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Time interleaving is a technique that uses multiple identical ADCs (although only ADCs are discussed in this article, all the principles also apply to the time interleaving feature of DACs) to process a sequence of regularly sampled data at a higher rate than the operating sampling rate of each individual data converter. In simple terms, time interleaving (IL) consists of time multiplexing an array of M identical ADCs in parallel.
This is shown in Figure 1. This results in a higher net sampling rate fs (sampling period Ts = 1/fs), even though each ADC in the array is actually sampling (and converting) at a lower rate, fs/M. So, for example, by interleaving four 10-bit/100 MSPS ADCs, a 10-bit/400 MSPS ADC can theoretically be achieved.
Figure 1. An array of n-bit ADCs interleaved M times. Each ADC samples at fs/M, resulting in a time-interleaved ADC sampling rate of fs. An example clocking scheme with M = 4 is shown in the lower half of the figure.
To better understand the IL principle, in Figure 1, an analog input V IN (t) is sampled by M ADCs, resulting in a combined digital output data sequence D OUT . ADC 1 first samples V IN (t 0 ) and begins converting it to an n-bit digital signal. T s seconds later, ADC 2 will sample V IN (t 0 +T s ) and begin converting it to an n-bit digital signal. Next, T s seconds later, ADC 3 will sample V IN (t 0 +2T s ), and so on. After the ADCM completes sampling V IN (t 0 +(M-1)×T s ), it begins the next sampling cycle, starting with ADC 1 sampling V IN (t 0 +M×T s ), and so on.
Since the ADCs output n-bits sequentially and the output order is consistent with the sampling operation just described, these digital n-bit words are sampled by the demultiplexer on the right side of the same figure. What is obtained here is the reassembled data output sequence D OUT (t 0 + L), D OUT (t 0 +L + T s ), D OUT (t 0 +L + 2T s ), ... . L represents the fixed conversion time of each individual ADC, and the reassembled data sequence is an n-bit data sequence with a sampling rate of fs. Therefore, although the individual ADCs (usually called "channels") are n-bit ADCs with a sampling rate of fs/M, the whole is equivalent to a single n-bit ADC with a sampling rate of fs, and we call it a time-interleaved ADC (to distinguish it from the channels). The input is essentially separated and processed individually by the ADCs in the array, and then successively reassembled at the output to form a high data rate representation D OUT of the input V IN .
This powerful technique has some practical challenges. One important issue is the digital assembly of the M data streams from the channels to reconstruct the original input signal V IN . If we look at the spectrum D OUT ; in addition to seeing the digital signal of V IN and the distortion introduced by the analog-to-digital conversion, we will also see additional and large spurious components called "interleaving spurs" (or IL spurs for short); IL spurs have neither the signature of polynomial type distortion - such as higher order signal harmonics (2nd, 3rd, etc.) - nor the signature of quantization or DNL errors. IL artifacts can be seen as a form of fixed-code noise in the time domain, caused by analog impairments in the channels, as they are modulated with the separated converted signals during the interleaving process and appear in the final digitized output D OUT .
Let's analyze a simple example to understand what might happen. Consider the case of a dual interleaved ADC with a sinusoidal input V IN at frequency f IN . Assume that ADC 1 has a gain of G 1 and ADC 2 has a differential gain of G 2 . In this dual IL ADC, ADC 1 and ADC 2 will alternately sample V IN . Therefore, if ADC 1 converts even samples and ADC 2 converts odd samples, the amplitude of all D OUT even data will be set by G 1 , and the amplitude of all D OUT odd data will be set by G 2 . Then, D OUT contains not only V IN , but also some polynomial distortion, but it is amplified alternately by G 1 and G 2 , just as if we amplitude modulated V IN with a square wave of frequency fs/2 . Doing so will introduce more spurious components. In particular, D OUT will contain a “gain spur” at a frequency of fs/2 – f IN , and unfortunately, the frequency of this spur tracks the input f IN and is within the first Nyquist band of the interleaved ADC (i.e., within fs/2), while it will also be aliased in all other Nyquist bands. The power/amplitude of this interleaving spur depends on the net difference between the two gains, G 1 and G 2. In other words, it depends on the gain error mismatch. And ultimately, it depends on the amplitude of the input V IN itself.
If the input is not a simple sine wave, but a fully band-limited signal as in a real application, then the "gain spurs" are not just interfering tones, but are fully scaled images of the band-limited input signal itself, appearing within the Nyquist band. This somewhat negates the advantage of increased bandwidth provided by interleaving.
Although we have only considered gain error mismatches between channels in the above example, other impairments can also cause interleaving spurs. Offset mismatches (differences between channel offsets) cause fixed frequency tones (“offset spurs”) with power proportional to the offset mismatch. Sample time skew occurs when some channels sample a bit earlier or later than the intended sequence . It introduces “time spurs” that are exactly the same frequency as the gain spurs (and superimposed with the same amplitude), but that increase in power as f IN increases and the input amplitude increases . Bandwidth mismatches between channels introduce additional spurious components with frequencies that depend on f IN , and just like time spurs, the spur power increases not only with input amplitude, but also with f IN itself. Again, in either case, the degree to which the output spectrum is degraded does not depend on the absolute value of the channel impairments (offset, gain, timing, frequency band), but on the relative mismatch or difference between the channels.
While the basic technique of time interleaving has been around for decades, the extent to which IL could be minimized limited its applicability in the past to low-resolution converters. However, recent advances in channel mismatch calibration and suppression of residual IL spurious components have made fully integrated, very high-speed, 12/14/16-bit IL ADCs possible.
This is when we need to categorize interleaving. We generally refer to two interleaved channels as working in a "ping-pong" fashion. Then we also distinguish between "light interleaving" and "heavy interleaving" when we describe the case of a small number of channels (such as 3 to 4 channels) and a large number of channels (such as more than 4 channels, often up to 8 or more).
When we simply interleave two channels to double the sample rate, we call it “ping-pong,” as shown in the block diagram in Figure 2 (a). This is the simplest case, and it has some interesting and useful properties. In this case, the interleaving spurs are located at dc, fs/2, and fs/2 – f IN within the first Nyquist band of the interleaved ADC . Therefore, if the input signal, V IN, is a narrowband signal centered at f IN —as shown in the first Nyquist output spectrum in Figure 2 (b)—the interleaving spurs consist of an offset spur at dc, another offset mismatch spur at fs/2, and a gain and timing spurious image centered at fs/2 – f IN , looking like an amplified copy of the input itself.
figure 2.
(a) Ping-Pong Solution
(b) Output spectrum when the narrowband input signal is below fs/4
(c) At this time, the input signal is between fs/4 and the Nyquist frequency fs/2
If the input signal V IN (f) lies completely between 0 and fs/4—as shown in Figure 2 (b)—then the interleaving spurs do not overlap the digitized input frequency. The bad news is that we can only digitize half of the Nyquist band, just like a single channel clocked at fs/2, although we still consume at least twice the power of that single channel. The interleaving spurious images at the upper end of the Nyquist band can be suppressed by digital filtering after digitization, eliminating the need for analog impairment correction.
But the good news is that because the ping-pong ADC is clocked at fs, the digitized output benefits from 3 dB of processing gain in dynamic range. In addition, the ping-pong ADC relaxes the anti-aliasing filter design requirements compared to using a single ADC clocked at fs/2.
If the narrowband signal is located in the upper half of the first Nyquist band, all considerations apply, as shown in Figure 2 (c), because the interleaving image spurs are moved to the lower half of the Nyquist band. Again, gain and timing spurs can be suppressed digitally after filtering and digitization.
Eventually, the input signal and interleaving spurious frequencies will overlap, and once the input signal frequency position crosses the fs/4 line, the interleaving images will corrupt the input spectrum. In this case, recovery of the desired input signal will be impossible, and the ping-pong scheme is unusable. Unless, of course, the channel-to-channel matching is tight enough to make the interleaving spurious content acceptably low for the application, or calibration is introduced to reduce the cause of the IL images.
In summary, frequency planning and some digital filtering can recover the narrowband digitized input in a ping-pong scheme, even in the presence of channel mismatch . Although the converter power consumption is roughly doubled compared to using a single ADC clocked at fs/2, the ping-pong scheme provides a 3 dB processing gain while relaxing the anti-aliasing requirements.
An example of a ping-pong scheme without any channel mismatch correction and the interleaving spurs it produces is shown in Figure 3. In this example, two dual-channel 14-bit/1 GSPS AD9680 ADCs are sampled at a rate that is alternately multiplied by a sine wave, returning a single combined output data stream at 2 GSPS. When we look at the first Nyquist band of the output spectrum of this ping-pong scheme (between dc and 1 GHz), we can see the input tone, which is a strong tone on the left at f IN = 400 MHz; we can also see a strong gain/timing mismatch spur at fs/2 – f IN = 2G/2 – 400 M = 600 MHz. We can also see a series of other tones due to distortion in the channel itself and other impairments, but all are below the –90 dB line.
Figure 3. The combined spectrum of the 2 GSPS output data from the ping-pong scheme, acquired using two AD9680s clocked at 1 GSPS with a sampling phase shift of 180°.
When there are more than two channels, the frequency planning described above is not as practical. We cannot restrict the location of the interleaving spurs to a small portion of the Nyquist band. For example, consider the case of a four-way interleaved ADC, as shown in Figure 4(a). In this case, the offset mismatch will increase the signal tone at DC, fs/4, and fs/2, while the gain and timing interleaving images are located at fs/4 – f IN , fs/4 + f IN , and fs/2 – f IN . An example of the interleaved ADC output spectrum is shown in Figure 4(b). Obviously, unless the input is within the bandwidth within fs/8, regardless of the location of f IN , the input will overlap with some of the interleaving spurs, and if the input is an extremely narrowband signal, we should not try to digitize it using a wideband interleaved ADC.
In this case, we need to minimize the IL spurious power in order to obtain a full Nyquist spectrum and a cleaner spectrum. To achieve this, we use calibration techniques to compensate for the mismatch between channels. After correcting the effects of the mismatch, the final IL spurious power will be reduced. Both SFDR and SNR will benefit from this reduction in spurious power.
Compensation methods are limited by the accuracy with which the mismatch can be measured and ultimately corrected. To further suppress residual spurs beyond what can be achieved with calibration, the order in which the channel input samples are sampled can be intermittently and randomly. By doing so, the modulation effects of the converted input signal due to uncalibrated mismatch discussed earlier are converted from fixed code noise to pseudo-random noise. As a result, the IL tones and interfering periodic codes are converted to pseudo-random noise-like components and add to the converter quantization noise floor and disappear, or at least the interfering spurious images and tones are diffused. At this point, the power associated with the IL spurious components is added to the noise floor power. Therefore, while distortion is improved, the SNR may be reduced by the amount of the IL spurious power plus the noise. The SNDR (SINAD) is essentially unchanged because it is composed of distortion, noise, and randomization; it simply shifts the IL contribution from one component (distortion) to another (noise).
Figure 4. (a) Four-way interleaved ADC (b) corresponding first Nyquist output spectrum showing interleaving spurs
The AD9625 is a 12-bit/2.5GSPS three-way interleaved ADC. The mismatch between the three channels is calibrated to minimize interleaving spurs. Figure 5(a) shows an example of the output spectrum with an input close to 1 GHz. In this spectrum, in addition to the input tone at approximately 1 GHz, the channels can be seen to have 2nd and 3rd harmonic distortion around 500 MHz and 4th harmonic distortion at the fundamental frequency. Interleaving mismatch calibration significantly reduces the power consumption of the interleaving spurs, and a large number of additional residual smaller spurious tones can be seen throughout the spectrum.
To further reduce these residual spurious components, channel randomization was introduced. A fourth calibration channel was added, and then the four channels were three-way interleaved, and the order was randomly changed by intermittently swapping the interleaved channels with the fourth. This is like one could throw three poles into the air like an acrobat, and then swap the fourth each time. By doing this, the residual interleaving spurious power is randomized and spread out to the noise floor. As shown in Figure 5(b), after channel randomization, the interleaving spurs are almost gone, while the noise power is only slightly increased, resulting in a 2dB reduction in SNR. Of course, it should be noted that although the second spectrum in Figure 5(b) is much cleaner than the distorted tone, the randomization cannot affect the 2nd, 3rd, and 4th harmonics because these harmonics are not interleaving spurs.
Figure 5. Output spectrum of the AD9625 clocked at 2.5 GSPS and with an input tone approaching 1 GHz.
(a) Sequential three-way interleaving; SNR = 60 dBFS, SFDR = 72 dBc, limited by the 3rd harmonic, near 500 MHz; however, significant interleaving spurs are visible throughout the spectrum.
(b) Three-way interleaving with random channel shuffling; SNR = 58 dBFS and SFDR = 72 dBc. Still dominated by the 3rd harmonic, all interleaving spurs are eliminated by spreading the power to the noise floor.
Another example of an interleaved ADC using channel randomization is shown in the spectrum in Figure 6. This time a quad interleaved 16-bit/310 MSPS AD9652 ADC is used. In the example of Figure 6, the four channels are interleaved in a fixed order and no calibration is performed to reduce channel mismatch. The spectrum clearly shows that the interleaving spurs are at the expected frequency locations and their high power is much higher than the 2nd and 3rd harmonics and limits the spurious free dynamic range to only 57 dBc.
Figure 6. Output spectrum of the AD9652, clocked at fs = 310 MHz, with a sinusoidal input of fIN ~70 MHz. In this case, no channel calibration and randomization is applied. The 2nd (HD2) and aliased 3rd (HD3) harmonics are visible at approximately 140 MHz and 100 MHz, respectively. Interleaving (IL) spurs are also visible. These are offset tones at dc, fs/2 (OS2 in the figure), and fs/4 (OS4 in the figure). Additionally, gain (timing) spurs are visible at fs/2-f IN (GS2 in the figure), fs /4+f IN (GS4+ in the picture) and fs /4- f IN (GS4- in the figure). The SNR lookup in this figure is artificially worse because some of the spurious content is mixed in with the noise power.
However, if the same ADC is foreground calibrated to reduce channel mismatch, the interleaving spurious power is significantly reduced, as shown in Figure 7. Similar to the previous example, the channel harmonic distortion is not affected, but the interleaving spurious power is significantly reduced by the channel mismatch calibration.
Figure 7. Output spectrum of the same AD9652 with the same input, but after calibration to reduce mismatch across the four channels. Compared to Figure 6, while the 2nd and 3rd harmonics are unaffected, the interleaving spurs are significantly reduced in power and the SFDR is improved by 30 dB, from 57 dBc to 87 dBc.
Finally, the spectral purity in Figure 7 can be further improved by randomizing the order of the channels, as shown in Figure 8. In this case, the randomization uses a patented technique that intermittently scrambles the order of the four channels without having to use another (fifth) channel, thus saving the power associated with that. As shown in Figure 8, after randomization, the resulting spectrum has only regular harmonic distortion.
Figure 8. Output spectrum of the above example with interleaving order randomization turned on. Randomizing the remaining interleaving spurs spreads their power into the noise floor and the corresponding peaks disappear. Only regular harmonic distortion can be seen. The SNR is almost unaffected because the spurious power from the interleaving tones and spreads out is negligible after mismatch correction.
Time interleaving is a powerful technique for increasing the bandwidth of data converters, and advances in mismatch calibration and elimination of residual spurious content through randomization techniques have enabled fully integrated, very high speed 12/14/16-bit interleaved ADCs.
In cases where the input signal is band-limited (such as in many communications applications), the ping-pong (two-way) interleaving method distributes interfering spurs away from the target input band through frequency planning. The spurious components can then be filtered digitally. Although this method requires almost twice the power consumption of a non-interleaved ADC operating at half the IL sampling rate to achieve the same spurious-free input bandwidth, it not only improves the dynamic range by 3 dB through processing gain, but also reduces the roll-off of anti-aliasing and flattens the filter before the ADC - because of the high IL sampling rate.
If the full input band of the IL converter is required to capture a wideband input signal, a higher order interleaved converter can be used. In this case, calibration and random scrambling can compensate and eliminate interleaving distortion and spurious components.
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