Array Gain for ADC Spurious Signals—A Measured Validation

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摘要

This article presents practical principles for optimizing direct sampling ADC spurious performance in phased array systems. Principles presented are supported by measured data on a commercially available X-band 16T16R direct sampling platform. ADC spurs are discussed and related to well-understood spurious limitations from radio frequency (RF) mixers. Measured data shows spurious performance across X-band for individual channels and dynamic range improvements as channels combine. The article concludes with a discussion of architectural considerations relevant to a scalable system design.

Introduction

Modern phased array systems are shifting toward digital beamforming, increasing the number of parallel digital receiver channels.¹ The digital beamforming process sums parallel receiver channels. If error terms are uncorrelated across channels, there can be a 10logN improvement as channels combine. This improvement in array gain can be significant as channel counts increase, creating additional financial value to the overall system.

Advances in radio frequency (RF) data converter technology, particularly higher sampling rates, are a key enabler for the increased channel count within phased array channel spacing constraints. RF data converter error terms impacting dynamic range include both noise and spurious signals. In this article, we focus on RF analog-to-digital converter (ADC) spurs, single channel vs. multichannel measurements, and methods to ensure array gain for ADC spurious performance.

X-Band 16T16R Validation Platform

The 16T16R Design

The ADXBAND16EBZAD is a 16-channel X-band direct sampling platform based on the AD9084. The module and block diagram are shown in Figure 1. The module includes four ICs, clock distribution, RF amplifiers, and power distribution. It is designed to mate with a commercially available FPGA evaluation board and is controlled with a MATLAB^® interface for rapid characterization and software development.²

Receiver Testing

Single-tone receiver measurements were taken by injecting a signal generator into a 16-way distribution and simultaneously capturing all 16 channels as shown in Figure 2a. A calibration was done to match amplitude and phase across channels prior to summing the data for evaluation. Channel metrics were evaluated using FFTs. A 12.8 GSPS ADC clock was used with decimation to a 400 MHz IQ data stream. A representative example of an individual channel and combined channel is shown in Figure 2b.

ADC Spurs

Analogy to RF Mixers

For RF mixers, the spurs are created from the harmonic content of the IF and LO frequencies produced in the mixing process. These are described as nxm products where n and m are integer multiples of the input frequencies. Frequencies of the spurs can be accurately predicted and drawn on a spurious products chart.³

ADC spurs are analogous to mixing spurs and can also be drawn on a spurious products chart. ADC spurs are created from a combination of harmonic content on the RF input, the clocks, and interleaving errors. Figure 3 shows a specific case for the AD9084 with a clock frequency of 12.8 GSPS. The x-axis is the frequency input, and the y-axis is the folded first Nyquist frequency output. The plot includes the second and third harmonics, interleaving terms of two and four, along with harmonics mixed with interleaving terms. By simply observing where lines cross, this graphical method provides a quick visual diagram for problematic spur frequencies.

Spurious Measurements

Single-channel and combined 16-channel spurious-free dynamic range (SFDR) measurements are shown in Figure 4. The single-channel measurements are the thin lines, and the combined measurement is the dark blue line.

1. The frequencies where spurs cross as shown in Figure 3 are visible in the SFDR data.
2. For all cases, the combined result improves SFDR regardless of the single-channel SFDR.
3. Comparing Figure 4 with Figure 2 shows that the 16-channel SFDR measurements of 85 dBc or better are noise floor limited. This is a promising result indicating that a 400 MHz IBW over half X-band is completely spur free for a direct sampling system using the AD9084.

Forcing ADC Spurs to Decorrelate

Measurements indicate ADC interleaving spurs and harmonics can be forced to be uncorrelated across channels, thus making array gain for ADC spurious signals practical. To ensure this outcome, some method of randomization is needed and should be built into the phased array architecture. A frequency randomization across channels would spread spurs.^4,5 For ADC clocks, this may not be practical; however, phase randomization is very practical when using the ADXBAND16EBZ design approach. The ADF4382 clock source has phase control that can be varied across channels. In our measurements, the ADC clock phase was compensated using the digital numerically controlled oscillator (NCO) phase control of the AD9084.

Consideration of each spurious type vs. phase is warranted:

• Harmonics rotate in-phase a multiple of the fundamental. With second Nyquist sampling, the phase of the harmonics can be rotated relative to each other. An example of an SFDR optimization after array calibration is described in the article “Hybrid Beamforming Transmit Calibration with SFDR Optimization” and also applies to spurious performance from direct sampling data converters.
• Interleaving spurs are limited by timing and gain errors in interleaved slices. It is important to ensure the residue error across channels is not correlated and varies per channel. This is evident in the measured results.

The description thus far applies to single-tone spurious signals. It is important to note that intermodulation products will remain correlated once the channels are calibrated.^1,3,6 Intermodulation products do not get array gain in the digital beamforming process. The intermodulation product benefit comes from the fact that with more channels there is less input power in each channel.

Conclusion

ADC spurs are described along with considerations in multichannel systems. With proper architecture spurious randomization provisions, ADC spurs can be shown to be uncorrelated across channels, making array gain for ADC spurs realizable.

Acknowledgment

There is a large engineering team that made this short summary of ADC spurious measurements possible.

1. Analog Devices field engineers who routinely ask, “How can this help my customer?” Although seemingly simple, this objective forms the basis of any engineering effort.
2. The entire Analog Devices Apollo Team.
3. The Analog Devices System Applications Team, specifically Sam Ringwood, who designed the ADXBAND16EBZ board, and Sid Das, who did the lab work.

References

¹ Salvador H. Talisa, Kenneth W. O’Haver, Thomas M. Comberiate, Matthew D. Sharp, and Oscar F. Somerloc. “Benefits of DigitalPhased Array Radars.” Proceedings of the IEEE, Vol. 104, No. 3, March 2016.

² “Apollo MxFE: 16Tx/16Rx X-band Radar Platform.” Analog Devices, Inc., June 2023.

³ Bert C. Henderson. “Mixers in Microwave Systems: Part 1.” WJ Communications, Inc., 2001.

⁴ Peter Delos and Mike Jones. “Digital Arrays Using Commercial Transceivers: Noise, Spurious, and Linearity Measurements.” IEEE Phased Array Conference, October 2019.

⁵ Peter Delos, Michael Jones, and Mark Robertson. “RF Transceivers Enable Forced Spurious Decorrelation in Digital Beamforming Phased Arrays.” Analog Devices, Inc., August 2018.

⁶ Peter Delos, Michael Jones, and Hal Owens. “A Measurement Summary of Distributed Direct Sampling S-Band Receivers for Phased Arrays.” Analog Devices, Inc., January 2022.

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