift results in an effective 0
degree phase shift, represented by the solid line of spectra 516
and 518.
[0049] FIG. 6 shows a spectrum 600 of the reconstructed digital
input signal that is output from the combiner shown in FIG. 1.
Spectra 604 and 606 represent the component sub-bands forming the
spectrum 600. Spectrum 602 represents an additional sideband from
the mixing described with respect to FIGS. 5A and 5B. In this
example, spectrum 602 is filtered out; however, in other examples
sub-bands can extend beyond the first-order harmonic frequency
F.sub.1. In this case, because spectrum 602 is generated from a
lower frequency sub-band it can be eliminated through destructive
combination.
[0050] Due to the relative phasing of the components of the remixed
signals, sub-bands in their original frequency range combine
constructively, while sub-bands outside of their original frequency
range are phased to combine destructively. Referring to FIGS. 5A,
5B, and 6, when combined, spectra 500 and 510 combine
constructively, which results in spectrum 604. Spectra 502 and 512
combine destructively as the spectra are out of phase by 180
degrees. Thus, the spectrum that remains within the baseband
sub-band is the original sub-band.
[0051] Similarly, for the sub-band from approximately F.sub.1/2 to
F.sub.1, spectra 506 and 516 combine constructively into spectrum
606, while spectra 504 and 514 combine destructively. Spectra 508
and 518 combine constructively into spectrum 602; however, spectrum
602 can be filtered out as it is beyond the expected input
frequency range, which in this example is about less than frequency
F.sub.1.
[0052] As illustrated by spectra 604 and 606, a transition occurs
around frequency F.sub.1/2 that is the result of the filtering
described above in reference to FIGS. 4A and 4B. The slopes of
spectrum 604 and spectrum 606 are complementary. Thus, when the
frequency components of the spectrums 604 and 606 are combined, the
resulting portion of the spectrum 600 substantially matches the
original frequency spectrum.
[0053] Accordingly, by mixing the digital input signal with various
harmonic signals, sub-bands of the digital input signal are passed
through the lower bandwidth of the DACs.
[0054] Although the mixed signals include overlapping sub-bands,
because of the phasing of the harmonic signals, the sub-bands
combine constructively and destructively when combined as described
above to create a substantially accurate analog reconstruction of
the digital input signal.
[0055] In some examples, the analog and digital harmonic signals
are frequency and phase aligned with each other. One way to align
the frequency and phase of the analog and harmonic signals is to
choose a mixing frequency that is a harmonic of a lower-speed clock
that is present in the DAC channels in the analog domain, but is
also correlated to the digital harmonic signals. In other examples,
a separate DAC channel serves as a reference frequency that is
multiplied with the mixing frequency of the analog harmonic mixers.
In some of the examples described above, the analog harmonic mixers
pass DC harmonic signals on all channels. Alternatively, the
digital input signal can be split into bands, and each band is
multiplied with the appropriate mixing harmonic signal. The digital
bands are then recombined before being converted to analog signals.
For each band, only one clock harmonic generates a mixing product
within the low-pass filter bandwidth of the DAC channel. The only
digital harmonic mixer that is required to handle a DC input is for
the low input band, which is mixed with the zero-th clock harmonic
(i.e., multiplied by 1 or passed straight through without actually
requiring a mixer).
[0056] In another alternative, the analog mixers can pass DC
harmonic signals on all channels by adapting a standard mixer
topology to perform harmonic mixing that includes the DC
components.
[0057] FIGS. 7A and 7B illustrate examples of a harmonic mixer,
which can represent any one or more of the harmonic mixers
discussed above. FIG. 7A illustrates a 2-way time-interleaving
switch. FIG. 7B illustrates an N-way time-interleaving switch.
[0058] In these embodiments, switches 780 and/or 781 are configured
to output a signal 782. When using the 2-way switch 780, an input
signal 784 or 786 is to output 782 in response to a control signal
788. When using the N-way switch 781, an input signal 784, 786, on
through to the Nth input 787, is switched to output 782, in
response to the control signal 788. For example, the switch 781 can
be a three-throw switch, a four-throw switch, etc., up to an
N-throw switch, which causes an input signal 784, 786, on through
to the Nth input 787 to spend 1/Nth of its time at the output 782.
As further paths and sub-bands are added, the harmonics of the
harmonic signals can be appropriately phased. In some embodiments,
the relative phase shifts of the harmonic signals can be spaced in
phase by time shifts of one period divided by the number of
sub-bands.
[0059] As the pulses get shorter compared to the overall clock
cycle, the harmonic content gets richer. For instance, for a
two-way or a three-way switch, the zero-order harmonic (DC) and the
first-order harmonic are used. For a four-way or five-way switch,
the zero-order harmonic, the first-order harmonic, and a
second-order harmonic can be used. For a six-way or seven-way
switch, the zero-order harmonic, the first-order harmonic, a
second-order harmonic, and a third-order harmonic can be used. As N
increases, the pulses get narrower, thereby generating the richer
harmonic content. The control signal 788 can be a signal having a
fundamental frequency of the first-order harmonic, or other
suitable harmonic frequency, described above.
[0060] All bands of the input signals 784, 786, on through to the
Nth input 787 go through the output path 782.
[0061] For example, referring to switch 780, the control signal 788
can be a square wave with a fundamental frequency of 20.3125 GHz.
As a result of the switching, output 782 receives the input signal
784 or 786 during one half-cycle of the control signal and receives
the other input signal during the opposite half-cycle. In effect,
the output 782 is the input signal 784 or 786 multiplied by a
square wave oscillating between zero and one at 20.1325 GHz, for
example. Such a square wave can be represented by equation (4).
0.5 + 2 .pi. sin ( 2 .pi. F 1 t ) + 2 3 .pi. sin ( 6 .pi. F 1 t ) +
( 4 ) ##EQU00001##
[0062] Equation (4) is the Taylor series expansion of such a square
wave. The DC and first two harmonics are listed. Here, F.sub.1 is
20.1325 GHz. Although the magnitudes of the components are
different, equations (1) and (4) include similar harmonics.
[0063] Input 786 is similar to input 784; however, the time period
over which the input signal 784 or 786 is routed to the output 782
is inverted relative to input 784. The effect is again similar to
multiplying the input signal 784 or 786 with a square wave defined
by equation (5).
0.5 - 2 .pi. sin ( 2 .pi. F 1 t ) - 2 3 .pi. sin ( 6 .pi. F 1 t ) +
( 5 ) ##EQU00002##
[0064] Similar to equation (4), equation (5) is similar to the
harmonic signal described in equation (2) above. Thus, the
multiplication effect of the switching of the switch 780 is
substantially similar to the mixing of a split signal with the
harmonic signal described above. In addition, in this example, the
switch acts as both the combiner and harmonic mixers. However, in
other embodiments, the switch 780 could be a single pole single
throw switch and act as a single harmonic mixer.
[0065] Although the relative magnitudes of the DC component and the
first-order harmonic are different, such imbalance can be corrected
through a compensation filter in the appropriate path. For example,
the sub-band described above between frequency F.sub.1/2 and
frequency F.sub.1 can have a different gain applied during
recombination in the combiner than a baseband sub-band.
[0066] In addition, equations (4) and (5) above also list
third-order harmonics. In some embodiments, the third-order
harmonics may be desired. However, if not, the effect of such
harmonics can be compensated with appropriate filtering. For
example, the input signals can be filtered to remove frequency
components above frequency F.sub.1. Thus, such frequency components
would not be present to mix with a frequency at 3*F.sub.1.
Moreover, filtering before a DAC can remove any higher order
frequency components that may otherwise affect the analog signal
due to aliasing.
[0067] In the event of interleaving errors due to 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, time-varying correction filter can be used to cancel the
interleave spurs.
[0068] Further, in some cases, the switches might not always
operate perfectly. For example, an errant switch might spend more
time in one direction than the other, thereby causing a skewed duty
cycle. The digital harmonic mixers can be configured to compensate
for phase or amplitude errors that may be present in the analog
harmonic signals by making subtle adjustments to the amplitude or
phase of the analog harmonic signals.
[0069] FIG. 8 is an example of another harmonic mixer. A switching
circuit 800 is configured to switch two input signals 808 and 810
alternatively to outputs 802 and 804 in response to the control
signal 806. The control signal 806 can again be a square wave or
other similar signal to enable the switches of the switching
circuit 800 to switch. During one half-cycle of the control signal
806, input signal 808 is switched to output 802 while input signal
810 is switched to output 804. During the other half-cycle, the
input signal 808 is switched to output 804 while input signal 810
is switched to output 802.
[0070] In some embodiments, the input signal 810 can be an inverted
and scaled version of the input signal 808. The result of such
inputs and the switching described above is a rebalancing of the DC
and other harmonics from the levels described above with respect to
the switch 780 of FIG. 7A. For example, input signal 810 can be a
fractional inverted version of the inputs signal 808. Instead of
switching between 1 and 0 with the switch 880 of FIG. 7A, the
effective output of outputs 802 and 804 can be switching between 1
and (2-.pi./(2+.pi.), for example. Thus, the amplitude and DC level
can be adjusted as desired to create the desired balance between
the harmonics.
[0071] FIG. 9 illustrates an alternative example of a harmonic
mixer. The harmonic mixer 970 includes a splitter 972, a mixer 975,
and a combiner 977. The splitter 972 is configured to split an
input signal 971 into signals 973 and 974. Signal 974 is input to
the combiner 977. As signal 974 is not mixed with another signal,
signal 974 acts as the DC component of a harmonic mixer described
above.
[0072] Signal 973 is input to the mixer 975. A signal 976 is mixed
with the signal 973. In some embodiments, signal 976 can be a
single harmonic, such as the frequency F.sub.1 described above. If
additional harmonics are desired, additional mixers can be provided
and the respective outputs combined in combiner 977.
[0073] In another embodiment, the signal 976 can include multiple
harmonics. As long as the bandwidth of the ports of the mixer 975
accommodate the desired frequency ranges, a single mixer 975 can be
used. However, since the DC component of the harmonic signals
described above is passed to the combiner 977 by a different path,
the ports of the mixer receiving signals 973 and 976 need not
operate to DC. Accordingly, a wider variety of mixers may be used.
Once the signals 979 and 974 are combined in the combiner 977, the
output signal 978 can be substantially similar to a mixed signal
described above.
[0074] In some embodiments, the splitter 972 can, but need not,
split the input signal 971 symmetrically. For example, a side of
the splitter that outputs signal 974 has a bandwidth that is at or
above the filtering cutoff frequency described above. A side of the
splitter 972 that outputs signal 973 has a frequency range centered
on a harmonic of the signal 976 and a bandwidth of twice or greater
of the filtering cutoff frequency described above. In other words,
the frequency response of the splitter 972 need not be equal for
each path and can be tailored as desired.
[0075] For example, FIG. 10 is a circuit diagram of an example
mixer topology 1000 that performs harmonic mixing with DC
components by adapting a diode-ring mixer to implement the analog
harmonic mixers for a two-way interleaved system. In this example,
a harmonic signal 1002, such as a mixer clock, can be input to a
diode ring 1004 through transformer 1006. The input signals 1008,
1010 can be applied to inputs 1012 and 1014. Accordingly, depending
on the harmonic signal, the input signals can be alternately
switched to the output 1016, the center tap of the transformer
1006. For example, the harmonic signal causes the right diodes to
turn on when the bottom of the transformer is positive and the top
is negative, or the left diodes to turn on when the polarity of the
transformer is reversed. In this manner, the two input signals
1008, 1010 are alternately routed to the output on opposite halves
of the harmonic cycle. Note that in this example, the diode-ring
mixer provides the combined function of two mixers and the
combiner.
[0076] In some embodiments, two paths and two overlapping sub-bands
are implemented. However, as mentioned above, any number of paths
and sub-bands can be used. In such embodiments, the number of
harmonics used can be equal to one plus one half of a number of
sub-bands, rounded down, where DC is included as a zero-order
harmonic. For example, for three sub-bands, only two harmonics can
be used. Using the above frequency ranges as an example, the
first-order harmonic can frequency shift frequencies higher than
frequency F.sub.1 to the baseband sub-band. The first-order
harmonics of the harmonic signals can be phased with 120 degree
relative phase shifts.
[0077] Accordingly, when a sub-band is in the proper frequency
range during combination in the combiner 58, the sub-band spectra
will have the same phase shift, such as a 0 degree relative phase
shift. In contrast, the three components of a sub-band in the
incorrect frequency range would offset in phase from one another by
120 degrees. The resulting spectra would destructively combine to
eliminate the incorrect sub-band. As further paths and sub-bands
are added, the harmonics of the harmonic signals can be
appropriately phased. In some embodiments, the relative phase
shifts of the harmonic signals can be spaced in phase by time
shifts of one period divided by the number of sub-bands.
[0078] 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 non-ideal components.
[0079] Another embodiment includes computer readable code embodied
on a computer readable medium that when executed, causes the
computer to perform any of the above-described operations. As used
here, a computer is any device that can execute code.
[0080] 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
non-transitory manner.
[0081] It will be appreciated that variations of the
above-disclosed systems and methods for generating waveforms and
other features and functions, or alternatives thereof, may be
desirably combined into many other different systems, methods, or
applications. Also various presently unforeseen or unanticipated
alternatives, modifications, variations, or improvements therein
may be subsequently made by those skilled in the art.
* * * * *