AN-823 APPLICATION NOTE One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com Direct Digital Synthesizers in Clocking Applications Time Jitter in Direct Digital Synthesizer-Based Clocking Systems by David Brandon resolution, which for clock circuits translates to delay adjust resolution, is typically 14 bits. This correlates to 0.022 degrees of phase offset resolution. In addition, excellent residual phase noise performance is available from a DDS-based clock system. This application note describes the Time Jitter performance that can be attained by using direct digital synthesizer-based (DDS) clock systems. The importance of frequency planning, output power, and reconstruction filtering in enhancing the jitter performance of these systems is demonstrated. The primary challenge in using DDS for low jitter clock generation is mitigating the deterministic time jitter that is generated due to the discrete spurious components that are present on the DDS output signal. The primary advantage in using a DDS for clock generation is the extremely fine frequency tuning resolution. The attainable tuning resolution for standard DDS products from ADI is 28 bits, 32 bits, or 48 bits. A 48-bit tuning word results in microhertz of tuning resolution for a 400 MHz system clock. Also, a DDS can be frequency tuned from DC to a maximum of onehalf of its internal system clock rate. However, in practice the upper frequency bound is usually limited to ~45% of maximum to accommodate external filtering requirements. Phase tuning FCLOCK (fc) To expand on this point, the process of generating a square wave for clocking from a DDS needs to be understood. Figure 1 shows ideal time and frequency domain representations at each point in the process. A real-world representation of the frequency domain is shown at the bottom of Figure 1. FILTER OUT DAC OUT LIMITER RECONSTRUCTION FILTER DDS CLOCK OUT 0 IDEAL TIME DOMAIN RESPONSE t t t IDEAL FREQUENCY DOMAIN RESPONSE f fc f 2fc f 1 1 3 5 7 "REAL WORLD" FREQUENCY RESPONSE f fc 2fc f f 1 Figure 1. The Process of Generating a Clock from a DDS Rev. 0 | Page 1 of 8 3 5 7 05758-001 ODD HARMONIC SERIES AN-823 As shown, the ideal time domain output of the DDS is a sampled sine wave. The ideal frequency domain representation of a sampled sine wave consists of the fundamental signal and its images. To convert the sampled sine wave into a clock signal, it must be processed in two steps. First, the signal must be filtered, usually a low-pass implementation, to remove the images resulting from the sampling process. Although not a perfect process, the reconstruction filter nominally converts the signal into a pure sine wave, as shown. The corner frequency of this low-pass filter is typically set at about 40% to 45% of the system clock to take advantage of the full tuning bandwidth while also sufficiently attenuating the images. Step two is to convert the filtered sine wave into a square wave by means of a limiter, sometimes referred to as a squaring circuit. The input of the squaring device acts as a comparator that, ideally, switches its output to the desired high or low logic state at the precise instant that the input waveform crosses a threshold voltage. To minimize noise coupling, it is advantageous to have a 2-wire, balanced connection between the DAC output and the limiter input. As seen in Figure 1, the real-world spectrum of an unfiltered DDS output is rich in spurious content. It contains DAC related harmonic distortion as well as the images of the fundamental frequency. The harmonics of the fundamental are a result of the nonlinearities of the DAC transfer function. The images of the fundamental reside above the cutoff frequency of the reconstruction filter. However, the harmonics of the fundamental are also reproduced in the images. Images that extend into the 1st Nyquist zone (DC to ½ fc), appear as aliased versions of the harmonics. Thus, the images may appear within the filter pass band. These in band images of the DAC harmonics as well as out-of-band images not sufficiently attenuated by the filter can contribute significantly to the jitter observed on the output of the limiter. The jitter present at the output of the limiter is due to spur-induced, cycle-to-cycle, modulation of the time interval at which the limiter threshold voltage is crossed. The jitter that is generated by this process is classified as deterministic jitter; it is related to the specific frequencies of the spurious content of the signal. The process of spurious components being converted to a phase, or timing error (jitter) via the limiting function is referred to as AM to PM conversion. If the bandwidth of the filter is reduced, either by using a low-pass filter with a reduced cutoff frequency, or a band-pass filter, the amount of spurious noise is reduced. Bandwidth limiting this spurious noise in turn reduces the magnitude of time jitter that is produced. The magnitude of the time jitter produced is proportional to the magnitude of the spurious components with respect to the slew rate of the fundamental signal. Because the DDS output is a sine wave, its slew rate is proportional to the signal frequency and amplitude. Noise coupling between the DAC output and the limiter input, including device noise from the limiter itself, can also contribute to increased jitter. In general, increased slew rate at the input to a limiter translates to less sensitivity to jitter induced by coupled noise. Because slew rate is proportional to frequency and amplitude, an increase in either parameter tends to improve jitter performance. The key points in minimizing jitter in DDS-based clock systems are maximizing the DAC output slew rate and implementing effective filtering of the DDS spurious components. The following series of bench data illustrates these points. Rev. 0 | Page 2 of 8 AN-823 The circuit configuration in Figure 2 shows a DDS-based clock generator, consisting of a DDS followed by a reconstruction filter and an AD9515 clock distribution device, used to provide the sampling clock for an analog-to-digital converter (ADC). The DDS sampling clock is derived from a Rohde and Schwarz SMA signal generator. Data was taken on two different DDSs, the AD9958 and the AD9858. The jitter measurement was made by using the clock derived by the DDS and the AD9515 to encode an ADC that subsamples a clean 170 MSPS sine wave. The ADC used in this test is the AD6645, a 14-bit, 100 MSPS device. By evaluating the contribution of the ADC’s differential nonlinearity and the thermal noise to the measured SNR, then applying the DDS-based clock and measuring the SNR, the added jitter attributable to the DDS-based clock can be derived from the following formula. ( ) − SNR 2 ⎞ ⎛ ⎛ 1+ ε ⎞ ⎜ 10 20 ⎟ −⎜ N ⎟ ⎠ ⎝2 ⎠ t JITTER rms = ⎝ 2πf IF where: SNR is the high frequency SNR of the ADC. N is the number of bits from the converter. ε is the converters average DNL plus thermal noise. fIF is the IF analog input frequency to the ADC. Further details on this formula and its use for evaluating the jitter on ADC sampling clocks can be found in ADI Application Note AN-501. AD6645 WENZEL AIN = 170.3 MHz AD9958, AD9858 ENCODE LPF/BPF AD9515 PECL ROHDE AND SCHWARZ SMA GENERATOR 500MHz AND 1GHz @ = 6 dBm Figure 2. DDS-Based Clock Generator and Jitter Measurement Circuit Rev. 0 | Page 3 of 8 05758-002 DDS AN-823 DISCUSSION OF TESTS AND RESULTS Using the configuration in Figure 2, a series of jitter measurements was taken to quantify the effects of filtering and frequency planning. Table 1 shows data for the AD9958 tests. The data confirms that better jitter performance is achieved as the frequency, or slew rate, is increased and as the filtering pass band is decreased. Jitter data was taken for three frequencies. At each of these frequencies three different filter configurations were used to demonstrate the impact of slew rate (frequency) and bandwidth limiting on the measured jitter. The power of the output level for each setting is also shown in order to monitor the slew rate at the limiter input for each test condition. Jitter ranges from about 4 ps rms for a 38.88 MHz output with a low-pass filter just below Nyquist, to 700 fs rms jitter for a 155 MHz output with a 5% filter. In each case the AD9515 maintains the jitter performance of the signal as its output is divided down. This is a key attribute of the AD9515 and similar products (see Table 4) as it enables, in combination with a DDS, subps jitter performance down to frequencies as low as 19 MHz. Note that this would be difficult to do if a DDS were to attempt to drive a squaring device directly at 19 MHz due to the slew rate effects mentioned previously. The nominal filter bandwidth is set to about 40% of the sampling rate, a general rule for setting the corner frequency in wideband DDS applications. For applications that do not need the wide bandwidth range, the filter bandwidth is then set such that the corner frequency is just above the highest output frequency needed. The intent here is to achieve an improvement in the jitter performance at the expense of tuning bandwidth. Last, Figure 2 shows the jitter when a 5% band-pass filter is used. The most filtering of wideband noise and spurious is obtained in this case and thus the best jitter performance, but most of the tuning bandwidth is sacrificed. In clock applications where the frequency remains constant, this drawback is of no concern. To further confirm the strong dependence on slew rate, additional data is taken with the AD9858 DDS (Table 2), which is capable of delivering 40 mA of output current to a 50 Ω load. This enables an increased output power relative to a 50 Ω load and the associated greater slew rate. The AD9958 and AD9959 are multichannel DDS devices, and their outputs can be summed together to increase output power. Table 1. Jitter Response AD9958 and AD9515 vs. Fout, Power, Frequency and Filter BW Product AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 AD9958/AD9515 DDS Sample Rate (MHz) 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 500 DDS Output DDS Output DDS Reconstruction Frequency Power Filter (MHz) (dBm) (MHz) 38.88 −3.6 200 LPF 38.88 −3.6 200 LPF 38.88 −4.7 47 LPF 38.88 −4.7 47 LPF 38.88 −3.3 5% BPF 38.88 −3.3 5% BPF 77.76 −3.8 200 LPF 77.76 −3.8 200 LPF 77.76 −4.9 85 LPF 77.76 −4.9 85 LPF 77.76 −3.8 5% BPF 77.76 −3.8 5% BPF 155.52 −5.5 200 LPF 155.52 −5.5 200 LPF 155.52 −5.6 5% BPF 155.52 −5.6 5% BPF Rev. 0 | Page 4 of 8 AD9515 Divider Output Setting 1 2 1 2 1 2 1 2, 4 1 2, 4 1 2, 4 2 4, 8 2 4, 8 AD9515 Output Frequency (MHz) 38.88 19.44 38.88 19.44 38.88 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 Jitter (rms) (ps) 4.1 4.1 2.4 2.4 1.5 1.5 2.5 2.5 1.5 1.5 1.1 1.1 1.5 1.5 0.68 0.68 AN-823 Table 2 shows the AD9858 with a 5% band-pass filter, a 225 MHz low-pass filter, and various levels of DDS output power. As expected, better jitter is achieved as power is increased and bandwidth reduced. With a 5% band-pass filter, the majority of spurs from the DAC are attenuated. The jitter in this case is much more dependent on noise coupling between the DAC output and limiter input; this is proven by the strong correlation between jitter improvement and increased slew rate. This data also indicates that better jitter performance is attained with the AD9858 relative to the AD9958 for similar levels of power and bandwidth. There are differences in spurious performance of DDSs that result in varying levels of jitter performance. When selecting a DDS for a clocking application, generally the device with best SFDR provides the best jitter performance. The AD9858 is also sampling at a much higher rate than the AD9958, so the images of the fundamental and lower order harmonics are further into the stop band of the reconstruction filter’s frequency response. Getting the required stop-band attenuation, as well as overall performance from the DAC reconstruction filters is nontrivial. Filter component parasitics and PCB board layout effects can impact the idealized filter response characteristics. Impaired stop-band attenuation and the resulting out-of-band noise feed-through result in degraded jitter performance. Table 2. Jitter Response AD9858 and AD9515 vs. Fout, Power, Frequency and Filter BW Product AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 AD9858/AD9515 DDS Sample Rate (MHz) 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 DDS Output Frequency (MHz) 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52 DDS Output Power (dBm) +7.7 +7.7 +7.7 +7.7 +2.6 +2.6 +1.1 +1.1 −3.2 −3.2 −4.6 −4.6 DDS Reconstruction Filter (MHz) 225 LPF 225 LPF 5% BPF 5% BPF 225 LPF 225 LPF 5% BPF 5% BPF 225 LPF 225 LPF 5% BPF 5% BPF Rev. 0 | Page 5 of 8 AD9515 Output Divider Setting 2 4,8 2 4, 8 2 4, 8 2 4, 8 2 4, 8 2 4, 8 AD9515 Output Frequency (MHz) 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 77.76 38.88, 19.44 Jitter (rms) (ps) 0.56 0.56 0.33 0.33 0.63 0.63 0.42 0.42 0.73 0.73 0.64 0.64 AN-823 TERMINOLOGY Time Jitter For the purposes of this application note the term jitter refers to time jitter. Phase noise is a frequency domain phenomenon. In the time domain, the same effect is exhibited as time jitter. When observing a sine wave, the time of successive zero crossings is seen to vary. In a square wave, the time jitter is seen as a displacement of the edges from their ideal (regular) times of occurrence. In both cases, the variations in timing from the ideal are the time jitter. Because these variations are random in nature, the time jitter is specified in units of seconds root mean square (rms) which corresponds to the area under a normal probability density function spanning one standard deviation around the mean. DDS For the purpose of this application note the term, DDS denotes the combination of a numerically controlled oscillator (NCO) and a digital-to-analog converter (DAC). Table 3. ADI High Frequency DDS Product Portfolio DDS Product Selection AD9858 AD9958 AD9959 AD9956 AD9540 AD9859 AD9951 AD9952 AD9953 AD9954 AD9852 AD9854 AD9851 AD9850 AD9830 Max Sample Rate (MHz) 1000 500 500 400 400 400 400 400 400 400 300 300 180 125 50 Frequency Tuning Resolution (Bits) 32 32 32 48 48 32 32 32 32 32 48 48 32 32 32 DAC Full Scale Current (mA) 40 10 10 15 15 15 15 15 15 15 20 20 20 20 20 DAC Resolution (Bits) 10 10 10 14 10 10 14 14 14 14 12 12 10 10 10 Number of Output Channels 1 2 4 2 2 1 1 1 1 1 1 2 1 1 1 Integer Divide Ratio 1 to 32 1 to 32 1 to 32 1 to 32 1 to 32 1 to 32 Number of Output Channels 2 3 3 5 5 8 Output Levels (Vary per Channel) LVDS/CMOS/LVPECL LVDS/CMOS/LVPECL LVDS/CMOS LVDS/CMOS/LVPECL LVDS/CMOS/LVPECL LVDS/CMOS/LVPECL Table 4. ADI Clock Distribution Product Portfolio Divider Product Selection AD9515 AD9514 AD9513 AD9512 AD9511 AD9510 Max Input Frequency (MHz) 0 to 1600 0 to 1600 0 to 1600 0 to 1600 0 to 1600 0 to 1600 Max Output Frequency (MHz) 0 to 1600 0 to 1600 0 to 800 0 to 1200 0 to 1200 0 to 1200 Rev. 0 | Page 6 of 8 AN-823 NOTES Rev. 0 | Page 7 of 8 AN-823 NOTES ©2006 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners. AN05758-0-2/06(0) Rev. 0 | Page 8 of 8