Microwave Journal
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Super-Nyquist Direct Digital Synthesis Enables Next Generation Radio Systems

September 14, 2020

A novel active filter, based on regeneration, provides tunability, variable bandwidth, stable high Q, fast frequency shifting and ease of integration. It allows any super-Nyquist image to be isolated, including frequencies far higher than the clock. A direct digital synthesizer (DDS) can directly modulate a signal with the modulation preserved in the image. The passband of the active filter can be adjusted to match the modulation, allowing dramatic simplification of radio design. These capabilities are confirmed using an Analog Devices AD9914 DDS. Both single and multi-pole filters are used to isolate multiple image tones.

Direct digital synthesis (DDS) is a long-established technique to generate RF signals. The fundamental output frequency is limited to less than half the clock frequency - the Nyquist limit. The DDS output includes image tones around the clock and its harmonic frequencies. These image tones are also usable, enabling the DDS to generate much higher frequency tones. Filtering is required to make use of these super-Nyquist frequencies by eliminating undesired tones, especially the fundamental. A fixed bandpass filter (BPF) can be used, but this limits the inherent agility of the DDS. With a fixed BPF, the DDS frequency range is limited to the non-overlapping range of single images. Further, a fixed BPF passes all spurs within its passband, typically requiring additional cleanup. Conventional tunable bandpass filters can be used to overcome this limitation, although their slow tuning speeds limit agility. They present integration challenges as well.

In RF processing there is typically a requirement to generate a signal of precise frequency and high purity. Often the application calls for an agile signal such that the generated frequency must be able to shift quickly while maintaining precision of instantaneous frequency and phase. DDS is a natural choice for generating such signals, as it has complete flexibility offered by digital processing - the waveform voltage values are stored in memory and converted to the desired signal by a digital-to-analog converter (DAC). The input clock sets the rate at which the voltage values of the DDS are output to the DAC. Frequency is determined by a stepping algorithm that determines the address increment in the DDS ROM lookup. The stepping algorithm can be complex and result in arbitrary frequency or phase modulated signals. Together with an IQ modulator, also done digitally, precise quadrature amplitude modulation and arbitrary waveform generation (ARB) signals can be produced.

The DDS digital value is output to a DAC and is converted to a quasi-analog waveform which produces a staircase-like signal with harmonic distortion. Also, the instantaneous output frequency is generally not commensurate with the input clock frequency, resulting in numerous spurious frequency components, some of which can be close in frequency to the desired frequency.

In a modern DDS implemented in non-exotic semiconductor technologies, the clock is limited to the low GHz range, meaning that the nominal output is limited to a few GHz. Typically, these signals can be upconverted, to support systems with higher frequency requirements, but with considerable added complexity and filtering.

Another alternative is possible. A DDS generates image tones around the clock and its harmonics. These tones are at lower power levels than the fundamental but are otherwise perfect copies.1 Using these image tones, i.e. super-Nyquist tones, it is possible to generate RF signals at many multiples of the DDS clock frequency. The primary challenge is filtering. A DDS output naturally contains a myriad of spurious signals. Using a super-Nyquist tone adds further difficulty with not only more spurious tones, but with one or more at higher power levels than the desired tone.

A previously disclosed agile tunable filter technology2 that makes use of regeneration, or positive feedback, can be used to realize a super-Nyquist DDS. Any integrated circuit technology with usable gain at the frequency of interest can be used to realize high Q tunable poles.3 Unlike earlier regenerative circuits, this is inherently stable and does not require quenching circuits. These regenerative filters have multiple resonators, and result in a single, stable, dominant pole. Dominant poles with Qs of over 5,000 have been demonstrated. They have been used in a three-pole filter, agile both in frequency and bandwidth.2 This enables the design of filters operating anywhere in the RF, microwave and mmWave spectrum. Filter tuning range can be arbitrarily large, depending on the implementation.

SUPER-NYQUIST DDS DESIGN

Figure 1

Figure 1 Super-Nyquist DDS block diagram.

A block diagram of the super-Nyquist DDS is shown in Figure 1. The unfiltered DDS output spectrum has many tones. The nominal DDS output tone, ff in the figure, is the direct fundamental output. There are various spurs, for example from the DDS clock (fc). Of interest here are the image tones, fi. These are exact copies of the fundamental, replicated around harmonics of the clock (xfc). Figure 1 shows the primary DDS output (ff) suppressed in favor of one of the higher frequency super-Nyquist images (fi).



The key to a super-Nyquist DDS is filtering. The basic requirement is to filter out the fundamental component (ff). A high-pass filter can be used, but then the output retains numerous spurs and all the higher frequency images. A conventional fixed-tuned bandpass filter is better, since it also eliminates other, unwanted, image tones and many other spurs. Since it is fixed-tuned, however, it has a relatively narrow super-Nyquist DDS frequency range. Just as the desired image moves with tuning, so do the other images, and the bandpass filter must eliminate the full range of all the other image tones and spurs.

This work takes the super-Nyquist DDS approach further. The tunable regenerative filter2 is controlled together with the DDS and can therefore precisely track one of the image tones, eliminating the fundamental and all other spurs. To further increase the super-Nyquist DDS frequency range, the filter is not limited to tracking just one image. It can be tuned from one image to the next to provide an extremely large frequency coverage. The filter comprises multiple high Q pole circuits to ensure very high spectral purity. Not only are the fundamental and unwanted images rejected, so are the clock tones and other spurs as well.

Because the DDS and filter are controlled in unison, frequencies can be switched to a new steady state frequency and phase in as little as 10 nsec. This is illustrated in Figure 2, which shows a MATLAB simulation of the DDS and filter combination. Figure 2a is the relative change in capacitance of the varactors in the filter, Figure 2b is the resulting change in the frequency of each regenerative pole and Figure 2c is the output voltage of the DDS-filter combination. The DDS output is programmed to change starting at t = 0, the same time as the varactor bias begins to change. A change in frequency initiated at t = 0 is completed within 10 nsec. Note that as the DDS and filter change, the amplitude of the output is reduced. For fast switching, it is important for the energy in the regenerative poles to remain constant; so, as capacitance is increased, amplitude must be reduced accordingly. Correcting for constant amplitude is trivial, for example with a subsequent variable gain element. This enables exceptionally agile frequency generation, far faster than is achievable with conventional phase-lock loop approaches used to generate higher frequencies and condition the fundamental DDS output.

Figure 2

Figure 2 MATLAB simulation illustrating varactor capacitance (a), regenerative pole frequency (b) and DDS-filter output change (c) with the DDS and filter controlled in unison.

Figure 3

Figure 3 Unfiltered AD9914 DDS output spectrum with a 2400 MHz clock and a 528 MHz fundamental output.

Figure 4

Figure 4 Frequency response of 3-pole filter tuned to 1875 MHz.

Figure 5

Figure 5 Filtered DDS output.

Figure 6

Figure 6 Unfiltered AD9914 DDS output spectrum with a 1100 MHz clock and a 326 MHz output.

Figure 7

Figure 7 Filtered DDS output.

Figure 8

Figure 8 Filtered responses for chirp modulations of 8, 25 and 50 MHz. Amplitudes are offset to aid visualization.

Figure 9

Figure 9 Phase noise of the 1820 MHz DDS image is not degraded by the filter.

This super-Nyquist DDS is also capable of arbitrary modulation. If the regenerative filter2 (see Figure 1) is a single pole filter, it only supports a single unmodulated tone. When the filter comprises multiple poles, its passband can be designed to match the modulation width. In fact, the passband width is variable, so it can be tuned to match changing modulation. The combination of the DDS and filter, therefore, provides excellent spectral purity along with exceptional agility.

EXPERIMENTAL RESULTS

Both a single pole and a three-pole regenerative filter2 are paired with an Analog Devices AD9914 DDS evaluation board. The AD9914 is capable of fundamental outputs of up to 1.4 GHz. It can operate with clock frequencies of up to 3.5 GHz. A 2.4 GHz clock can be internally generated from a 100 MHz reference, or an external clock signal can be provided. The filter technology supports tunability over large frequency ranges, an octave or more. The achieved tuning range depends on the design of passive resonators and tuning circuitry. For this work, a filter with a tuning range from 1.65 to 1.95 GHz is designed using varactors to tune coupled line resonators. One to three active poles are available, each with an independent variable Q that can exceed 5,000. The poles are independently adjustable, so passband width is variable. Passband ripple is controllable and is impacted by the passband width.

For a baseline, the AD9914 is operated with its internal 2.4 GHz clock, and its output frequency set to 528 MHz. The output spectrum is shown in Figure 3. The dominant output at 528 MHz is clearly seen. Its second harmonic, at 1,056 MHz is visible, but greater than 50 dB lower in power. The clock spur is visible at 2.4 GHz, as is its second harmonic at 4.8 GHz. Image tones are also present. The images of the clock fundamental are at 2,400 – 528 = 1,872 MHz and 2,400 + 528 = 2,928 MHz. They are 12 and 19 dB below the fundamental level, respectively. The images of the clock second harmonic are at 4,800 – 528 = 4,272 MHz and 4,800 + 528 = 5,328 MHz. They are 26 and 32 dB below the fundamental level, respectively. Clearly the image tones have useful power levels, while the DDS second harmonic output is significantly suppressed. Many other spurs are visible, which is typical of a conventional DDS output.

A cascade of the AD9914 and three-pole filter tuned to a 10 MHz bandwidth around 1,875 MHz is measured. The filter response is shown in Figure 4 and the filtered DDS output is shown in Figure 5. The spectral display contains only a handful of visible spurs. The dominant tone is now the 1,872 MHz image. The fundamental tone, at 528 MHz, has been suppressed and does not exceed the noise floor, greater than 90 dB below the image. There are some low-level spurs between 500 MHz and 1.2 GHz. These are ambient broadcast signals and can be ignored. The highest spur visible in the spectrum, the second harmonic of the image at 3,744 MHz, is 58 dB below the image. Other spurs are visible at 2,928, 4,272 and 5,328 MHz. These are other image tones and are at least 65 dB below the desired 1,872 MHz image.

To demonstrate the ability to select higher order images, the AD9914 is operated with an external clock at 1,100 MHz and set to a 326 MHz output frequency. The unfiltered spectrum shown in Figure 6 includes a strong fundamental tone and many spurs, most notably image tones around the clock and its harmonics. The low frequency image of the second clock harmonic is at 2,200 – 326 = 1,874 MHz. The filtered output is seen in Figure 7. The 326 MHz fundamental output is completely suppressed. The remaining spurs are primarily other images and are at least 50 dB below the desired 1,874 MHz image.

Modulated Signals

The AD9914 is capable of synthesizing modulated signals. The filter bandwidth can be adjusted to the bandwidth of the modulation. The effect is illustrated in Figure 8. The AD9914 is set for chirp modulation of 8, 25 and 50 MHz centered at 525 MHz. The filter is set to isolate the image of the chirp with an 1,875 MHz center frequency. Note that a slow chirp is used to aid in visualization in accordance with Fourier analysis. Also note that the 25 MHz trace in Figure 8 is offset by -2 dB and the 8 MHz trace is offset by -4 dB so that the responses are better visualized. The filter’s bandwidth is set to 10 MHz (0.5 percent bandwidth). The 8 MHz chirp is within the passband and has an essentially flat response over frequency. The 25 MHz chirp exceeds the filter bandwidth and the signal is attenuated by 12 dB at its frequency extremes. Similarly, the 50 MHz chirp far exceeds the filter bandwidth, and the signal is attenuated by as much at 40 dB at its limits.

Phase Noise

Phase noise, especially close to the carrier, is a key characteristic for any signal generator or transceiver. This approach, where a tunable active filter is cascaded with a DDS, does not significantly impact phase noise because the only active element of the filter is the amplifier. Amplifiers generally do not add significant phase noise.

Figure 9 shows three phase noise measurements. The blue trace is the phase noise of the direct 580 MHz output of the AD9914 DDS. The orange trace is the phase noise of the 1,820 MHz image, also directly from the AD9914 DDS. The phase noise of the 1,820 MHz signal is degraded by 12 dB. This is because the output level of the 1,820 MHz image is 12 dB lower than the reference level of the 580 MHz fundamental, as theory predicts.1 Notably, the phase noise of the filtered signal is essentially the same as the unfiltered 1,820 MHz signal. Both the signal and the phase noise see the same level of gain as they pass through the filter. This confirms that the filter does not contribute phase noise.

CONCLUSION

The combination of a conventional DDS and an agile tunable filter can provide output frequencies much higher than half the clock to realize a super-Nyquist DDS. The tunable filter eliminates the fundamental tone and isolates the selected image, directly enabling synthesis of higher frequency signals without resorting to exotic semiconductor technologies. Further, with the use of exotic technologies, even higher frequency signals can be synthesized.

The examples discussed use a popular DDS product, the AD9914 and a regenerative tunable filter. The specific filter has a 1.65 to 1.95 GHz tuning range. Images are successfully isolated, one from the clock fundamental, and another from the second harmonic of the clock. The filter is tunable in frequency and bandwidth, ideal for supporting agile systems. This is illustrated with the chirp modulation capability of the AD9914. The filter bandwidth is adjusted to slightly greater than the chirp range to effectively isolate a chirp image. The tunable filter is based on stable regeneration, and the only active elements are in the gain stages. As such, the filter does not add phase noise.

This super-Nyquist DDS enables a new generation of agile and cognitive radios. High frequency signals can be directly synthesized, and with the inherent adjustability of the DDS and the filter, truly agile signal synthesis is possible. Modulated synthesis and selection of high frequency images, as demonstrated, allows tremendous simplification of transmit architectures. The capabilities of this DDS approach also enable simplification of receive architectures along with high levels of agility.

References

  1. Analog Devices AppNote 450968421, “A Technical Tutorial on Digital Signal Synthesis,” Section 10, December 1999, pp. 8992.
  2. F. Schindler, J. Nielsen, D. Rosenauer and T. Raschko, “A New Generation of Integratable Frequency Agile Bandpass Filters,” Microwave Journal, May 2019, pp. 86102.
  3. J. S. Nielsen and R. Nichols, August 14, 2018, Variable filter, US patent 10,050,604 B2.