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Interleaving ADCs: Debunking the myths

29 Jun 2015  | Gabriele Manganaro, Dave Robertson

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Time interleaving is a technique that enables the use of multiple identical analogue-to-digital converters [1] (ADCs) to process regular sample data series at a faster rate than the operating sample rate of each individual data converter (Black & Hodges, 1980) (Manganaro, 2011). In very simple terms, time interleaving (IL) consists of time-multiplexing a parallel array of M identical ADCs, as shown in figure 1, to achieve a higher net sample rate fs (with sampling period Ts=1/fs) even though each ADC in the array is actually sampling (and converting) at the lower rate of fs/M. So, for example, by interleaving four 10b/100MSPS ADCs one could in principle realize a 10b/400MSPS ADC.

To better understand the principle of IL, in figure 1 an analog input Vin(t) is sampled by the M ADCs and results in a combined digital output data series Dout. ADC1 will sample Vin(t0) first and begin converting it into an n-bit digital representation. Ts seconds later, ADC2 will sample Vin(t0+Ts) and begin converting it into an n-bit digital representation. Then, Ts seconds later, ADC3 will sample Vin(t0+2Ts) and so on. After ADCM has sampled Vin(t0+(M-1)Ts), the next sampling cycle starts with ADC1 sampling Vin(t0+MTs) and this carousel carries on.

As the n-bit outputs of the ADCs become sequentially available in the same order as just described for the sampling operation, these digital n-bit words are collected by the demultiplexer shown on the right hand side of the same figure. Here the recombined data out sequence Dout(t0+L), Dout(t0+L+ Ts), Dout(t0+L+ 2Ts),... is obtained. L stands for the fixed conversion time of each individual ADC and this recombined data sequence is an n-bit data series with sample rate fs. So, while the individual ADCs, often referred to as the "channels", are n-bit ADCs sampling at fs/M, the ensemble contained in the box is equivalent to a single n-bit ADC sampling at fs, and we will refer to that as the time-interleaved ADC (distinguishing it from the channels). Basically the input is sliced and separately processed by the ADCs in the array and then consistently re-assembled at the output to form the high data rate representation Dout of the input Vin.

Figure 1: An array of M time-interleaved n-bit ADCs. The sample rate of each one is fs/M, the resulting sample rate of the time-interleaved ADCs is fs. An example of clocking scheme for the case of M=4 is depicted on the lower part of this figure.

This powerful technique is not free of practical challenges. The key issue manifests itself when the M data streams coming from the channels are digitally assembled together to reconstruct the original input signal Vin. If we look at the spectrum of Dout, in addition to seeing the digital representation of Vin and the distortion introduced by the analog-to-digital conversion, we will also see additional and substantial spurious content, termed "interleaving spurs" (or IL spurs, in short) (Harris, 2013) (Harris, 2013). IL spurs neither have the signature of polynomial type distortions like higher order signal harmonics (2nd, 3rd etc.), nor the signature of quantization or DNL errors. IL artifacts can be seen as a form of time-domain fixed pattern noise and are introduced by analog impairments in the channels that, due to the interleaving process, modulate with the sliced converted signals and ultimately show up in the final digitized output Dout.

Analyzing a simple example
Let's begin understanding what might be happening by analyzing a simple example. Consider the case of a two-way interleaved ADC with a sinusoidal input Vin at frequency fin. Assume that ADC1 has a gain G1 and that ADC2 has a different gain G2. In such a two-way IL ADC, the ADC1 and ADC2 will alternate in sampling Vin. So if ADC1 converts the even samples and ADC2 converts the odd samples then all the even data of Dout has an amplitude set by G1, while all the odd data of Dout has an amplitude set by G2. Then Dout doesn't only contain Vin along with some polynomial distortion, but it has been subject to the alternate magnification of G1 and G2 just as if we were instead amplitude-modulating Vin with a square wave at frequency fs/2.

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